Product Marketing Element in the Luxury Car Industry

This essay discusses the role of product (a marketing element) in the luxury car industry. Various frameworks of strategic marketing management are reviewed and applied to the context of the luxury car industry. The essay argues that product decisions should not be done in isolation, as they are rather complex concepts that transcends the physical products itself, so a comprehensive approach is necessary during the strategic marketing process.

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Many of the business functions, including but not limited to marketing, have received strategic relevance in contemporary business discussions (Olson et al. 2005). This means that marketing is viewed (i.e. strategic marketing) as a strategically important component in business decisions in order to better reach and satisfy customers and to improve organisational performance (e.g. productivity and profit). Therefore, marketing should not be considered as a distinct business function that is only involved in promoting the product and sensing customer needs (Caru, 2008). In reality, strategic marketing closely collaborates with other functions to effectively differentiate from competing firms in a particular market by answering three rudimentary questions, which are where, and how the organisation should compete. This means that if strategic marketing is applied, it is well probable that strategic planning will have a close and an intensive dialogue with the marketing department (Smith et al. 1999).
This essay intends to critically analyse the role of the product marketing mix in the luxury car industry. The reason why the product marketing mix was chosen is that this element plays an elevated role for those industries where there is a physical product sold (Trott, 2011). This does not mean that in other more service orientated industries (such as the banking and financial sector) the product mix have a lower role, however, marketing managers may want to focus more on other elements of the marketing mix to deliver an enhanced customer experience. Generally speaking, the key criterion for product is that it must satisfy existing or emerging customer needs in competitive markets, so organisations must place an extra emphasis on communicating why their products are superior to that of their competitors (Grönroos, 1997). This could be particularly true in the luxury car market industry where the competition between existing brands could be intensive.
Short overview of the industry and its trends
First and foremost, a key distinctive factor of the luxury car market is that its performance (i.e. sales volume) is less affected by changes in the macro environment (Bordley, 1993). The recent financial crisis severely hit the car manufacturing industry, however, the demand fluctuation in emerging markets was offset by a growing desire for luxury cars in emerging markets, such as China and the Middle East (Rapoza, 2014). The luxury car market is dominated by three brands, which are Mercedes Benz, BMW and Audi, altogether controlling the majority of the sales in this sector (Behrmann, 2016). The industry is expected to grow in the future, however, manufacturers and resellers must ensure that they closely follow developments in their external environment. The aforementioned brands are expected to maintain their market leading position, however, many other brands (such as Vauxhall) are also trying to enter the luxury market, mainly through by changing their product mix (i.e. the use of premium materials in the interior or including such design features (e.g. large diameter wheels) that used to be the hallmark of luxury car products (Morton, 2013).
The relative importance of the product mix in the luxury car industry
It is widely understood that organisations must first carry out an internal analysis if they are pursuing strategic marketing and if they want to ensure that their products will be successful in their selected market(s) (in this case the luxury car industry) (Stevens et al. 1993). According to the 5C framework, organisations should analyse their customers’ need, their resources to produce and distribute a particular product, their industry context, competitors’ strategy, performance and whether or not forming strategic alliances could be a rational choice (Kaynak, 2005). To give relevant examples to the luxury car industry, the following assumptions regarding the 5C model could be taken:

exiting and unsatisfied consumer needs (need for safety, prestige, luxury feeling without compromising the automobiles’ functionality);
company resources: does the organisation have access to luxury suppliers or does it possess the necessary skills and expertise to manufacture luxury goods in house (e.g. high performance engines for Mercedes Benz AMG performance line cars);
context: the products must follow changes in the external environment (e.g. growing interest towards electric cars or other miscellanies changes);
competitors: identification of competing firms and benchmarking against them to develop a differentiated product;
collaborations: is there any opportunities to form strategic alliances with suppliers? Many luxury cars openly associate themselves with other brands (e.g. Brembo).

Once an organisation has assessed the above mentioned constraints (and preferably devised strategies to overcome these), the constraints must be linked with the marketing mix. Although this paper solely focuses on the role of product in the marketing mix, it must not be forgotten that strategic marketing may only contribute to organisational success if an integrated approach is adopted (Keller, 2001). The STP process (segmentation, targeting, positioning) is also a critical part of this holistic methodology, so product decisions must also be consistent with the selected market(s)’s needs. Therefore, achieving business success is done through the development of a close with between the product, the customer and the marketing (Mohr et al. 2009). As such, a luxury car must have those product attributes which are sought after by the luxury car customer and the external communication strategy (i.e. the marketing communication) should clearly set out a product that is highly valued by potential customers (Martin, 1998).
The product levels in the luxury car industry
Despite the fact that the author of this paper previously argued that products are often perceived to be physical items, the theory of product levels illustrate that successful organisations must address all layers of the of product level diagram (Kotler et al. 2016). These levels are hierarchical, so the suggested holistic approach is also recommended for product management in order to ensure that customers are provided with a consistent product experience, given that each level closely reflects the target market’s (luxury car buyers) expectations.
The core product (even if it name suggests otherwise) is an intangible element of the product. It essentially entails the realisable benefits from the product use. In general terms, people purchase cars to facilitate their transportation from point A to point B, as other alternative modes of transportation (e.g. bus, taxi, walking … etc.) might not satisfy customer needs. The basic transportation need is overly generic for luxury car manufacturers, so understanding the psychology behind purchasing a good that well exceeds realistic customer needs is of paramount importance (Shukla, 2012). Luxury cars are seldom purchased for their convenience – other car makers could perfectly satisfy transportation needs too, so there has to be another rationale behind a high value purchase. Although this paper is too short to enlist the possible psychological factors influencing luxury car purchases, it is realistic to assume that these decisions are overly driven by emotions (Kapferer, 1998). People driving luxury cars intend to communicate their status or they want to leverage on state-of-the art technology and safety features that somewhat counterbalance the irrational choice of luxury cars. Correspondingly, luxury car manufacturers must convince prospective buyers of the presence of these attributes, and seemingly the three market leading brands are succeeding. BMW, Audi and Mercedes Benz are recognised as status brands and their technological advancement and safety features are well above the industry’s standards. In essence, this is the first step that customers examine before they actually visit a luxury car saloon to discuss further details of the product with a sales associate.

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The next product level is more tangible in its nature, as it encompasses the actual product (the actual car model, e.g. BMW X5, S-Klasse or S6) and its visual aspects (such as colour, style, quality, chassis contour… etc.) (Kotler et al. 2016).  Even though it is hard to separate this level from the actual product, it is important to emphasise that the core and the actual product must complement each other, so if a luxury car is designed to offer buyers a status symbol, this should be reflected in the car’s physical appearance and certainly in other parts of the marketing mix (e.g. price, place, people) to maintain consistency.
Whilst it is tempting to categorise goods into either services are products, there is often a continuum between the two polar ends of the spectrum, so luxury car manufacturers should also focus on the augmented product level (Zimmerman and Blythe, 2013). The augmented product level is mostly composed of service elements, such as after sale warranties, the delivery of the luxury car, maintenance services, financing and a quality customer care to address any customer concerns before, during and after the purchase. The concept of product level shows that the physical product is often just a fraction of the product marketing mix, as successful sellers must address each level in their product management. As it was previously suggested, a concerted approach to marketing is necessary, so luxury car manufacturers must warrant that other components of their marketing strategy (e.g. other elements of the marketing mix) are consistent with their product decisions (Kotler et al. 2016). If these recommendations are adhered to, organisations are able to establish product leadership, which is essential to maintain anticipation and excitement towards the products and to increase the number of new and existing customers (Cooper, 2005). This must be accompanied by a continuous product innovation (instead of just adding variety to products without any value or inspiration) so that luxury cars’ superiority is maintained.
Product Assortment – Product Width, Length and Depth
A final consideration for product management in the luxury car market is product assortment. Product assortment entails all products that the seller offers for consumers (Thompson, 2000). Product width refers to the number of different product lines a manufacturer carries (e.g. high performance hatchbacks, Sport Utility Vehicles (SUVs), sedans, minibuses… etc.); product length measures the number of product variants within one category (e.g. optional car features, such as GPS or blind spot monitor… etc.), while product depth shows the total number of variants available at a particular manufacturer.
Serving all segments is seldom possible, so organisations must carefully analyse potential customer segments to target, while also maintaining the financial interest of shareholders (Crane and Northeastern, 2012). The luxury car industry (or a matter of fact, the luxury good sector in general) could be considered to be in a highly specific market, opportunities in increasing product width is not always possible. For example, as introduced during lectures, Dyson manufactures vacuum cleaners, air treatment equipment and hand dryers, which are seemingly completely different products, nevertheless exiting resources could satisfy production needs for all products and there are definitely cross selling opportunities (i.e. commercial vacuum cleaner buyers might also be interested in air treatment equipment). In case of the luxury car industry, such synergies could be more difficult to attain, since the deployment of capacities for different product lines could be difficult, although Mercedes has successfully diversified into the heavy truck industry seemingly without compromising its luxury perception in its consumer market.
Product length assortment consideration is more common in the luxury car industry, as within the passenger car product category, a high number of variants has been developed (Kotler et al. 2016). As previously mentioned, luxury cars come in a variety of forms, satisfying varying customer needs. While this product decision satisfies customer needs, it is also a kind of product diversification that helps luxury car manufacturers to shelter themselves from economic cycles – conceivably during the economic recession, large luxury cars were sold in lower volume, yet a cheaper model variant remained affordable to the target without compromising on quality.
To conclude, the essay demonstrated the role of the product marketing element in the luxury car industry. It was gradually explored why careful product considerations are necessary in order to ensure a consistency in an organisation’s marketing strategy and marketing process. It was also highlighted that thinking of products as physical items is not advisable to fully understand what a product is – instead, as the theory of product levels has shown, products must provide a holistic consumer experience in the luxury car industry.

Behrmann, E. (2016) Mercedes on pace to win 2016 global sales crown from BMW. Available at: (Accessed: 15 January 2017).
Bordley, R. F. (1993) ‘Estimating automotive Elasticities from segment Elasticities and First choice/Second choice data’, The Review of Economics and Statistics. 75(3), p455.
Carù, A. (2008) Strategic market creation: A new perspective on marketing and innovation management. Chichester, United Kingdom: John Wiley & Sons.
Cooper, R. G. (2004) Product leadership: Pathways to profitable innovation. New York, NY: Basic Books.
Crane, F. G. and Northeastern (2012) Marketing for entrepreneurs: Concepts and applications for new ventures. London: SAGE Publications.
Grönroos, C. (1997) ‘Value‐driven relational marketing: From products to resources and competencies’, Journal of Marketing Management. 13(5), pp.407-419.
Kapferer, J.-N. (1998) ‘Why are we seduced by luxury brands?’, Journal of Brand Management. 6(1), pp.44-49.
Kaynak, E. (2005) Marketing issues in western Europe: Changes and developments. New York, NY, United States: International Business.
Keller, K. (2001) ‘Mastering the marketing communications mix: Micro and Macro perspectives on integrated marketing communication programs’, Journal of Marketing Management. 17(7-8), pp.819-847.
Kotler, P., Keller, K. L. and Brady, M. (2016) Marketing management. Harlow, United Kingdom: Pearson Education.
Martin, C. L. (1998) ‘Relationship marketing: A high‐involvement product attribute approach’, Journal of Product & Brand Management. 7(1), pp.6-26.
Mohr, J. J., Sengupta, S. and Slater, S. (2009) Marketing of high-technology products and innovations. Boston, MA, United States: Prentice Hall.
Morton, R. (2013) Insignia: Vauxhall’s luxury company car. Available at: (Accessed: 15 January 2017).
Olson, E. M., Slater, S. F. and Hult, G. T. M. (2005) ‘The performance implications of fit among business strategy, marketing organization structure, and strategic behavior’, Journal of Marketing. 69(3), pp.49-65.
Rapoza, K. (2014) Emerging markets to drive automotive comeback. Forbes. Available at: (Accessed: 15 January 2017).
Shukla, P. (2012) ‘The influence of value perceptions on luxury purchase intentions in developed and emerging markets’, International Marketing Review. 29(6), pp.574-596.
Smith, P. R., Berry, C., Pulford, A. and Baxter, M. (1999) Strategic marketing communications: New ways to build and integrate communications. London: Kogan Page.
Stevens, R. E., Sherwood, P. K., Dunn, P. and Winston, W. (1993) Market analysis: Assessing your business opportunities. New York: Haworth Press.
Thompson (2000) Strategic Management. New York, NY, United States: McGraw-Hill Education.
Trott, P. (2011) Innovation management and new product development (5th edition). Harlow, England: Financial Times/Prentice Hall.
Zimmerman, A. and Blythe, J. (2013) Business to business marketing management: A global perspective. London: Taylor & Francis.

A General Overview of the Element Platinum

A general overview of the element platinum



The purpose of this report is to describe and detail the findings of my research into the metal platinum. The first section of this report will investigate the chemical, physical, mechanical and thermal properties of platinum. The second section will cover the various methods of how platinum is produced, and it’s uses in industry. The third and final section of this report will analyse the health and safety implications platinum can cause to the body, and a brief overview of the environmental impacts.

The properties of platinum

Platinum is a very dense and heavy material, but it is also quite soft, malleable and ductile. Platinum has a melting point higher than most other metals. Platinum is also considered a noble metal due to how unreactive it is. Platinum is fairly resistant to acids and will not oxidise in air, so it will not tarnish or rust.

    Chemical properties:

CAS number


Thermal neutron cross section

9 barns/atom

Electrode potential


Ionic radius




X-ray absorption edge

0.1582 Å

Electrochemical equivalent



   Physical properties



Melting Point


Boiling Point


    Mechanical properties

Tensile strength

125-165 MPa

Modulus of elasticity

171 GPa

Bulk modulus

230 GPa

Shear modulus

62 GPa

Poisson’s ratio


Elongation at break


Hardness, Vickers


    Thermal Properties

Thermal expansion co-efficient (@200C/680F)

9.10 µm/m0C

Thermal conductivity

69.1 W/mK

Platinum production and it’s uses in industry

Platinum is usually found from ores of elements such as nickel and copper during mining of those materials but can also be found in placer deposits. Platinum will usually be found with several impurities which we do not want and must separate the platinum from. One method that can be used to remove the impurities from the mixture is to take advantage of platinum’s density by adding a liquid which will allow the impurities to float away. Platinum being very unreactive can be mixed with hydrochloric and sulphuric acids and will not react whereas many other substances will react. The remaining mixture can then be filtered to separate the impurities and the platinum. Platinum in its raw form (Platinum and all other platinum group metals) can be purified with aqua regia (1:3 mix of nitric and hydrochloric acid), which causes platinum, gold and palladium to be dissolved removing them from the other platinum group metals. The gold must then be separated next by precipitating it will Iron(II) Chloride and filtering the gold away. The platinum can then be precipitated away by adding ammonium chloride to produce a precipitate of ammonium chloroplatinate. This will then be filtered away and heated to obtain platinum.

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The industry that most heavily uses platinum is the automotive industry which uses it as an auto-catalyst. In the exhaust system of a truck or car, a fine coating of platinum will be present to act as a catalyst to speed up the reaction between O2, CO and other hydrocarbons to produce CO2 and H2O. Having this coating of platinum will also reduce the number of sulphur particles output into the atmosphere. The Chemical industry uses platinum as a catalyst also to increase the rate of reaction of a given reaction and to reduce its activation energy, savings costs for the manufacturer.  The most notable use of platinum as a catalyst is in the production of nitric acid. However, the greatest demand for platinum in the chemical industry comes from the production of speciality silicones. Platinum compounds are used in a large variety of materials from electrical wire insulation to lubricants. The electronic industry made use of platinum as platinum was coated onto the platters used in HDDs as platinum enabled data storage. However, SSDs have become more common today and therefore the use of platinum in the electronic industry has decreased. The glass manufacturing also employs the use of platinum due to its ability to withstand temperatures of 1700 0C. Also, platinum will not react with the materials and silicates used in the manufacture of glass. For 40 years the petroleum industry has used platinum as a catalyst in cracking longer hydrocarbon chains into smaller, more useful ones such as diesel and kerosene. In the medical industry, platinum is used in all pacemakers and in other medical devices such as defibrillators and stents. Platinum is the material of choice here due to its unreactive nature. However, platinum also has anti-cancer potential with cisplatin drugs being produced commercially since the 1970s.

Health and safety implications of platinum

The toxicological effects of platinum in humans are limited to the complex halide salts and the antitumor agent cis-platin and similar compounds of cisplatin. These compounds are some of the most potent sensitizers known. Workers exposed to these compounds showed symptoms of itching, watering of the eyes, repeated sneezing, rhinorrhoea (runny nose), chest tightness, wheezing, shortness of breath, cough and cyanosis. Some workers even developed scaly erythematous dermatitis with urticaria (hives). The development of symptoms after exposure to these platinum compounds has ranged from a few weeks to several years. However, the longer the exposure the more severe the symptoms and the longer they will generally last. The most potent compounds of these complex halide salts are hexachloroplatinic acid and the chlorinated salts ammonium hexachloroplatinate, potassium tetrachloroplatinate, potassium hexachloroplatinate and sodium tetrachloroplatinate. Ammonium chloroplatinate is formed in the separation of platinum and palladium before being heated to give platinum.

With platinum being heavily used in the automotive industry to reduce greenhouse gas emissions very little consideration has been paid to the possible effects of platinum emissions in exhaust systems to the public. A small study with only 3 test subjects who were highly sensitive to platinum salt concentrations, were tested using particulate exhaust samples where concentration exceeded 5 µg/ml, which is normally enough to evoke a response. All test subjects failed to show a positive response. This is most probably due to the platinum emissions being metallic and not in salt form.

Cisplatin which is used in cancer chemotherapy has caused nephrotoxicity with both tubular and glomerular lesions, severe nausea and vomiting, ototoxicity with tinnitus and hearing loss, and sensory peripheral neuropathy. Carboplatin can also be used as it is less nephrotoxic it has induced bone marrow suppression.


CLEARE, M.J. Immunological studies on platinum complexes and their possible relevance to autocatalysts. In: Proceedings of the International Automotive Engineering Congress and Exposition, Cobo Hall, Detroit, 28 Feb.–4 March 1977. Detroit, MI, Society of Automotive Engineers, 1977 (SAE Report 77061).

An essential element of business

Human resource management is an essential element of every business. Employee relation is a very vast and complex topic. There have been numerous theories that have been developed in regards to employee relation. These theories have been a part of our daily lives and it is seen that even though people tend to be following the processes it is quite rare that the focus falls on the theories themselves. As explained by Adam and Meitz (1993): ‘By choosing a theory one organises reality’. There has been a wide and vast range of theories that have been developed over the years. There are a number of different roles that people tend to undertake within the organisations and each one of the roles are equally important for the success of the business. One of the most important however is that by leaders. Leaders play a crucial role in the organisations including several elements like training and mentoring as well (Adam and Meitz, 1993). Training and mentoring are two essential elements for every business. In the case of new employees to a job, it is seen that there is a need for new training and mentoring to be introduced within the organizations. These training and mentoring is based on the employee profiles and the levels based on which the employees can learn and develop. Hence for every company recruiting newer employees this is a very essential aspect. Mostly in the case of new employees these form the basic understanding of the organization and the job (Beer, Lawrence, Quinn Mills, and Walton, 1985). This paper will discuss two very essential aspects of the business, i.e. the concept of individual differences and the organizational roles and situations. The main aim of the paper is to discuss how people take up their roles in the organizations and how well the group situations are managed within the organization.
Individual Differences:
Murray and Kluckholm have divided the psychology studies of people into three main sections. They explain, ‘Every man is in certain respects (a) like all other men, (b) like some other men, (c) like no other man’. Considering the term Individual differences psychology, the main focus of this theory is based on the second level of study. The study of individual differences psychology is one where the theorist and experts study the differences in the individual behavior. The concept of individual differences is very important as it helps creating an average of the variations in the differences of individuals. This is an essential concept in organizations and employee behavior as with the various personalities of people within the industry, there is also a chance that the expected reactions might not be the same from all employees. Hence when a leader works towards managing a group, it is essential that the leader is able to understand and associate with each employee. This will help the leader understand the most effective form of leadership that can be implemented within the teams and the organization as a whole (Gazendam, 1993).

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Motivation is the most important aspect of any organization. It is essential for competitiveness, cost effectiveness that in simpler words is staying alive. Practice what you preach. For effective understanding of the employees and their individual differences, a few underlying principles can be used (Goleman, 2006). These include using: Surveys- Changing behaviour, and hence, attitudes, is difficult unless you can identify as a start point. In all companies there are a number of employees who resist change and are unwilling to accept any change of any kind. Use of Good Practice: Being a manager does not require training for leadership skills, or having a set number of principles for a job or set systems. It is important to understand that theories that have been developed over the years are only meant for references and not to be used as a bible for every move. Policies and Procedures: In every company, or even a group of companies, nothing ever happens unless there’s a simple policy or procedure for making the thing happen. These policies and procedures should be set out and should include, what should happen, who needs to manage it, how it should take place, how it is monitored, etc. need to be encompassed in these policies (Grint, 2001).
Organisational Roles and Situations:
The term Organizational Roles refers to the technical positions that are occupied by both the leaders as well as the employees in an organization and the processes and procedures that occur in the day to day business. Leaders act as change agents within organizations. They motivate as well as build the trust and confidence of the people within the organization. There have been a number of different theories and approaches that have been developed in the past by various authors and experts in the field (Goleman, 2006). Daniel Goleman’s approach consists of six major styles of leadership. In his book Primal Leadership, he has highlighted that good leaders are effective because they create resonance. Based on this he explained resonance can be done in six ways, which in turn lead to the leadership styles. These styles included visionary leadership, coaching leadership, affiliative leadership, democratic leadership, pacesetting leadership and commanding leadership (Goleman, 2006).
Leaders require to be very careful with the decisions they make because every decision they made has an effect on the lives of the employees. Thus Goleman argues that true leaders are a product of the decisions that they take and thus a true leader is one who thinks through all the factors before taking a decision and after considering every possibility. Mintzberg’s argument that the decisions of leaders are diluted by the half truths is a very positive and right argument. Another aspect that needs to be considered in any organization includes the training of employees. Training a group involves a lot more efforts as well as costs than training a single employee. The main similarity of training the employees and a group is that the content always remains the same (Buchanan and Huczynski 2004). However when training an individual, it is possible to help them out on improving the process and finding ways to overcome issues. This cannot be done in the group training (House & Shamir, 1993). Training an individual can be done while working on the job which allows the employees to also get a feel of the systems and ask questions which they would have otherwise been reluctant to ask in a group.
Organisational Behaviour and its Impact:
Being able to take up new roles and styles of management is one of the biggest challenges in an organisation. Management theories are in a number if ways the first and most essential elements of business which every manager will require to know and understand to be able to successfully lead a team. It is essential to realise the importance of these theories for every manager (Buchanan and Huczynski, 2004). The fair and employment laws that have been implemented by the government have a lot of relevance to the everyday work. It is essential for managers to have a strong knowledge of these laws to ensure that all employees are treated in a fair and ethical manner (Koestenbaum, 2002). One of the best ways to create a supportive environment in the work place is to communicate to the employee and bring out ways and modes to help one another achieve the fair employment within the work place. A communication strategy which involves meeting initially by the manager to discuss the same with the employees, after which the employees can initiate a meeting anytime they feel something within the office is not fair. This is more of an open communication and should be for the entire team rather than just the employee and managers. The impact of the leaders’ performance and behaviour within an organisation has a high impact on the overall performance of the business. Mintzberg has argues that leadership and management required to be aligned to the organizational development. Mintzberg also argued that it is up to the internals of the organization to make the right choice of the leaders rather than externals, who do not have complete knowledge of the organization and its people (Locke, Edwin 1975). Mintzberg has discussed some very important aspects of leadership and has emphasized on important aspects like the half truths. The half truth that has been used by managers in a number of ways is that people are ‘human resources’ (Locke, Edwin, 1975). Mintzberg argues and highlights that it is incorrect to refer to human beings as ‘human resources’. He argues that half truths are dangerous mainly because of the fact that they can affect the actions of the leaders to be not well thought out and planned (Grint, 2001). Also the half truths are not reasonable and require to have been taken as a huge threat to the managers and leaders of organizations. Considering the various examples that he has enlisted in the argument, it is clear that the half truths cause a the leaders to make ineffective decisions and also in some terms can be the underlying factors for the organizations moving into the wrong path and moving towards failure to some extent (MICA, 2004). It is clear that basing the leadership decisions on half truths can be very damaging not only to the company but also to the lives of the employees that are involved. Thus Mintzberg’s argument is very appropriate and it is important to understand and differentiate among the half truths and the other half truths (MICA, 2004).
Effectiveness of Organisational Behaviour:
As has been mentioned earlier, the ability to change the behaviour of a leader based on the employees and the needs of the team. Of all the different leadership modes that are present in various organisations, one which has proved to be very effective and efficient is that of a charismatic leader. In a situation where decisions need to be taken very fast and with accuracy, the most effective leader would be the charismatic leader (House & Shamir, 1993). Charismatic leaders mainly refer to people with an elusive and also an indefinable personality trait which in a number of terms seems unnatural and is considered to be supernatural. These traits have been expressed to be traits like ability to lead, charm, persuade, influence and inspire others (Beer, Lawrence, Quinn Mills and Walton, 1985). According to Weber: charisma is ‘a certain quality of an individual personality, by virtue of which s/he is set apart from ordinary people and treated as endowed with supernatural, superhuman, or at least specifically exceptional powers or qualities. These are such as are not accessible to the ordinary person, but are regarded as of divine origin or as exemplary, and on the basis of them the individual concerned is treated as a leader’. He also says, ‘resting on devotion to the exceptional sanctity, heroism or exemplary character of an individual person, and of the normative patterns or order revealed or ordained by him’.
Every leader irrespective of whether a charismatic, authoritative or even a transformational requires to have a team and followers to be able to lead them. Hence it is clear that a leader only leads the way and helps the others to follow him and meet the goals of the organization. In situations where the leaders require having complete support of the followers, the most effective form of leadership again is the charismatic leadership (House & Shamir 1993). A few of the best examples include Fidel Castro, Winston Churchill, Bill Clinton, Mahatma Gandhi, Adolf Hitler, Sathya Sai Baba, Joseph Smith and Werner Erhard. All of these leaders have been able to contribute in their own way to their organizations.
As has been understood from the above discussion, Charismatic leaders are known for their approach to every big and small problem. The actions of the leaders have a cumulative effect on the changes that they tend to bring about in the people. There are several similarities between the charismatic leaders and transformational leaders. The most essential and basic difference is their focus. The transformational leaders focus on transforming the organisation and in some cases the followers as well, while the charismatic leaders prefer to let things remain the same and do not want to change things. In the case of charismatic leaders it is quite easy for the followers to get carried away while talking to the person because of the strong aura that they have. The charismatic leaders are a combination of both ‘people’ as well as ‘organisation oriented’. Hence the charismatic leaders to a great extent are great leaders and provide a lot of results to the organisation as a whole.
As seen from the above discussion, the leaders play a major role in the over organizational behavior and the overall effectiveness of the organizations. The ability to understand the needs of each individual and to work towards providing all employees with the right treatment to be motivated is the main job and role of the leader. As seen in the above discussion the role of human resource management is very high in every company. The success of a company is directly dependent on the performance of the employees and the right choice of employees can take the company a long way and can provide the company with excellent results. For an individual to be a successful leader it is essential that they have a clear vision and aim for the team. The behavior of the managers and leaders has a strong and direct impact on the employee productivity (Koestenbaum, 2002). This is majorly because employees tend to follow their leaders. If a leader needs to be successful it is essential that the leaders have the ability to be open to feedback, ready to accept their flaws and willingness to give in their best to the team. ‘All leaders challenge the process’ (Kouzes, J., & Posner, B., 2002). It is essential that leaders view the status quo and ask themselves why. Only by asking why and challenging the assumptions that instituted the status quo can a leader be effective. Hence to be able to fulfill their role in the organization, it is important that the leaders are aware of their surroundings and are able to work in sync with all the other roles within the organization. This will not only increase the level of team work but will also increase the overall success of the organization as well.

Overview of Bismuth Element

Periodic Table Page for Bismuth-

Symbol- Bi

Atomic number- 83

Atomic weight- 208.98


Element Classification- other metals

The element bismuth (Bi) is a solid element. Its atomic number is 208.98 which is the number of protons in the nucleus of an atom. Bismuth belongs in the nitrogen family on the periodic table. Bismuth-209 was once thought to be natural and stable element, but more studying of bismuth-209 has shown that it does decay. Bismuth can be found in places like Peru, Mexico, Japan to name a few (Chemistry Learner). Bolivia has the most bismuth deposits. The melting point of bismuth is 271.3 degrees Celsius (2002).

The element bismuth was discovered at some point in 1400 AD, but was not named an element until years later. It was identified as an element in 1753 by Claude Geoffroy (It’s Elemental). Bismuth was at times confused with lead and tin. It is gathered during mining and the refining of lead, copper, tin, silver, and gold.

Bismuth gets its name from German words meaning white mass (It’s Elemental). Bismuth is white with a little bite of pink color, and it is brittle. Bismuth is used in many different things. It is normally mixed with other elements. Previous uses of bismuth in history were for printers and caskets. Although at that time bismuth was not known to be an element (Chemistry Learner).

There are two common bismuth alloys mentioned in the nitrogen elements book. The names are Field’s metal and Wood’s metal. Fields metal contains bismuth, indium, and tin, and Wood’s metal contains bismuth, lead, tin, and cadmium. Both the metals are used in many fire sprinklers. (Roza 2010)

Some of the things that bismuth is used for now is fire sprinklers, fire detectors, and electric fuses, because of its low melting alloys (It’s Elemental). Bismuth is also used at nuclear plants “to carry radioactive fuel to the core of certain nuclear reactors. It also helps cool the reactors” (2002). Some of the other things that bismuth is used in is paints, make-up, and some medications (It’s Elemental).

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Pepto bismol is one medication- which contains bismuth subsalicylate which can help with an upset stomach. In small doses bismuth is usually not harmful to people. Continuous exposure can cause minor kidney damage, and in large does can be fatal. In the nitrogen elements book it also states that children with chicken pox should not take medication that contains bismuth. It has been linked to rare disease called Reye’s syndrome, which can be fatal. (Roza 2010) Reye’s syndrome is extremely rare that causes confusion, swelling of the brain, and liver disease. (2018 Reye’s syndrome)

Also in 2014 water had to be lead free, and bismuth was being looked at as a replacement (Soft schools). Most switched to copper-bismuth brass alloys. The cost of bismuth was a much less costly alternative than silicon (Bismuth vs. silicon in lead-free products).

Bismuth is even used for cancer imaging. Bismuth is an alternative to gold which is very costly to use. A doctor by the name of Mamdooh Algathami and a team tried bismuth nanoparticles. The bismuth doubled the radiation to the cancerous tissue. The doctor quoted that “by enhancing radiation in the tumor, doctors may be able to decrease the initial dose of radiotherapy, which will hopefully result in fewer side effects for the patient while having the same impact on the cancer.” Bismuth nanoparticles were tested and showed to increase the radiation dose by 90 percent. (Metal Nanoparticles)

Reactions of the element bismuth differ depending on what it is mixed with. When bismuth is mixed with air it forms a different type of bismuth known as bismuth (III) oxide. The flame from it is bluish white. When bismuth is mixed with water at red heat it reacts and forms the same as when it is mixed with air. When bismuth is mixed with halogens it forms several different types of bismuth. Then when bismuth is mixed with certain acids it can dissolve (bismuth element).

Bismuth is a fragile metal and it has a metallic look about it. Bismuth is also the least of all the metals to be magnetized. When it goes from a liquid to a solid it expands, and it does not conduct electricity very well. Bismuth is not bothered by hydrochloric acid and mildly bothered by hot sulfuric acid, but is dissolves very quickly nitric acid (Bismuth Chemical Element).

Bismuth is a very beautiful metal and collectors enjoy it. Bismuth can be made in a lab or in kitchens. Bismuth 209 is what is found in nature. Some fishing sinkers are also made from bismuth because it can be melted down and it is not poisonous to birds and humans like lead. (Roza 2010)

As mentioned earlier that bismuth is normally a byproduct in mining and refining of other metals- Bismuthinite (Bi2S3) and bismite (Bi2O3) are the most important ores. Bismuth is refined using the Betterton-Kroll process. The process involves first adding calcium and magnesium to molten lead-bismuth. This forms a dross which is solid impurities float on top of the molten material. Then the dross is skimmed off the pure molten lead. The next step involves treating the compounds with chlorine. The chlorine forms compounds with the calcium and magnesium. This frees up the bismuth. (Roza 2010)

Works Citied Page

                 “Bismuth vs. Silicon in Lead-Free Products.” Apollo Valves,

                 “It’s Elemental.” It’s Elemental – Isotopes of the Element Barium,

                 Metal Nanoparticles May Improve Cancer Treatment,

                 “Reye’s Syndrome.” Mayo Clinic, Mayo Foundation for Medical Education and Research, 8 Aug. 2018,

                 Roza, Greg. The Nitrogen Elements: Nitrogen, Phosphorus, Arsenic, Antimony, Bismuth. Rosen Central, 2010.

                 “World Book 2002 Book 2 B.” World Book 2002 Book 2 B, World Book, 2002, p. 383.

3D-finite Element Analysis of Beam Design

Any design and development activities involves in huge amount of time and money in bringing out the final product to the market, whilst functionality of the product being crucial under all scenarios without fail or malfunctioning over a period of time.
Earlier design was carried out by the conventional methods from planning to final manufacturing of a components and the behavior of the product was understood only when it was not meeting its functionality.
Recent developments in the above said area is vast, as this enables an engineer to study the behavior of a component/assembly, whist suggesting precautionary measures or a possible solution in validating the member thereby saves an organization time and effort.
Thanks to the recent developments in the field of Stress analysis, along with the CAD packages, which actually enable us to visualize the component in 3D and analysis and design, validate it before it is actually released for manufacturing.
Furthermore the robustness of CAE packages enables us to visualize the behavior of the component/assembly when it is actually put to work defining constrains under which it has to perform.
Industries strongly rely on these packages to reduce the time and money involvement of a company and it is important for an Engineer to adapt the methods presented in this paper in the right approach so as to meet the design criteria which should be practical in nature.
This paper demonstrates the Design of a beam which has to be validated under several constrains/operating conditions, and understanding its behavior under these real time situations.
Application of Stress methods using “Solid Works Simulation” package is demonstrated to understand the behavior of the beam.
3D Finite element analysis is one of the approaches in understanding the behavior of the load paths under different situations and with different boundary conditions.
Several beam sections are validated to design the best beam under the given load conditions and the best beam based on several criteria are made, by demonstrating several plots.
Hand/Theoretical calculations and results from Simulation are interpreted in order to study the behavior of the beam.
Methods of this Stress Simulation and relevant steps are explained by plotting various plots like the Stress, Displacement and Factor of Safety by relevant comments at certain stages are done for the company to understand the process and design validation.
Further it is important for the safety engineer to understand the usage of 3D finite element method so as to interpret the results and to make design changes before the component being put it function.
Beam analysis: [Part 1]
The figure below shows the beam on which the loads are acting at points P1, P2 and P3 of magnitude 18KN, 26KN and 20KN respectively.
Beam 1 and 2 are bolted with pins through the two beams and the beam is supported at two locations. Analyzing the above situation, several considerations are needed in order to apply and analyze the situation. The above situation is a case of “simply supported beams at either ends and loaded at the center”.
Design phase:
The given sections are designed using Solid works package as per the dimensions provided.
The cross-section of beams designed is plotted below.
Consider the cross-section 1 for analysis.
Below shows the cross-section 1 with dimensions being A= 0.3m, B=0.3m respectively.
3D element solid element type analysis using finite element method:
Cross-section 1: [Beam with circular hole]
As shown above the assembly is created using solid works as “Solidworks.asm” format and is meshed and analysis is carried out. Several steps are carried out like constrains, load conditions, assigning material are done in order to study the behavior of the assembly.
Load points are defined at three locations as shown; either of the beams is connected by means of metal pads of 3mm thick with pins to support them. As we apply the loads at points P1, P2 and P3, simulation is carried out and a report on the desired results is obtained and are plotted below.
Further to the design of the beam with relevant dimensions, simulation of the assembly is carried out using Solid works simulation. Several boundary conditions are implied, like the loads at the given locations, applying material, bolts at four locations and finally meshing the assembly to perform the analysis.
Repeating the above procedure for rest of the cross-sections for design of beam, following plots will account for the values of Von-misses stress, displacement and factor of safety.
Deflection Calculations:
From the bending moment diagram, we observe that the maximum deflection occurs at the centre of the beam. The maximum load due to all the three loads can be found out. By using the Principle of Superposition, the deflection due to each load can be interpolated to the centre.
Consider a load ‘P’ acting on a beam AB at a distance of ‘a’ from end ‘A’ as shown in figure. The bending moment plot shown in figure above, shows a discontinuity at the point x=a.
Solving for each of the lengths of the beam
For length AD,
(d2y /dx2) = (M/EI) = (Pbx/EIL) ——–1
Integrating equation 1, we get,
y = (Pbx3/6EIL)
For length DB,
y = (Pax3/2EI) – (Pax3/6EIL) + B1x + B2
To determine the four constants A1 and A2, two boundary conditions and two continuity conditions are used.
For segment AD, y (0) = 0 = A2
For segment DB,
y (L) = 0 = (PaL2/3EI) + B1L + B2
Equating the deflections and slope on both segments at x=a, and solving the four equations, we get,
A1 = – (Pb/6EIL) (L2 – b2)
A1 = 0
B1 = – (Pa/6EIL) (2L2 + a2)
B2 = – (Pa3/6EI)
Hence we get the following equation, for length “AD”
y = (Pbx/6EIL) (x2 – L2 + b2) ……. (2)
Considering the load P1 = 18KN, the deflection at midpoint, we have,
P = 18000N, x = 1.4m, b = 1.9m, L = 2.8m, E = 220 X 109N/m2. Substituting these values in equation (2), we get
y = (2.9407 X 10-8) / I m
Hence, below are the values

For cross section 1: y1circle = 0.04523mm
For cross section 2: y1oct = 0.0454mm
For cross section 3: y1sqr = 0.0465mm
For cross section 4: y1isect = 0.06022mm

For segment AD, using the expressions obtained for B1 and B2 in the deflection equation, we get,
y = – (Pa/6EIL) [(x3/2) – (x3/6L) – {x (2L2 + a2)/6L} + (a2/6)] ————–2
Considering the load P2 = 20KN, deflection at mid point can be calculated using,
P = 20000N, x = 1.4m, a = 1.7m, L = 2.8m, E = 220 X 109 N/m2.
Substituting the above values in equation (2), the deflection at mid point D is found to be:
y = (2.2074 X 10-8)/I m

For cross section 1: y2circle = 0.03395mm
For cross section 2: y2oct = 0.0341mm
For cross section 3: y2sqr = 0.0349mm
For cross section 4: y2isect = 0.0452mm

Similarly, considering the load P3 = 26000N, deflection at mid point is,
y = (54.0484 X 10-9)/I m

For cross section 1: y3circle = 0.0831mm
For cross section 2: y3oct = 0.0835mm
For cross section 3: y3sqr = 0.0854mm
For cross section 4: y3isect = 0.1107mm

Total deflection is given by:
y = y1 + y2 + y3

For cross section 1: y = 0.1622mm
For cross section 2: y = 0.1630mm
For cross section 3: y = 0.1668mm
For cross section 4: y = 0.2161mm

Factor of safety for the beams.
Factor of safety is given by the formula:
FOS = ?yield / ?max
Given, yield stress of the material, ?yield = 650N/mm2
Using the above data, we get,

For cross section 1: FOS = (650/8.6) = 75.58
For cross section 2: FOS = (650/8.64) = 75.23
For cross section 3: FOS = (650/8.84) = 73.53
For cross section 4: FOS = (650/11.46) = 56.72

By the above results, the cross section with the highest FOS can be chosen for designing the beam. Hence it can be recommended to choose the cross section with circular hole for final design.
Part 2
The zone is red color is critical, means it has high stress and displacement. Hence clamping used will play a major role.
From the plot, the maximum displacement at this location is 0.6511 mm, which is less than the customer’s expectations and hence the design is safe.
As this displacement is almost 3.8 times of the specified value [2.5mm], no design changes or precautions would be needed. Therefore,
Maximum displacement Part 3
Finite element method is one of the methods widely used and applied among the industries in the recent years and is used to study the behavior of the part by assigning various properties on to it.
Method of simulation:
Static studies in Solid works simulation calculate displacements, reaction forces, strains, stresses, failure criterion, factor of safety, and error estimates. Available loading conditions include point, line, surface, acceleration (volume) and thermal loads are available.
Below criteria are important and are followed in this document so as to obtain values which are realistic in nature;
The approach is done in three phases and are,

Bottom up assembly-Phase 1
Defining load points-Phase 2
Simulation-Phase 3

Phase 1.
Assembly of beams with relevant dimensions was done with fully defining the sketch geometry.
Generating bosses with desired lengths and creating the profile as needed.
Mates being defined between each parts using mate options in assembly mode.
Phase 2.
Split of 10mm was done at the top surface of the beam was done in order to imply point loads.
Phase 3.
Solid works simulation tool was used to access the simulation options.
Steel was applied from the material database for all the components in the assembly.
Connections were defined so as to make the assembly a rigid structure by defining the locations and this creates an effect of holding both the beams by means of bolts.
Fixtures create an effect of holding the beam as required and are done at the either ends.
Loads in terms of Newton were applied on to the points which were defined at phase 2.
Mesh size was defined for the entire assembly and this inturn divides the geometry and several nodes are created for analysis.
Finally the meshed model will provide us the study report, Von-misses stress, Factor of safety and Displacement of all the four cross-sections are obtained.
Possible mistakes in simulation:
It is up to the safety engineer in order to take extreme care before the analysis is performed so as to avoid the failure or inaccurate results during or before the simulation is actually performed. Mistakes should be avoided to the maximum extent while conducting simulation, as this might deviate the results and are not practical in nature and hence lead to misinterpretation.
Some of them are listed below.

Applying the material: This result in wrong stress and strain plots, displacement plots, Factor of safety, this inturn results in wrong load path distribution.
Defining boundary conditions: Defining boundary conditions is crucial in terms of accurate results. Loadings should be done as per the real situation and unwanted assumptions have to be avoided.
Generating mesh: Applying mesh is one of the important criteria as this procedure being the base on which the elements of the member or the beam is divided into several millions of individual pieces and are analyzed by applying degrees of freedom.
Mesh size: Mesh size is important in order the material/component to take the load conditions. Larger mesh could result in small deflection and results may not be practical in nature.
Clamping face: Wrong clamping face in simulation would completely alter the end result and this leads in wrong interpretation of the results obtained from the stress plot, displacement plots and Factor of safety.

Mesh sizes and types:
Solid works simulation currently includes solid continuum elements, curved surface shell elements (thin and thick) and truss and frame line elements. The shells are triangular with three vertex nodes or three vertex and three mid-edge nodes. Solids are tetrahedral with four vertex nodes or four vertex and six mid-edge nodes. They use linear and quadratic interpolation for the solution based on whether they have two or three nodes on an edge. The linear elements are also called simplex elements because their number of vertices is one more than the dimension of the space. The size of each element indicates a region where the solution is approximated by a spatial polynomial. Most finite element systems, including SW Simulation, use linear or quadratic complete polynomials in each element. You can tell by inspection which is being used by looking at an element edge. If that line has two nodes the polynomial is linear.
If it has three nodes then the polynomial is quadratic.
When the model is set for simulation, the program sub-divides the model into many tetrahedral small elements, these small points share a common point called as “NODE”. Below shows the small element where a common node is shared by curves, lines and edges.
Difference between hand calculation and simulation:
Few difference do exists between theoretical and hand calculations.
Hand calculations: Hand calculations are often called as theoretical calculations, because of the fact that it does not take into consideration of several constrains could not be defined as we could do it in simulations.

Material cannot be assigned in hand calculations.
Mesh cannot be created for better and accurate result.
Deflection, stress plot, displacement plots could not be visualized in hand calculations.
Several assumptions might be required and thereby accounts in the deviation of the result from that of simulation.
Hand calculations are based on the available formulae like from the design data hand book and are not different compared to simulation results.
Result analysis like the animation of the result and high stress regions could not be obtained from hand calculations.
Changes in boundary conditions would require repeating the procedure in hand calculations and time consuming process.

Study of 3D-Finite element analysis of beam design assembly, address the capabilities of simulation. The idea of using the presented methods and techniques helps in optimizing the product before manufactured.
This helps an industry in being changing their design at this stage based on the results obtained from simulation. Simple to complex parts/assemblies are simulated by this method, by defining several boundary conditions.
The advancement in FEA area is vast, and has the capabilities of creating an environment of real time engineering situation and much finer results could also be obtained, as it provides options for finer mesh and hence more accurate the results.
Finally this method of optimizing or validating the product at the initial level before design is done, has its own advantages, whilst it is worth understanding the customer’s requirement along with understanding the basic concepts of FEA makes a worth effort towards any engineering problem.
Hence I strongly suggest for any organization to follow the process of FEA and get the full benefit of the same, as they could save time in the process of optimization of the product.

Class tutorial.
S Timo shenko and D H young. 5th Edition. Elements of strength of materials.
Strength of materials by Bela I. Sandor.
Solid works study material.
Strength of materials by Ferdinand L. Singer and Andrew Pytel, 3rd Edition
Strength of materials by Surya Patnaik and Dale Hopkins, Title: A new unified theory for the 21st century.


Finite Element Analysis of a Rocker Arm

Finite Element Analysis of a Rocker Arm


Component Description


1.1.            Component Function

The rocker arm is an oscillating,  two-arm lever that provides a means of actuating the valves in the combustion chamber of an internal combustion engine. It translates the radial motion of the profile of the cam lobe through a fulcrum into linear motion for opening and closing the intake and exhaust valves.  It also provides a means of multiplying the lift ratio.

During operation, the rocker arm experience stresses and undergo deflection. Severe rocker arm deflection causes inefficient engine performance, and often results in metal fatigue leading to increased wear and friction in the valve train and eventually engine failure.

Figure 1: Diesel engine valve train showing rocker arm (1)

1.2.            Component Geometry

The rocker arm is a two-arm lever that pivots about a fulcrum. One end is connected to the push rod which rests over cams on the camshaft, while the other acts on the spring-loaded valve stem and pivoted on the rocker shaft.

Figure 2:(From left) 3-D model of the rocker arm and the 2-D geometry


1.3.            Service Loading

The rocker arm is subjected to compressive load at the fulcrum on the rocker shaft during the opening and closing of the valves.  The forces acting at the valve end (FE) include; the gas back pressure on the valve, the spring force and the force due to valve acceleration. There is also the load at the cam end, (FC) which is transmitted to the rocker arm through the push rod.

Figure 3: Free Body Diagram of Rocker arm depicting the location of the acting forces: FE and FC

Methodology (154)

         Two-Dimensional Idealization

In a rocker arm, the constraint at the pivot hole and the applied loads at both ends, all act in a plane, parallel to the cross-section plane of the rocker arm.

To estimate the stress concentration of the geometry, it is idealized as a shell and shaped in the profile of the planar cross section of the rocker arm under the assumption that the rocker arm is completely solid with only the holes drilled through as seen in Figure 4. The two-dimensional idealization makes it easier to deal with and the main stresses are obtained with reasonable accuracy.

Figure 4: 2D geometrical Idealization using Autodesk Inventor

2.2.            Loading, Boundary Conditions and Constraints

The rocker arm has two major loads applied on either end respectively:

Force due to exhaust valve loading; FE

Force due to cam action through the push rod; FC

The main forces will be calculated based on the Diesel Engine specifications below.

Type of Engine

Turbocharged 6-cylinder, Diesel Engine, 2523CCm2DiCR Engine.

Number of Cylinders


Engine capacity

2523 CC

Maximum Engine Power

46.3 kW @ 3200 rpm

Maximum Torque

195 Nm @ 1440 – 2200 rpm.

Table 1: Diesel Engine Specification (2)

Mass of the valve mv


Diameter of the valve head dv


Lift of the valve   h


Cylinder pressure Pc


Maximum suction pressure Ps


Diameter of fulcrum pin d1


Diameter of boss D1


Rocker arm ratio


Engine Speed

3200 RPM

Angle action of cam (Ɵ)


Spring rate k

23 N/mm

Spring Preload P1


Weight of associates parts with valve w

0.882 N

Acceleration of valve a

1550 m/s2

Table 2: Input data for calculation of applied load on rocker arm (2)

Total load on valve:

Initial spring force:
= 24.249 N

Force due to valve acceleration with valve weight:

Maximum load on the rocker arm for exhaust valve:

Load on push rod side of the rocker arm:
 Fc=Fe×Rocker arm ratio=1859.54N

A pinned constraint is applied on the pivoting hole in all degrees of freedom.

Finite Element Representation

         Modelling and Justification of Shell type

The material for the rocker arm; carbon steel is assumed to be homogeneous and isotropic with details in Table 3.

Young’s Modulus (GPa)


Poisson’s ratio


Density (kg/m3)


Yield Strength (MPa)


Ultimate Strength (MPa)


Table 3: Carbon Steel Material Properties

Plane stress idealization is assumed because the thickness in the z-direction is smaller than the length in the x-y plane. Given the 2D geometry, it is idealized as a plane stress model and shell elements must be used. The shape of the element can either be triangular or quadrilateral and the element order is either linear or parabolic.

Element Size

Maximum von-Mises Stress


(Triangular element)

Maximum von-Mises Stress (MPa)

(Quadrilateral element)






























Table 4: Comparison of Element type and order

The element type chosen for the meshing is the second order quadrilateral element. This was due to the accuracy and consistency of the von Mises stress values obtained when the Force FE is applied on the rocker arm in comparison to other element types. Therefore, it has proven to be the best for this geometry.

To accurately represent the pinned pivot constraint, a pinned, rigid body connector was applied at the centre point and connected to the pivot hole so all the nodes at the hole can better represent the motion.  For each loading scenario, one hole must have a fixed constraint the other has the load applied for the solution to be solved. This can be seen in Figure 5 and Figure 6.

Figure 5: Mesh diagram for FC loading scenario

Figure 6: Mesh diagram for FE loading scenario

Contour Plots

After the finite element model was solved, the maximum Von-Mises stress was recorded. The finite element contour plot for each loading scenario can be seen in Figure 7 and Figure 8.

Figure 7: FE loading scenario

Figure 8: FC loading scenario

When Force FC was applied, it predicted the largest maximum von-Mises stress compared to when Force FE was applied. Hence, FC is the worst-case loading scenario and the stress obtained from this scenario will be evaluated.

4.1.            Justification of results parameter

The von Mises stress is chosen as the main result parameter to be evaluated. This is required to evaluate the failure rate of the rocker arm, since it is made of a ductile material and is largely likely to fail as a result of shearing action. The von Mises stress yield criterion predicts failure for a ductile material, when the von Mises stress becomes equal to the yield strength.

The contour plot predicts the maximum von Mises stress value as 203.3MPa, occurring at the neck of the rocker arm.  This value is within the Yield strength for carbon steel of 415MPa.

Mesh Convergence

In order to explore the effects of mesh density on the prediction from the finite element model, several finite element models were generated, varying the number of elements from 39 (coarsest mesh) to 12069 (finest mesh) from element sizes ranging from 0.2mm to 20.5 mm. The von Mises stress from the worst-case scenario were calculated and compared, to study the influence of mesh density on the stresses predicted, as shown below.

Number of elements











Von Mises stress (MPa)











Table 5: Effect of mesh density

From Figure 9, the stress converges to the maximum possible value of 203.3 MPa.


In this case, them model produced acceptable results. The maximum stress was 203.3 MPa and was localized mostly and the neck of the rocker arm which is where the stress was expected to be most concentrated. The convergence of the results shows that the result is not significantly dependent on the choice of discretization and is an indication of the validity of the accuracy of the prediction. Also, the result obtained under both loading conditions, indicating the same location (the neck of the rocker arm) as where the maximum von Mises stress is predicted and where failure is likely to occur provides further validation of the result. However, the component was assumed to be completely solid except for the holes. In reality, the 3D geometry (Figure 2) is a better representation of the component and the aforementioned assumption is a relatively poor one. Apart from the applied loads, the component would be subjected to thermal stresses. Furthermore, though plane stress was assumed, the thickness of 19 mm was relatively large compared to the length of 50.8 mm. To validate the model, plane strain assumptions may be made during the next analysis in which a displacement-controlled test can be used to identify the strain that causes failure.


1.) Diesel Engine Valve Train. Nuclear Power Training. [Online] [Cited: November 14th, 2018 at 21:34.]