Use of the Finite Element Method and Computational Fluid Dynamics in Motion Analysis of Complex Shapes, With Examples from Sports

Use of the Finite Element Method and Computational Fluid Dynamics in Motion Analysis of Complex Shapes, With Examples from Sports

Takeshi Asai (Tsukuba University, Japan)
DOI: 10.4018/978-1-4666-5011-4.ch014
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In the research and development of sports, Finite Element Methods (FEMs) and Computer Fluid Dynamics (CFD) are frequently used as tools to examine the transformation of a solid and the flow of a fluid, respectively. This chapter presents a simplified approach to understanding the FEM and CFD and their basic equations, providing the foundation for a theoretical understanding of the two methods. To facilitate an understanding of the application of the FEM to sports research, an analysis of the impact of landing on the human body is presented. Similarly, the application of CFD to sports research is illustrated through a flow analysis around spiked shoes. This chapter will not only enable students to study CFD but also introduce them to literature on the FEM and CFD with regard to other sports to encourage them to study further.
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In recent years, there has been a rapid evolution in computer technologies and numerical analysis techniques that allows increasingly complex and diverse problems in motion analysis to be solved with relative ease. This chapter will briefly outline two surprisingly easy-to-use numerical analysis techniques—the finite element method (FEM) and computational fluid dynamics (CFD)—along with examples of their application in analysing the motion of the human body while playing sports. It is hoped that this information will encourage broader use of these techniques to solve complex motion analysis problems.


From a mechanical point of view, the motion analysis domain can be broadly classified into three categories: rigid body mechanics, solid mechanics, and fluid mechanics. In reality, many studies have shown these categories to be interlinked in a complex manner that has traditionally made it difficult to predict the motion of complex shapes. To approach this problem, it is helpful to have an understanding of the respective analysis methods for the different types of mechanics. FEM and CFD represent analytical methods for deformable body mechanics and fluid dynamics, respectively, and are briefly outlined here along with examples of their application to the motion of the human body in sports.

Finite Element Method

FEM was used to calculate the strength of an airfoil by engineers and researchers at the Boeing Company in 1956; this is regarded as the beginning of its application in engineering (Togawa, 1979). The uniqueness of FEM is that it resolves a continuum having a complicated shape and properties by dividing it into small elements (mesh) with simple properties and assembling these elements into a whole in order to predict the object’s behaviour. When the mechanical properties of a deformable body are investigated, a theoretical analysis is usually performed, primarily on the basis of the body’s material mechanics. This approach seeks an analytical solution in all domains using simplified postulates; thus, it is elegant but poses problems such as ‘being able to handle only simple shapes’ and ‘requiring considerable knowledge of mathematics’ (Figure 1). In contrast, FEM is unique because it can provide a solution even for complicated shapes if mesh division is possible. The solution is only approximate and may sometimes vary according to the accuracy of the division of the mesh. However, this tool is applicable over an extremely wide range of conditions.

Figure 1.

Beam model in strength of materials (a), real airplane (b) and airplane model using FEM (c)

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