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Introduction to Finite Element Analysis in Solid Mechanics

1 Chapter 2 Introduction to Finite Element Analysis in Solid Mechanics Most practical design calculations involve components with a complicated three - dimensional geometry, and may also need to account for inherently nonlinear phenomena such as contact, large shape changes, or nonlinear material behavior. These problems can only be solved using computer simulations. The Finite Element method is by far the most widely used and versatile technique for simulating deformable solids. This chapter gives a brief overview of the Finite Element method, with a view to providing the background needed to run simple simulations using a commercial Finite Element program. More advanced Analysis requires a deeper understanding of the theory and implementation of Finite Element codes, which will be addressed in the next chapter.

12 coordinates. For an axisymmetric analysis, the x 2 axis must coincide with the axis of rotational symmetry. 3. Nodal displacements. When the solid deforms, each node moves to a new position. For a three dimensional finite element analysis, the nodal displacements specify the three components of the displacement field u(x) at each node:

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