Question

2. Shape functions What are they used for? (List at least 3 uses) Explain how to obtain the shape functions for a 1D bar element Explain how to obtain the shape functions for a 2D beam element Explain how to obtain the shape functions for the Q4 element* Differences between a higher and lower order element

Answer 1

The shape function is the function which interpolates the solution between the discrete values obtained at the mesh nodes. Therefore, appropriate functions have to be used and, as already mentioned, low order polynomials are typically chosen as shape functions. In this work linear shape functions are used.

For three-dimensional finite element simulations it is convenient to discretize the simulation domain using tetrahedrons, Thus, linear shape functions must be defined for each tetrahedron of the mesh, in order to apply the Galerkin method

The element shape functions are stored within the element in commercial FE codes. The
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