What is shape function of tetrahedron?

Answer 1

The shape functions of a tetrahedron are mathematical functions used in finite element analysis to interpolate the values of a field variable (such as displacement or temperature) within the tetrahedral element based on its nodal values. For a tetrahedron with four vertices (nodes), the shape functions are typically linear and can be expressed in terms of barycentric coordinates, which are defined relative to the tetrahedron's volume. Each shape function corresponds to one vertex and is equal to one at that vertex while being zero at the other vertices, ensuring that the interpolation accurately represents the variation within the element.