The Finite-Dimensional Weak Form - Basis Functions - Lesson 4

In this lesson, we begin with the finite-dimensional weak form for linearized elasticity and then define the basis functions and construct representations for the fields of interest. For this class of problems, the basis functions are scalars while the degrees of freedom are vectors. We then derive the basis functions for an 8-noded hexahedron element by mapping it to a bi-unit cube. We thus have an isoparametric mapping for our geometry and we can also derive the gradients of the fields of interest by differentiating these basis functions.