5. Finite Element Implementation

The weak formulation of the boundary value problem serves as a starting point for the numerical solution of the problem. In this chapter, a spatial finite element discretization is used to generate a semidiscrete structural equation. Choosing a formulation considering the transverse shear distortions is also chosen due to the lower and easier-to-fulfill continuity requirements of the shear flexible finite elements (\(C^0\) continuity) compared to the requirement for shear-rigid elements (\(C^1\) continuity) (Oñate, Structural analysis with the finite element method linear statics: volume 2. Beams, plates and shells. Springer, Dordrecht, 2013, [6]). Thus only the zeroth derivative of the degrees of freedom has to be continuous. In contrast to the classical, shear-soft Bathe–Dvorkin element (Bathe and Dvorkin, Int J Numer Methods Eng 21(2):367–383, 1985, [2]), in-plane displacements are taken into account. The implementation is based on the global degrees of freedom introduced in the previous chapter.