Finite Element Analysis of Geometric Nonlinear Problems

This chapter focuses on the finite element analysis of geometrically nonlinear problems. It first introduces the fundamental kinematic relationships used in finite deformation solid mechanics, followed by a discussion of the variational formulation for finite deformations and the higher-order spectral quadrature element analysis of Mindlin plates and shells. Finally, numerical examples are provided for two-dimensional, three-dimensional, and plate and shell problems based on the higher-order spectral quadrature element method.