ABSTRACT
This chapter discusses the structural elements, that is, beams, plates, and shells, which may be components in 2D or 3D structural systems. It focuses on an important subclass of nonlinear problems: ones involving large displacements, large rotations, and material nonlinearity, but small strains. Flexural behavior of slender beam, plate, and shell elements is traditionally modeled using the Kirchhoff theory "normals remain normal" approximation. The chapter considers the geometric stiffness of a finite volume of material. Linear and geometric stiffness matrices have often been used to formulate linearized bifurcation buckling as an eigenvalue problem, in which it is assumed that prebuckling displacements are small, so that the prebuckling state can be determined from a linear analysis. The Mindlin plate theory was originally developed for thick plates in which transverse shear deformation is approximately accounted for. The chapter also describes the process of degeneration of isoparametric continuum finite elements as a method of formulating isoparametric plate and shell finite elements.
