ABSTRACT
The constitutive theories describing relations between Cauchy stress tensor and infinitesimal strain are generally based on generalized Hooke's law. The outcomes from each one of these methods are identically the same in terms of the resulting finite element formulations and the associated element equations. Generally it is a matter of choice and preference as to which method one chooses. This chapter converts grid point displacements to element nodal displacements in the element local coordinate systems. The Euler-Bernoulli beam theory is based on the assumption that the plane sections remain planar and normal to the longitudinal axis of the beam after deformation. The main objective of the finite element formulations presented in this chapter for linear structural mechanics is to illustrate the concept of local coordinate system, 1D elements in 2D and 3D space, and to present some representative finite element formulations for bending of beams.
