A Galerkin approximation for homogeneous anisotropic elastic beams

Abstract

In this work a Galerkin type method is used to approximate the displacement field of a homogerieous anisotropic beam. Following a technique introduced by M. Vogelius allti I. Babu ka¹, and extended by B. Miara² to platés and by B.Miara and L.Trabucho to beams, we construct an approximate solution of the three-dimensional anisotropic clasticity problem as a series of solutions of one and two-dimensional problems. For sufficiently smooth data, we approximate the error, in the H1 norm, as a function of the loading. tho geomentry and ofelesticity constants of the beam.

Keywords:

• Galerkin
• Elasticity. Beams