Geometrically nonlinear theories for curved beams and shells

Abstract eng:
We outline a variational procedure to derive geometrically nonlinear theories for lower dimensional elastic bodies. We emphasize a geometric viewpoint and employ general curvilinear coordinates for describing the reference (or undeformed) and current (or deformed) configurations. It is observed that the local elastic strain (or change of length of an infinitesimal segment) is precisely characterized by the metric tensors of two configurations induced by the ambient 3D Euclidean space. Upon assuming small elastic strains and linear stressstrain laws, we immediately obtain the strain energy associated with deformations. The equilibrium configuration can then be found as the energy-minimizing state of the total free energy. This framework recovers a number of classic simplified theories for beams and shells if appropriate kinematic assumptions are made.

• Export as: BibTeX | MARC | MARCXML | DC | EndNote | NLM | RefWorks
• Add to your basket