Variational Methods in the Theory of Beams and Lattices

Synonyms

Calculus of variations; Minimum principles; Rod theory

Definitions

With the minimum total potential energy principle, the question concerning equilibrium configurations of beam systems can be formulated as minimization problems. After postulating a particular form of the potential energy for a conservatively loaded system, the calculus of variations leads to necessary and sometimes even sufficient conditions for energy-minimizing equilibrium configurations.

Introduction

Intrinsic beam theory makes use of one-dimensional generalized continua to model the mechanical behavior of three-dimensional beam-like objects. While a one-dimensional continuum corresponds to a deformable curve in space, parameterized by a single parameter, say $s \in I \subset \mathbb {R}$, a generalized continuum is augmented by further kinematical quantities whose state depends merely on the very same parameter. Accordingly, a configuration of a beam is fully described by a set of functions {y _...