THE CONSTRUCTION OF VARIATIONAL-PRINCIPLES

A method of constructing variational principles (VPs) for a class of p roblems in mechanics is presented. The VPs are derived from variationa l problems equivalent to satisfying constitutive relations. The physic al side of such a derivation scheme consists in setting up variational problems by considering the minimum rate of energy accumulation and d issipation. In doing so one can distinguish the mechanisms of energy a ccumulation and dissipation, which define the number of variables in t he VP. The Ws are constructed for a system of transfer equations in th e steady case and for the problem of the seepage of an incompressible fluid in a deformable medium of complex rheology. The proposed approac h simplifies the procedure for constructing dual Ws and can be used to construct other VPs for media with complex theology. The derivation o f the VP remains the same for problems whose solution is defined by th e minimum of potential energy. (C) 1997 Elsevier Science Ltd. All righ ts reserved.