大变形耦合热弹性动力学的变分原理

Variational Principles for Coupled Thermoelasticity with Finite Displacement

应用半反推法及动态差分变换和初终值条件的新处理法 ,建立了各向异性线性材料大变形耦合热弹性动力学的经典型 (即不含卷积的非 Gurtin型 )统一变分原理族 ,从而为应用有限元法求解奠定了理论基础 .

A family of variational principle of classical type (non Gurtin type and not involving convolutions) for the entitled problem of linear anisotropic materials was derived directly from the governing equations and boundary/initial conditions via a new dynamic (continuous) differencing transformation technique. By such technique the time derivative term in the coupled heat conduction equation is eliminated, so that the semi inverse method of eatablishing generalized variational principles proposed by He can be successfully applied, and almost all the boundary conditions and initial conditions can be converted into natural ones. The present theory aims at rendering a general, rigorous theoretical basis for the finite element method.