基于Chandrasekharaiah广义线性理论的热压电力学的耦合广义变分原理

系统推导了热压电力学的变分原理。若应用传统的拉氏乘子法，由于会出现临界变分现象，不能得到本文的结果。本文指出临界变分是拉氏乘子的固有特性，半反推法是克服临界变分的有效途径之一。应用半反推法，根据Ｃｈａｎｄｒａｓｅｋｈａｒａｉａｈ关于压电材料的广义线性弹性理论，直接从控制方程及边初值条件，得到了经典意义上的一个耦合广义变分原理。本文的理论将给有限元方法、无单元方法及一些变分直接方法（如Ｒｉｔｚ法，Ｔ

A variational principle for thermopiezoelectricity based on Chandrasekharaiah's generalized linear theory

The present paper concentrates on the construction of a generalized variational principle(non Gurtin-type and not involving convolutions)for thermopiezoelectricity.The traditional approach(Lagrange multiplier method)might fail due to the variational crisis occurring during the derivation of generalized variational principles.The paper reveals that the phenomenon of the variational crisis is the inherent character of the multiplier method,to overcome the variational crisis,several novel methods have been proposed,of which the semi-inverse method is emphasized.Following Chandrasekharaiah's generalized linear thermoelasticity theory for piezoelectric media,a classical generalized variational principle is established directly from the field equations and boundary/initial conditions via the send-inverse method.Present theory provides a more complete theoretical basis for the finite element applications,and variational based meshless method(element-free method),and the other direct variational methods such as Ritz's,Trefftz's and Kantorovitch's methods.