梁板壳的摄动变分原理

The Variational Principle of Perturbation of Beams,Plates and Shallow Shells

本文建立了粱、薄板及扁壳的摄动变分原理,它是求解固体力学非线性问题的一个理论基础,可以将非线性问题化为线性问题来处理。同时,利用它可以建立摄动有限元法、摄动有限条法、摄动加权残值法及各种摄动样条函数方法。

In this paper,the variational principles of the perturbation method for beams,plates and shallow shells have been established by the author,which is the theoretical basis for the solution of the nonlinear problems of the solid mechanics,as the perturbation method may be used to reduce the non linear problems into a series of linear problems.And, these estoblished variational principles may also be helpful to establish those joint methods as perturbation FEM,perturbation FSM,perturbation MWR and perturbation spline-fuuction-method.