弹性力学混合状态方程的弱形式及其边值问题

WEAK FORMULATION OF MIXED STATE EQUATION AND BOUNDARY VALUE PROBLEM OF THEORY OF ELASTICITY 1)

导出了弹性力学混合状态方程和边界条件弱形式的统一方程，此法使函数的选择无需事先完全满足边界条件，对于各种不同的边值问题可以用统一形式处理。

Prof Tang clarified importance of mixed state equation of elasticity, and first gave Hamilton canonical equation by modifying Hellinger-Reissner variational principle At the same time author pointed out that the study of solution of mixed state equation has still not been well developed though it has a wide spread application prospect.This is because Hamilton equation must satisfy comples boundary condition in continuous medium mechanics which is its difficult point, Fan and Ding applied the mixed state equation to investigated laminated plate and shell, and overcame the disadvantage in the ordinary successive approximations method, in which a lot of unknowns that appear at the real or fictitious interfaces had to be dealt with But all of above papers adopted rigorous equilibrium and boundary conditions, their solution can be only relied on special technique So those methods would be difficult to be popularized In addition, it is impossible to obtained the analytical solution for plates with complex boundary conditions In this paper, by introducing Hellinger-Reissner variational principle,universal weak formulation of mixed state equation including boundary condition are presented An unified approach and the general solution of these equations are also given Plates with different boundary condition can be dealt with by uniform formulas The present study make trial functions which need not satisfied all the boundary conditions in prior, and extends and unifies the solution of the theory of elasticity