基于S—R分解定理的极矩弹性力学增量型能量原理和广义变分原理

INCREMENT FORMS OF PRINCIPLES OF ENERGY AND GENERALIZED VARIATIONAL PRINCIPLES IN POLAR ELASTICITY OF LARGE DEFORMATION WITH S-R DECOMPOSITION THEOREM OF THE DEFORMATION GRADIENT

采用拖带坐标系的应力张量增量和变形梯度S—R分解定理意义下的应变张量增量,本文证明如在大位移、大变形途径中,存在有唯一的势能与余能函数,则可建立大变形极矩弹性理论的最小势能原理和最小余能原理。在此基础上用泛函的扩宗量变换与Lagrange乘子法结合建立了具有 _j^i、 _j^i、 _i、 ~i、五类独立变分宗量的广义变分原理,它是目前极矩弹性力学中最一般的广义变分原理。

Under the condition of only one function of potential energy and complementary evergy existing in strain way about large deflection and deformation, the principles of least-potential energy and least-complementary energy in polar elasticity of large deformation are established by using stress increment in co-moving coordinate system and strain increment which is difined by S-R decomposition theorem. By means of the method of increasing variational functions and lagrange's method of multipliers, the generalized variational principle in which there are the independence of five kinds of variational functions ( _1~1, _1~1, _1~1, _1~1, )are also established.