载流条形薄板的非线性应力与变形分析

在所建立的载流条形薄板的非线性磁弹性基本方程--运动方程、几何方程、物理方程和电动力学方程的基础上,通过变量代换,整理成含有10个基本未知函数的标准柯西型方程.采用差分及准线性化方法,将含有10个基本未知函数的偏微分方程组,变换成能用离散正交法编程求解的准线性微分方程组.由此计算分析两边简支条形薄板在电磁场和机械载荷耦合作用下的应力与变形,研究侧向电流和外磁场强度对载流条形薄板的磁弹性效应.

NONLINEAR STRESS AND DEFORMATION ANALYSIS OF THIN CURRENT-CARRYING STRIP-PLATES

The nonlinear magneto-elastic basic equations of thin current-carrying strip-plate are built,based on the kinetic equations,the geometric equations,the physical equations and the electrodynamics equations of thin current-carrying plate,the normal Cauchy form nonlinear differential equations,which includes ten basic unknown functions in all,are obtained by means of variable replacement method.Using the difference method and quasi-linearization method,the nonlinear differential equations,which include ten basic unknown functions in all,are reduced to a sequence of quasi-linear differential equations,which can be solved by the method of discrete orthogonalization.The stresses and nonlinear deformations of thin strip-plate with two simply supported edges under the coupled action of the electromagnetic field and mechanical load are calculated,the magneto-elastic effects on thin current-carrying strip-plate by the side current and electromagnetic induction density are studied.