混合变量的最小势能原理及其应用

应用修正的功的互等定理,提出了小变形线性弹性理论混合变量的最小势能原理。混合变量总势能对位移和应力取变分极值的欧拉方程和自然边界条件分别为平衡方程,静力边界条件和位移边界条件。以该原理为基础,导出了弯曲矩形板的相应原理。同时,应用该原理计算了一悬臂矩形板的弯曲。推导和分析表明,该原理兼有最小势能原理和广义势能原理两者的优点。应用显示,这是一求解矩形板弯曲的一般方法。

Principle of minimum potential energy with mixed variables and its application

Principle of minimum potential energy with mixed variables of linear elasticity for small deformation theory is proposed by the use of the corrected reciprocal theorem.On taking variation of total potential energy with mixed variables with respect to displacements and stresses,Euler＇s equations and natural boundary conditions to be the equations of equilibrium,mechanical bound-ary conditions and geometrical boundary conditions are obtained respectively.On the basis of the principle,the principle related to bending of rectangular plates is derived.Meanwhile,the principle is applied to calculating the bending of a cantilever rectangular plate.The derivation and analysis show that the principle has advantages both the principle of minimum potential energy and the generalized potential energy principle.The application shows that it is a general approach for solving the bending of rectangular plates.