摘要:
本文给出了修正的Castigliano定理,与经典的Castigliano定理相比较,修正的Castigliano定理应用方便而且广泛。对经典Castigliano定理的修正是在两个方面,第一个修正是以外载荷与影响函数乘积的表达式代替经典Castigliano定理中余能密度对集中力偏导数的表达式,这一修正为我们在复杂载荷作用下的计算带来极大的简便;第二个修正是在经典Castigliano定理中引入了非齐次边界位移与影响函数乘积的表达式,这一修正为求解复杂边界条件的问题提供了理论基础。我们还说明了如何应用修正的Castigliano定理求解表面结构力学问题的方法。最后,作为修正的Castigliano定理的应用算例,我们求解了两邻边固定另两邻边自由的矩形板的挠曲面方程。
Abstract:
This paper gives the modified Castigliano's theorem, which is more convenient and more extensive for applications than the classical Castigliano's theorem. The modifications to the classical Castigliano's theorem are in the two respects, the first respect is that the expression of the partial derivative with respect to the concentrated load P of the complementary energy density in the classical Castigliano's theorem is replaced by the expression with the products of the external loads and influence functions, the modification brings us greatest simplicity and greatest convenience for calculations under various loads; the second is that the expressions with the products of the inhomogeneous boundary displacements and the influence functions are introduced into the classical Castigliano's theorem,the modification provides the theoretical fundamental for solving the problems of various boundary conditions We show also the method of how to apply the modified Castigliano's theorem to solve the problems of the surface stractural mechanics, hinally, as a calculated example of the application of the modified Castigliano's theorem we solved the equation of the deflection surface of the rectangular plate with two adjacent built-in edges and other two adjacent free edges.