非线性弹性平面位移问题的一组解析解

A group of analytical solutions for the displacement of nonlinear elasticity plane

针对一种复杂的应变能密度函数形式 ,在平面位移情况下 ,对定义在初始构形上的超弹性基本方程进行了直接的解析求解 .求解过程中完整地保留了非线性偏微分方程组的原始数学形式 ,未做任何假定及条件简化 ,以任意函数的泛函形式给出了一组相应问题的位移解析解 .作为解答的应用 ,讨论了斜边固支 ,两邻边承受线性分布荷载作用的三棱柱平面位移问题 ,给出了相应问题的解析解 .

The plane displacement of hyperelasticity was discussed. Aimed at a complex strain energy density function,a group of hyperelasticity governing equations defined on initial configuration were solved. The original mathematics form of nonlinear partial differential equation was kept in the solving process without any assumptions and simplifications. A group of relative displacement analytical solutions was presented with arbitrary functional form. As an application of the derived solution, a plane displacement was discussed in its entirety with respect to a column that has constant triangular cross section which inclined plane was fixed rigidly and two right angle planes were subjected to linear load respectively. A group of analytical solutions for the relative displacement were presented.