按位移求解弹性力学平面问题的解析构造解研究

针对弹性力学平面问题偏微分方程组的位移法,引入多指数函数,提出了含未知参量的指数函数、三角函数和线性函数组合形式的位移函数解析构造解。建立了任意边界条件与未知参量之间所满足的非线性代数方程组,确定了边界节点条件和未知参量的数量关系。推导了具有对称位移边界的位移函数解析构造解。构建了位移函数构造解的精度判定方法。求解了具有对称位移边界条件的矩形板算例的位移解与误差分析。研究结果可为位移法理论和实际工程应用提供参考。

Study on analytic construction solutions about solving elasticity plane problems by displacement method

As to solving partial differential equations about elasticity plane problems by displacement method,a multi-exponential function method is introduced.Analytical displacement function expression with the exponential function,trigonometric and linear function and unknown parameters is proposed.Displacement function analytic expression with symmetric displacement boundary is derivated.Nonlinear algebraic equations between arbitrary boundary conditions and unknown parameters is established and number relation is decided.Precision determining method about displacement analytic function is built.Practical example with symmetrical displacement is analyzed.The result canbe used to solve theoretical and practical problem.