文档介绍：Chapter 7 Diffenence Solution to the Question of Plain
Elasticity
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第七章平面问题的差分解
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Chapter 7 Difference Solution to the Questions of Plane
DIFFERENCE SOLUTION TO THE QUESTIONS OF PLAIN
§7-1 Derivation of Difference Formula
§7-2 Difference Solution to Steady Temperature Field
§7-3 Difference Solution to Unsteady Temperature Field
§7-4 Difference Solution to Stress Function
§7-5 Example of Difference Solution to Stress Function
§7-6 Difference Solution of Stress Function to the
Question of Temperature Stress
§7-7 Difference Solution to Displacement
§7-8 Example of Difference Solution to Displacement
§7-9 Displacement Difference Solution to more
Continuous Object
Exercise of《 Difference Solution to Plane Questions 》
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第七章平面问题的差分解
平面问题的差分解
§7-1 差分公式的推导
§7-2 稳定温度场的差分解
§7-3 不稳定温度场的差分解
§7-4 应力函数的差分解
§7-5 应力函数差分解的实例
§7-6 温度应力问题的应力函数差分解
§7-7 位移的差分解
§7-8 位移差分解的实例
§7-9 多连体问题的位移差分解
习题课
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The typical solutions to the theory of elasticity have a certain limits. When the elastic objects’ boundary conditions and loads are a plex ,always the rigorous solution to boundary questions of the partial differential equations can’t be found。Thus the numerical solutions have an important practical meaning。Difference solution is one of the numerical solutions。
Difference solution is a method that uses difference equations (algebra equations) instead of basic equations and boundary conditions (sometimes they are differential equations), and translates the solutions to differential equations into algebra equations.
DIFFERENCE SOLUTION TO THE QUESTIONS OF PLAIN
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平面问题的差分解
弹性力学的经典解法存在一定的局限性,当弹性体的边界条件和受载情况复杂一点,往往无法求得偏微分方程的边值问题的解析解。因此,各种数值解法便具有重要的实际意义。差分法就是数值解法的一种。
所谓差分法,是把基本方程和边界条件(一般均为微分方程)近似地改用差分方程(代数方程)来表示,把求解微分方程的问题改换成为求解代数方程的问题。
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§7-1 Derivation of Difference Formulation
We make a square grid on the surface of elastic object,by using two group lines which are parallel to the coordinate axes and the distance of two parallel lines is h . Shown in Fig.