轴向载荷作用下弹性梁的对称性分析
Symmetry analysis of an elastic beam with axial load
摘要：
利用Lie对称方法构造了轴向载荷作用下弹性梁的封闭解。考虑了梁的质量和二阶惯性矩等物理特性随空间变化的情况。利用李对称性求解了一个不适合用简单方法求解的变系数四阶偏微分方程。我们加入边界条件，然后与数值解进行比较。
英文摘要：
We construct the closed form solution of an elastic beam with axial load using Lie symmetry method. A beam with spatially varying physical properties such as mass and second moment of inertia is considered. The governing fourth order partial differential equation with variable coefficients which is not amenable to simple methods of solution, is solved using Lie symmetry. We incorporate boundary conditions and then compare with the numerical solution.
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