Question

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内容：在推导正交各向异性悬臂梁的解析解过程中，构造了一个含待定系数的应力函数，再根据弹性力学中的应力和位移边界条件，逐一来确定待定系数，最终通过Airy应力函数解法，给出了应力和位移的解析表达式，并退化到正交各向同性的情况，与已有的结论一致。为了进一步验证应力与位移解析表达式的正确性，采用了有限元方法进行比较。通过Patran软件构造悬臂梁的真实模型，并且施加了相应的边界条件，再由Nastran程序来计算出有限元的数值结果。通过绘制应力和位移曲线，将解析解与有限元结果作出了比较，得到的结论是：解析解结果与有限元计算结果几乎一致，二者吻合的较好。

Answer 1

In the derivation of analytical solutions for orthotropic cantilever beam process, the structure of a stress function with undetermined coefficients, and then under the elastic stress and displacement in the boundary conditions of the coefficients one by one to the end through the Airy stress function solution, given the analytical expressions of stress and displacement, and degradation to the orthogonal isotropic case, consistent with previous results. To further verify the analytical expressions of stress and displacement of the correctness of using the finite element method were compared. Patran software construction through the true model of cantilever and the corresponding boundary conditions imposed, then Nastran finite element program to calculate the numerical results. Stress and displacement curves by drawing, the analytical solution and finite element results to make comparisons, to the conclusion that: analytical solution and finite element calculation results were almost identical, the better agreement between the two.

Answer 2

是In the derivation of analytical solutions for orthotropic cantilever beam process, the structure of a stress function with undetermined coefficients, and then under the elastic stress and displacement in the boundary conditions of the coefficients one by one to the end through the Airy stress function solution, given the analytical expressions of stress and displacement, and degradation to the orthogonal isotropic case, consistent with previous results. To further verify the analytical expressions of stress and displacement of the correctness of using the finite element method were compared. Patran software construction through the true model of cantilever and the corresponding boundary conditions imposed, then Nastran finite element program to calculate the numerical results. Stress and displacement curves by drawing, the analytical solution and finite element results to make comparisons, to the conclusion that: analytical solution and finite element calculation results were almost identical, the better agreement between the two