基于有限元的弯矩计算中若干问题探讨

在岩土工程的数值计算中，除了将岩土材料本身划分为实体单元外，设置在岩土体中，与岩土材料相互作用的其他材料也常常划分为实体单元，比如桩基、堤坝防渗墙和面板等。由于对桩基、防渗墙等往往需要利用内力和弯矩进行设计，这就提出了如何利用有限元得到的应力和位移信息计算结构弯矩的问题。通过对一悬臂梁的计算分析就这一问题进行探讨，发现用应力计算弯矩为提高精度需要划分较多单元。用位移计算可以减少单元划分的工作量，但计算易出现振荡，结果不可靠。同时，对剪切闭锁现象等进行了探讨。

Discussion on bending moment calculation by finite element method

Solid element is often used to simulate soil and rock in geotechnical engineering. Other structures such as pile, cut-off wall and concrete panel are also often simulated with solid element when then are embedded in soils. Internal force and bending moment are important for design of these structures, so it is necessary to calculate bending moment with stress and displacement obtained by finite element method(FEM). This problem is studied by analyzing a cantilever beam. It shows that enough elements are necessary when bending moment is calculated with stress, whereas oscillation occurs and leads to unreliable results when bending moment is calculated with displacement. Shear locking and its influence is also investigated herein.