地下工程中一类位移敏感度分析方法

Design Sensibility Analysis Based on Incremental Motion Equation Applied in Underground Engineering

通过对增量形式的有限元运动方程直接微分,推导了地下问题所涉及的一类关于结构几何属性的位移敏感度分析算法,编制了相应程序,以含有单元生死问题的承受横向荷载的悬臂梁以及分时段施加荷载的简支梁作为算例,同时采用作者提出的算法和经典理论解、差分法就挠度对梁惯性矩的敏感度进行了求解,并就求解精度、求解效率等进行了对比,结果表明,新法的求解结果是可靠的,由于该算法是以有限元法为基础,可考虑诸如施工过程等因素,应用范围广,且计算效率较高,适合于用来对地下工程领域涉及的尺寸类敏感度问题进行分析。

By means of the direct differentiation of the discretized incremental motion equation, one algorithm for computing the design sensibility of displacement with respect to geometry attribute was developed to deal with some excavation problems in the underground engineering. Two numerical examples ： a cantilever beam with spring support and simple supported beam with point load varied with time, were conducted to verify the proposed DSA method. The results of Design Sensibility analysis of deflection with respect to the inertia moment induced by the proposed method, FD, respectively, were compared with the analytical solution on the accuracy. It demonstrated that the DSA method presented by this paper is reliable. Meanwhile, this method enjoys some advantages including efficient computation and that the factors, such as excavation process, could be taken into account.