求解经典梁弯矩的两种正则化方法

在计算结构力学中，应力(弯矩)的数值求解有很大的实用价值．本文以经典梁问题为典型模型，先用位移型有限元求出变形位移场，然后通过这些有误差的数据，利用正则化思想，构造出求解梁弯矩的两种新型数值求解方法．理论分析和数值模拟都证明了算法的有效性和合理性．

Two Regularization Methods for Solving Bending Moment Field of Classical Beam Problems

In the context of computational structural mechanics, a numerical solution of stress field (bending moment field) is of great importance in practice. With the classical beam problem as a typical example, the displacement field is first computed by the usual finite element method. With these approximate values, by means of the Tikhonov regularization method, two numerical methods are then proposed to solve the bending moment field involved. Theoretical analysis and numerical simulation were given to show the efficiency of both methods. The basic idea behind the paper can be extended to study similar high-dimensional problems.