用已知位移反求平面应变问题的弹性模量

Back Analysis for Determining Elastic Modulus of Structure Corresponding to Plane Strain by Known Displacements

本文利用阻尼最小二乘法求解平面应变问题的结构弹性模量。通过分析阻尼最小二乘法和平面应变有限元方程的特点,将雅可比矩阵的诸元素表示为弹性模量和位移的显式函数,避免中心差分代替导数带来误差。另一方面,充分利用边界约束条件,加快求解过程,数值计算表明:收敛速度快,稳定性好。

Damped least square method in combination with finite element method is used to back analysis for determining elastic modulus of structure corresponding to plane strain. It has been found that each element of Jacobian matrix can be expressed as explicit function of polynomial of degree 1 of elastic modulus and displacements so as to avoid the error caused by replacing differentiation by centered difference. On the other hand, the solving process can be quicken if the boundary constraint condition is fully considered. The method is characterized by a rapid convergence and good stability according to numerical calculation performed.