摄动边界元法在随温度变化线胀系数反问题中的应用

Application of Perturbation Boundary Element Method in Inverse Problem with Temperature Dependent Thermal Expansion Coefficient

将摄动法和边界元法相结合求解物性值随温度变化的热弹性问题，先用摄动法将变系数微分方程转化成常系数微分方程，再按边界元法求解．又采用摄动边界元法和卡尔曼滤波，由有限个观察点的位移值，反算出随温度变化的线膨胀系数．算例表明本文方法简便、有效．

The perturbation method and boundary element method were used to solve the thermoelastic problems with temperature dependent material properties. The differential equations of variable coefficient were changed into the differential equations of constant coefficient by the perturbation method. The boundary element method for solving this problem was proposed. The inverse method is a combination of the perturbation boundary element method and the Kalman filter. The thermal expansion coefficints related to temperature can be concluded by the displacements at observation points. The numerical examples show this method is valid with simplicity.