热黏弹性梁拟静态弯曲问题的解析分析

Analytical Analysis for Quasi-static Bending Problem of Thermo-viscoelastic Beam

基于平面应力假设和热黏弹性材料的积分型本构关系,建立了以位移分量为未知量的热黏弹性梁静动力学分析的二维数学模型。针对拟静态弯曲问题,首先,在Laplace变换域,引入位移势函数,将控制方程解耦;其次,根据给定的平面温度场和边界条件,采用分离变量法,引入热应力函数,得到了热黏弹性梁的热应力分布;最后,利用Laplace逆变换,获得了热黏弹性梁拟静态弯曲热应力响应的解析解,考察了热载荷作用下几何、黏弹性等参数对梁应力和位移的影响。

The two-dimensional mathematical model of static/dynamic analysis of a thermo-viscoelastic beam with displacement components as unknown variables was established based on the plane stress hypothesis and thermo-viscoelastic integral constitutive relationship.For quasi-static bending problems,the governing equations were decoupled by introducing displacement functions in Laplace transformation domain.The thermal stress distributions of the thermo-viscoelastic beam were obtained by using the method of separation of variables and thermal stress functions given the plane temperature field and boundary conditions.The analytical solutions of quasi-static bending thermal stress responses of the thermo-viscoelastic beam were obtained by using inverse Laplace transformation,the influences of geometric and viscoelastic parameters to stress and displacement distributions were also investigated.