热载荷作用下功能梯度材料梁的热粘弹性弯曲

Thermo-viscoelastic Bending of Functionally Graded Beam under Thermal Load

由记忆型非均匀热粘弹性材料的积分型本构关系出发,在时空可分离松弛函数假设和平截面几何假设下,通过引进“结构热函数”,建立了FGM梁热粘弹性弯曲问题的数学模型及其简化Gurtin型变分原理。在热弹性参数沿厚度方向呈幂律形式变化和热粘弹性松弛函数空域部分沿厚度方向呈指数形式变化的情况下,借助Ritz解和解析解,研究了热载荷作用下材料组分对热弹性/热粘弹性挠度响应和应力分布的影响,发现了热应力反向分布现象。

According to the integral type constitutive relation for non-homogeneous thermo-viscoelastic materials with memorial effects, a mathematical model and its simplified Gurtin type variational principles for thermo-viscoelastic bending of functionally graded beams were set up with the help of the introduction of ＂structural thermal function＂ on the assumption that the plane section remains plane and normal to the beam axis and the relaxation functions may be separated into spatial parts and temporal parts. In the case of that across the thickness thermoelastic parameters vary according to a power law distribution and the spatial parts of thermo-viscoelastic relaxation functions vary exponentially, the influence of material constituents on thermoelastic/thermo-viscoelastic deflection responses and stress distributions under thermal loads was investigated by Ritz solutions and analytical solutions, and the inverse thermal stress distribution phenomenon was found.