多孔双向功能梯度板瞬态热应力分析

Transient Thermal Stress Analysis of Porous Bi-directional Functionally Graded Plates

为了研究多孔双向功能梯度板在热荷载作用下的应力变化特征,本文由定解条件结合传热学基本定律得到平面温度场及应力场解析解,运用解析法求解研究模型的应力场,通过算例分析加热时间、沿板长方向的孔隙率控制参数A_(x)、沿板厚方向的孔隙率控制参数A_(y)以及4种边界加热函数对多孔双向功能梯度板热应力分布的影响规律。结果表明:1)板内热应力等高线表现为非对称分布,最大压应力积聚于上边界处且最小压应力积聚于右下区域;2)孔隙率控制参数A_(x)的取值变化不改变板内最大及最小热应力的坐标位置;3)加热时间及孔隙率控制参数A_(y)取值的变化导致板内热应力等高线的变化较大,而孔隙率控制参数A_(x)及上边界加热函数对板内热应力影响作用不显著。

In order to study the stress variation characteristics of porous bi-directional functionally graded plate under thermal loading,the analytical solutions of the plane temperature field and the stress field are obtained by using the fixed solution conditions and the basic laws of heat transfer,the stress field of the model is solved by using the analytical solution method.The effect of the heating time,porosity control parameter A_(x) along the length direction of the plate,porosity control parameter A_(y) along the plate thickness direction,and four types of boundary heating functions on the thermal stress distribution of the porous bi-directional functionally graded plate were analyzed by using a numerical example.The results show that the thermal stress field in the plate is asymmetrically distributed,the maximum compressive stress is accumulated at the upper boundary,and the minimum compressive stress is accumulated in the lower right area;the porosity control parameter A_(x) doesn′t change with the coordinate position of the maximum and minimum thermal stress in the plate;the changes in heating time and porosity control parameter A_(y) along the plate thickness direction lead to great changes in thermal stress contour in the plate,while the porosity control parameter A_(x) and the type of the upper boundary heating function have less effect.