变截面功能梯度棒的一维全约束热应力

The One-dimensional Thermal Stress Analyse of a Functionally Graded Beam with Complete Displacement Constraints

求解了变截面功能梯度棒的一维全约束热应力问题.假设棒在热膨胀主轴上没有剪应力只有纵向应变,且沿热膨胀的主轴,棒的线膨胀系数和弹性模量呈幂函数变化.材料力学观点下计算了棒自由时的缩短量和棒受未知拉力时的伸长量,并借助全约束假设令其相等,确定未知拉力值,进一步得到棒沿热膨胀主轴上热应力分布的解析解.结果进行退化后可得到与均匀棒相关问题完全一致的结果.数值算例详细的分析了圆孔半径以及功能梯度参数等对热应力的影响.

Under the view of mechanics of materials, the one-dimensional thermal stress problem of a functional gradient beam is studied. To make the analysis tractable, the proper- ties of the functionally graded beam, such as elastic modulus and coefficient of linear thermal expansion, are assumed in power forms and vary the principal axes of stress. First of all, the transverse shrinkage of free beam when the temperature drops is obtained, and the elongation of the beam under a unknown tension is calculated. Secondly, using the assuming of com- plete displacement constraints, the unknown tension is obtained. At last, the one-dimensional thermal stress in analytical form is found. The derivation is verified by the simplified result in a special case. Numerical results are presented to show the effects of functional graded parameters and hole diameter of beam on the thermal stress graphicly.