摘要
求解了功能梯度棒-弹簧系统的一维约束热应力问题.假设棒只存在轴向应变且线膨胀系数和弹性模量与位置坐标是呈幂函数变化,通过得到描述问题的方程组,进而得到棒热应力分布的解析解.结果经退化可得到均匀棒以及功能梯度棒若干问题的解析解.数值算例分析了功能梯度参数等对热应力的影响.
The one-dimensional thermal stress problems of a functionally graded beam-spring system are studied. To make the analysis tractable, the properties of the functionally graded beam, such as elastic modulus and coefficient of linear thermal expansion, are assumed in power forms and vary the location coordinate. Under the view of mechanics of materials, the one-dimensional thermal stress distribution in analytical form is found. The derivation is verified by the simplified results in the special cases of the beam-spring system and the functionally graded beam. Numerical results are presented to show the effects of functionally graded parameters of beam on the thermal stress.
出处
《数学的实践与认识》
北大核心
2016年第13期154-159,共6页
Mathematics in Practice and Theory
基金
国家自然科学基金(11362018)
福建省自然科学基金(2011J01001)
兰州大学西部灾害与环境力学教育部重点实验室开放基金项目(Klmwde201406)
关键词
功能梯度材料
棒-弹簧系统
约束
热应力
functionally graded materials
beam-spring system
constraints
thermal stress
