区间参数梁结构热弹耦合效应分析

研究了含有区间参数梁结构在温度载荷和力载荷共同作用下的热弹耦合动力响应问题．建立了热弹耦合动力学有限元模型，给出了对结构瞬态温度场和动力响应进行相互交替迭代求解的耦合计算方法，其中，结构瞬态温度场利用有限差分法求解，结构动力响应则利用时间积分法求解．针对区间变量的有限元方程，基于各变量在区间范围内为均匀分布的近似处理，利用改进的蒙特卡罗方法求解，获得动力响应的区间范围．通过悬臂梁算例，分析了热弹耦合效应对动力响应的影响，并针对结构的弹性模量和热膨胀系数区间范围增大的情况进行了比较和分析，得出这两参数以及结构变形大小是影响耦合效应的主要因素．

Analysis of thermo-elastic coupling effects of the beam structure with interval parameters

The dynamic response of thermo-elastic coupling of the beam structure with interval parameters is studied under both the thermal load and force load. The dynamic model of thermo-elastic coupling is set up using the finite element method. The coupled calculation method is proposed for solving the transient temperature field and dynamical response by iterative solution, in which the finite difference method is used for solving the transient temperature field, and time integration method is used for solving structural dynamic response. The equations for the model with interval parameters are solved by the improved Monte Carlo numerical simulation method assuming that each variable is uniformly distributed, and then the interval distribution range of the dynamic response is determined. Finally, the thermo-elastic coupling effect on the dynamic response of the cantilever beam is analyzed. Numerical examples show that the thermo-elastic coupling effect is mainly determined by the increased interval range of the elastic modulus and thermal expansion coefficient influence and the magnitude of deformation.