功能梯度材料广义热弹性响应

摘要

基于Lord-Shulman热弹性理论,选取温度和位移及其一阶导数作为状态变量,结合Laplace积分变换,采用状态空间法建立功能梯度材料的一维广义热弹性响应的层合模型,作为应用,考虑组分材料体积份数按幂率变化的功能梯度无限大平板,数值分析在冲击性热机载荷作用下的温度、应力以及位移响应.结果表明,在冲击性热机载荷作用下,热流延迟项以及组分材料的体积含量变化对功能梯度结构的热弹性响应有着显著的影响.%Based on the thermoelasticity theory of Lord-Shulman and taking the temperature, displacement and its first-order derivative as the state variables, a lamination model was established for one-dimensional generalized thermoelastic response of functionally graded materials by using of the Laplace transform and state space approach, As an application of this model, a functionally graded plate with an infinite functional gradient and the volume fractions of the material composition varying as power function was considered and the temperature stress, and displacement response of the plate to thermo-mechanical shock was numerically analyzed. The result showed that the heat flow delay term and variation of volume fraction of material constituents had remarkable influence on the thermoelastic response of the functionally graded structures.