【摘要】 基于三维热弹性理论，研究了变温与荷载共同作用下固支层合板的热力学行为.引入状态空间法，以位移和应力为状态变量建立状态方程.在平面内采用微分求积法对状态变量进行离散，并依据层间位移与应力连续条件，推导层合板顶、底界面状态变量之间的传递关系.结合板内温度场及表面力学边界条件，计算得到位移与应力的解析解.分析了变温、层数及材料属性对层合板位移和应力分布的影响.结果表明：随着外部温度升高，层合板内位移与应力呈线性增大，且材料属性的温度依赖性对该过程的影响显著；在相同外部变温与荷载作用下，相同尺寸的层合板因材料属性差异，随着层数增加，x方向位移与xy面内剪应力均显著减小，表明可通过调整层数与材料组合优化变温环境下层合板的结构设计.更多还原

【Abstract】 Based on three-dimensional thermoelasticity theory, the thermo-mechanical response of the laminated plates with the temperature-depended material properties was investigated under the combined action of temperature and load. The state-space method was employed to formulate the governing state equation with displacements and stresses as the primary state variables. The state variables were subsequently discretized in the in-plane directions by the differential quadrature method. Based on the interlaminar continuity conditions, the transfer relationship of the state variables between the top and bottom surfaces of the laminated plate was derived. The exact solutions of displacement and stress were obtained by combining the temperature field and the mechanical boundary conditions on the surfaces of laminated plate. The effects of temperature variation, number of layers and material properties on the displacement and stress distribution in the laminated plate were analyzed. The results show that as the external temperature rise is increased, the displacements and stresses within the laminated plate are increased proportionally, and the temperature dependence of material properties significantly influences this behavior. Under the identical thermal and mechanical loading conditions, the laminated plates of identical geometry with different material constituents exhibit pronounced reduction in the x-direction displacement and the xy-plane shear stress with the increasing of layer number. The structural performance of laminated plates in thermally varying environments can be enhanced through strategic optimization of layer numbers and constituent materials.更多还原