层合板热弹性问题混合状态Hamilton半解析法

Mixed state Hamilton semi analytical method on thermal elastic problem of laminates

从单斜晶材料热弹性问题分析的Ｈｅｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ泛函表达式出发，推导了混合边界条件下热弹性问题分析修正的Ｈｅｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ泛函表达式；建立了复合材料层合板热弹性问题分析的混合状态Ｈａｍｉｌｔｏｎ等参元列式；给出了状态方程的求解过程．克服了各种板理论由于引入各种假定而带来的误差，为正确求解层合板的热应力（特别是多层厚板的层间热应力）问题提供了一种分析的新途径．数值结果表明了本法的正确性和有效性．

Deducing from the Hellinger Reissner functional expression of the thermal elastic problem of the monoclinic materials, the modified Hellinger Reissner functional expression on the thermal elastic problem of the mixed boundary conditions is obtained. The mixed state Hamilton isoparameter element equations to study the thermal elastic problem of the composite laminates is set up. And, the solving procedure of the state equations is also given. The loss which is caused by the introduction of the assumptions of plate theories is avoided. This method presents a new way on the study of the thermal stress problem of the laminates (especially for the interlaminated thermal stress of the multi layer thick laminates). The numerical results show the correctness and the utility of the method.