层合开口桩壳热应力问题的解析解

基于具有任意混合边界条件的Hellinger－Reissner广义变分原理，在柱坐标系下，导出正交各向异性层合开口柱壳混合状态方程和边界条件算子方程的弱形式，建立了层合开口柱壳的热应力混合方程，化混合方程为Hamilton正则方程，在求解中利用Hamilton矩阵的性质和矩阵传递法，保证了层间应力和位移的连续性，给出了任意厚度层合开口柱壳在热荷载和机械荷载共同作用下的解析解。本文提出的方法弱化了求解方程，物理概念清晰，无需特殊技巧，具有一般性和便于推广。本文也为验证其它数值方法的正确性和计算精度提供了考题和依据。

ANALYTICAL SOLUTION OF THERMAL STRESSES FOR OPEN LAMINATED CYLINDRICAL SHELL

Weak formulation of mixed state equations including boundary conditions of openlaminated cylindrical shell was presented in a cylindrical coordinate system based upon themodified mixed Hellinger-RCissner variational principle. Thermal stress mixed state equation foropen cylindrical shell was established. Mixed equation was changed into Hamilton canonicalequation. For applying the transfer matrix method and taking the advantage of Hamiltonianmatrix in the calculation, analytical solutions were obtained for open laminated cylindrical shellof arbitrny thickness under thermal and mechanical loadings.The principle and methodsuggested here have clear physical conceptS. The present stUdy have the equations weakenwithout special treatment.So this method would be easily popularized in dynamics analysis ofelasticity. The solutions and resultS given here may serve as a benchmark for other numericalmethods.