复合材料层合壳体热弹耦合简化模型

为有效分析复合材料层合壳体单向耦合的热弹性问题,基于变分渐近方法(VAM)建立热弹性简化壳体模型.根据Hamilton扩展原理建立层合壳体三维能量方程,并利用壳体固有小参数将三维能量渐近扩展为系列二维近似能量方程.将近似能量转换为工程常用的Reissner-Mindlin形式,并推导三维场重构关系以准确重构沿厚向的三维场分布.通过热/力环境下4层复合材料层合壳体的柱形弯曲算例验证:该理论建模速度快(等效单层板模型,相比三维有限元法可减少2～3阶计算量);具有很好的非线性逼近能力(收敛于精确解).

A Simplified Thermoelastic Model for Composite Iaminated Shells

To effectively analyze the one way coupled thermoelastic problem for composite laminated shells, a simplified thermoelastic shell model based on the variational asymptotic method (VAM) was developed. The 3 D energy functional for composite laminated shell was established according to the Hamilton extended principle. Then the 3 D energy was asymptotic expanded into a series of 2 D approximation energies by taking advantage of the inherent small parameters. Finally, the approximate energy was converted to the form of Reissner Mindlin model, and the 3 D recovery relationships were deduced to accurately predict the 3 D field distribution along the thickness direction. The cylindrical bending example of a four layer composite laminated shells under the sinusoidal surface load and temperature field shows that the modeling speed is fast (equivalent single layer model, which can reduce two or three order calculations compared to the 3 D finite element method), and the nonlinear approximation ability is excellent (convergent to the exact solution).