复合材料层合壳体热弹耦合简化模型_复合材料壳体
摘 要：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)。
关键词：复合材料力学；简化模型；变分渐近法; 三维应力重构；复合材料层合壳
中图分类号：TB330.1
文献标志码：A
文章编号：1674-4764（2012）04-0053-06
A Simplified Thermoelastic Model for Composite Iaminated Shells
ZHONG Yifeng1a,1b, CHEN Lei1a,1b, YU Wenbin2, ZHANG Liangliang1a,1b
（1a.School of Civil Engineering；1b.Key Laboratory of New Technology for Construction of
Cities in Mountain Area, Ministry of Education, Chongqing University, Chongqing 400045, P.R.China；
2.Department of Mechanics and Aerospace Engineering, Utah State University, Logan 84322, USA）
Abstract: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).
Key words:composite material mechanics; simplified model; variational asymptotic method; 3D stresses recovery; composite laminated shells
近20年来，先进复合材料结构因其高强度、高模量、可设计性等优点已广泛应用于航天航空、机械、土木等领域。由于复合材料不同成分、不同纤维方向的热膨胀系数相差很大，相比于各向同性材料对温度的改变更加敏感，复合材料板/壳结构的热响应已成为近年来复合材料力学热点课题之一［1-2］，出现了各种复合材料板/壳理论。Ng等［3］应用古典层合理论(CLT)分析了复合材料圆柱壳的热残余应力和自由振动，由于忽略了横向剪切效应，该理论仅对薄壳有效；为克服CLT的缺陷，Pradyumna等［4］基于一阶剪切变形理论(FOSDT)分析了复合材料层合壳体在热环境下非线性动态稳定性，但模拟弯曲时数值计算结果严重失真，产生“横剪自锁”现象，其原因在于总应变能中包含横向剪切应变能的项在量级上不正确，沿厚度方向变化的剪切应变线性假设与上下表面剪应力为零自相矛盾，需人为地引入与几何形状和材料相关的剪切修正因子来解决这一矛盾；为提高沿厚向的应力/应变预测精度，各国学者纷纷把研究重点转向了高阶剪切变形理论，Li等［5］用高阶壳理论分析了复合材料圆柱壳在热环境下的非线性屈曲和后屈曲性能，Nosier等［6］基于层合理论确定湿热环境下正交铺层/角铺层壳体的局部位移函数和层间应力，但仍无法准确预测面内的不连续性和沿厚度方向的横向位移分量。