中厚度复合材料夹芯层板变分渐近精细模型

Refined Model for Composite Sandwich Laminates of Moderate Thickness Based on the Variational Asymptotic Method

为准确预测对中厚度复合材料夹芯层板分层开裂至关重要的沿厚向应力/应变分布,利用板固有小参数将原三维板分析严格拆分为沿厚向的一维分析和二维板非线性分析,并将原三维能量渐近扩展为系列二维近似能量泛函;通过对近似能量泛函中主导变分项(含翘曲项)的渐近修正,得到与原三维模型尽可能接近的近似能量,从而构建无需任何场变量假设的精细模型,并转换为工程常用的Reissner模型形式.通过4层复合材料夹芯板柱形弯曲算例表明:基于所构建模型重构的三维场精度较一阶剪切变形理论和经典层合理论更好,与精确解基本一致;由于所构建的变分渐近模型为等效单层板模型,在保证足够精度的前提下,相比三维有限元计算可减少2～3阶计算量,在精确性和有效性间取得较好的折衷.

In order to accurately predict the stress/strain distribution along the thickness direc- tion, which is very important to the interface cracking of the composite sandwich laminate of moderate thickness, the small inherent parameter was used to rigidly decouple the original 3D plate into 1D analysis along the thickness direction and 2D nonlinear plate analysis. The 3D en- ergy was approximately extended into a series of 2D energy functionals, in which the leading i- tems were asymptotically corrected to match the original 3D energy as close as possible. Then, a refined model was built up without any field variable assumptions, and converted to the form of Reissner model for engineering applications. The cylindrical bending example of a sandwich plate with four layers shows that the 3D field reconstituted by this theory agrees better with the exact results than those by the first-order shear deformation theory and classical laminated the- ory; it＇ s amount of computation can be reduced up to 2 ~ 3 orders than 3D finite element meth- od because the variational asymptotic model is an equivalent singie-layer plate model, indicating a good tradeoff between the accuracy and efficiency.