层合板几何非线性问题的计算分析

Geometric nonlinear analysis of laminated composite plates

采用有限元分析方法研究了基于一阶剪切变形理论的层合板的几何非线性问题。首先介绍了考虑von-Kármán应变的层合板几何非线性问题的基本方程,然后推导了其有限元离散及非线性方程的牛顿-拉夫逊解法,随后列举一些数值算例证明了有限元分析方法在处理层合板几何非线性问题上的准确性。重点分析了层合板的挠度和层间应力随作用力的非线性变化情况,以及不同的铺设方案对层合板几何非线性行为的影响。

Geometric nonlinear analysis of laminated composite plates based on the first order shear deformation theory is studied using finite element method. Governing equations of laminated composite plates with von-Kármán strains are presented, finite element method and the Newton-Raphson method is applied to generate and solve the nonlinear equations respectively. Numerical examples show that finite element method gives accurate results in geometric nonlinear analysis of composite laminates. The influences of pressure magnitude on deflections and stresses of the plate are researched, lamination schemes on the nonlinear behavior of laminated composite plates are also investigated.