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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。
The geometrical nonlinearity of laminated plates based on the first-order shear deformation theory is studied by means of finite element analysis. First of all, the basic equations of the geometrical nonlinear problem of laminates considering von-Kármán strain are introduced. Then the Newton-Raphson method for the discretization and nonlinear equations of the finite element is deduced. Then, some numerical examples are given to prove that the finite element method Accuracy in dealing with geometric nonlinearity of laminate. This paper mainly analyzes the non-linear variation of deflection and interlaminar stress with force and the influence of different laying schemes on the geometric nonlinear behavior of laminate.