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Nonlinear analysis of plates and laminates-using the element free Galerkin method

机译：板和层板的非线性分析-使用无元素Galerkin方法

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A meshless method based in a Galerkin formulation, the element-free galerkin method (EFGM), has been extended for the use in the elastic and elasto-plastic analysis of anisotropic symmetric laminates. A Reissner-Mindlin plate theory, which is a first-order shear deformation theory (FSDT) is considered and briefly described in order to define the displacement field and the strain field. The approximation functions are calculated considering a moving least squares (MLS) approach which is consistent provided the basis is complete in the polynomials up to a desired order. A modified version of the Newton-Rapson method is used for the solution of the nonlinear system of equations and an anisotropic yield surface, Hill yield surface, is considered. The elasto-plastic algorithm of solution is described. Several problems of laminate bending are solved and the obtained solutions are compared with finite element solutions which show that the mesh-less approach developed is an alternative to the finite element method (FEM) for the solution of problems with material nonlinearity.
机译：一种基于Galerkin配方的无网格方法，即无元素galerkin方法（EFGM），已被扩展用于各向异性对称层压板的弹性和弹塑性分析。为了定义位移场和应变场，对Reissner-Mindlin板理论（一阶剪切变形理论（FSDT））进行了考虑并进行了简要描述。近似函数是在考虑最小二乘（MLS）方法的情况下计算得出的，只要该方法在多项式中的基础完全达到所需的阶数，就可以保持一致。牛顿-拉普森方法的修改版用于求解非线性方程组，并考虑了各向异性屈服面Hill屈服面。描述了解决方案的弹塑性算法。解决了层压板弯曲的几个问题，并将获得的解决方案与有限元解决方案进行了比较，结果表明，开发的无网格方法是有限元方法（FEM）替代材料非线性问题的一种方法。

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