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中文核心期刊

基面力概念在几何非线性余能有限元中的应用

Application of the base forces concept in geometrically nonlinear finite element method on complementary energy

  • 摘要: 以基面力为基本未知量描述一个弹性系统的应力状态并表征单元的余能,将大变形的余能分解为变形余能部分和转动余能部分,采用Lagrange乘子法放松单元的平衡方程,利用已有的弹性大变形余能原理建立了一种几何非线性显式有限元模型,编制了相应的几何非线性余能原理有限元程序. 数值算例表明:该方法具有较好的收敛性和计算精度,可进行大载荷步的大位移、大转动计算.

     

    Abstract: In this paper, a new explicit expression of thegeometrically nonlinear finite element method was developed on thecomplementary energy principle for the large displacement and large rotationproblem on the basis of the concept of base forces as fundamental variables.The complementary energy of an element under large deformation case isdivided into the deformation part and rotation part. The formulations of thecontrol equations for the base forces finite element method are obtainedusing the Lagrange multiplier method, and an explicit displacementformulation of nodes is given. The numerical results are compared with thoseof the theoretical solution and the assumed displacement finite elementmethod based on potential energy principle. It has been demonstrated thatthe new finite element formulations proposed in this paper is effective,accurate, and capable of simulating the large rotation case under one largeload step.

     

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