基于S-R和分解定理的无网格Galerkin法求解几何非线性问题

针对几何非线性问题,基于S-R和分解定理与更新拖带坐标描述法,从运动变换的角度出发,由虚功率原理建立全局弱式积分方程.采用无网格Galerkin法(EFG)求得该问题的数值解.对于非线性问题的数值计算,通常采用增量和迭代法.S-R和分解定理给出了一种新的应变张量,该应变张量能合理地反映大位移大转动情况下物体的应变状态及转动情况,而且有利于求解几何非线性问题.数值算例验证了该方法的合理性和有效性.

Element Free Galerkin Method for Geometrically Nonlinear Problems Based on the S-R Decomposition Theorem

Aiming at geometrically nonlinear problems and using movement transformation as a point of departure,a global weak form integral equation was established from the virtual power principle on the basis of the S-R decomposition theorem and updated co-moving coordinate formulation.Numerical solutions were obtained by using element free Galerkin method(EFG).Usually,incremental and iterative methods are used to solve the nonlinear problems of numerical calculation.S-R decomposition theorem brings out a new strain tensor,which can reasonably reflect the state of stain and rotation on the condition of large displacement and large rotation,and are helpful in solving geometrically nonlinear problems.Numerical examples have shown that this method is reasonable and effective.