Zonal free element method for solving 2D elastoplastic dynamic problems

In this paper, an elastoplastic dynamic analysis method based on the zonal free element method (ZFrEM) is introduced to solve material nonlinearity problems in dynamic systems. By integrating the collocation element technique with the generalized smoothed Galerkin weak form, a robust and computationally efficient numerical analysis framework is developed As a meshfree method, the ZFrEM discretizes the computational domain into a series of points, where the free elements are constructed by using the collocation points and their surrounding nodes. The ZFrEM borrows the concept of Lagrangian isoparametric elements from the finite element method to form shape functions for each node within the free elements. In the constitutive equation describing the problem, the traditional motion equation is used, with damping forces neglected. The associated flow rule is adopted to characterize the evolution of plastic strain, and isotropic hardening models are employed to simulate material nonlinearities. The Newton–Raphson iterative scheme and Newmark temporal discretization technique are used to solve the dynamic nonlinear problems. Three numerical examples are given to verify the accuracy and convergence of the presented method in solving the elastoplastic problems.