Open AccessANALYSIS OF FINITE ELEMENT SOLUTION CONSERVATIVE SMOOTHING INFLUENCE ON THE ZERO ENERGY MODES SUPPRESSION
Author(s) -
А. И. Кибец,
M.V. Bezhentseva
Publication year - 2021
Publication title -
problemy pročnosti i plastičnosti
Language(s) - English
Resource type - Journals
ISSN - 1814-9146
DOI - 10.32326/1814-9146-2021-83-1-101-110
Subject(s) - finite element method , mathematics , mathematical analysis , discretization , smoothing , mixed finite element method , boundary value problem , geometry , physics , statistics , thermodynamics
The problem of high-speed penetration of a non-deformable cylinder into a steel plate is considered. The defining system of equations is formulated in Lagrange variables in a three-dimensional formulation. The equation of motion is derived from virtual work capacities balance. Kinematic relations are recorded in the metric of the current state. The relations of the flow theory with kinematic and isotropic hardening are used as equations of state. The contact interaction of the cylinder and the plate is modeled by non-penetration conditions. The numerical solution of the problem under given boundary and initial conditions is based on the moment scheme of the finite element method and “cross” type explicit time integration scheme. To discretize the defining system of equations with respect to spatial variables, 8-node isoparametric finite elements with multilinear form functions are used. To suppress the high-frequency oscillations of the numerical solution, the procedure of nodal displacement velocities conservative smoothing is used. The smoothing algorithm is based on the momentum conservation law, focused on finite element grids consisting of blocks that are mutually unambiguously mapped to a unit cube. To analyze the nodal displacement velocities monotonicity, the numerical solution splitting in the directions of the finite element grid lines is used. As the results of computer modeling have shown, the finite elements of the plate are exposed large deformations and rotation angles as a rigid whole during local intense dynamic loading. The conservative smoothing procedure influence on the numerical solution stability is analyzed. It is shown that in the problem under consideration, without applying the conservative smoothing procedure, zero-energy modes develop in the contact zone in the finite-element grid of the plate (an hourglass-type instability) and the collision process cannot be modeled before the cylinder rebounds.