Calculation of impact-contact problems of thin elastic shells taking into account geometrical nonlinearities within the contact region

authored by: E. Stein, Peter Wriggers
Abstract: During impact of elastic bodies, contact stresses are transmitted in time-depending contact surfaces. In many impact contact problems, large displacements and rotations appear only in the contact surface and in a certain neighbourhood. Therefore, it is efficient to consider geometrical nonlinearities only in this region, and to describe the remainder of the body within the geometrical linear theory. This leads to substructure techniques where only properties of the nonlinear elements need be modified during the impact contact process. The principle of virtual work for nonlinear thin shells is expressed using the total Lagrangian formulation, and the geometrical nonlinearity of thin shells is described in the frame of moderate rotation theory. The contact conditions lead to inequalities for the normal stresses and displacements in the contact interfaces. Therefore, the numerical algorithm involves two superposed iterations: for the computation of contact forces and contact areas and for the geometrical nonlinearity. The iteration procedure has to be carried out in each time step. The spatial discretization using finite element techniques leads to a system of ordinary differential equations which is integrated over the time using the Newmark algorithm. Numerical results were obtained for the impact contact problem of spherical shells. For these examples, the impact forces and the contact pressure distribution are presented for several parameter combinations. Results are controlled by conservation laws in integral form, and compared with results from geometrical linear theory.
Organisation(s): Institute of Mechanics and Computational Mechanics
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 34
Pages: 861-880
No. of pages: 20
ISSN: 0045-7825
Publication date: 09.1982
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, Physics and Astronomy(all), Computer Science Applications
Electronic version(s): https://doi.org/10.1016/0045-7825(82)90092-5 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{6822db70f5644c77962e42c61e5d6173,
title = "Calculation of impact-contact problems of thin elastic shells taking into account geometrical nonlinearities within the contact region",
abstract = "During impact of elastic bodies, contact stresses are transmitted in time-depending contact surfaces. In many impact contact problems, large displacements and rotations appear only in the contact surface and in a certain neighbourhood. Therefore, it is efficient to consider geometrical nonlinearities only in this region, and to describe the remainder of the body within the geometrical linear theory. This leads to substructure techniques where only properties of the nonlinear elements need be modified during the impact contact process. The principle of virtual work for nonlinear thin shells is expressed using the total Lagrangian formulation, and the geometrical nonlinearity of thin shells is described in the frame of moderate rotation theory. The contact conditions lead to inequalities for the normal stresses and displacements in the contact interfaces. Therefore, the numerical algorithm involves two superposed iterations: for the computation of contact forces and contact areas and for the geometrical nonlinearity. The iteration procedure has to be carried out in each time step. The spatial discretization using finite element techniques leads to a system of ordinary differential equations which is integrated over the time using the Newmark algorithm. Numerical results were obtained for the impact contact problem of spherical shells. For these examples, the impact forces and the contact pressure distribution are presented for several parameter combinations. Results are controlled by conservation laws in integral form, and compared with results from geometrical linear theory.",
author = "E. Stein and Peter Wriggers",
year = "1982",
month = sep,
doi = "10.1016/0045-7825(82)90092-5",
language = "English",
volume = "34",
pages = "861--880",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
number = "1-3",
}