TY - JOUR

T1 - Calculation of impact-contact problems of thin elastic shells taking into account geometrical nonlinearities within the contact region

AU - Stein, E.

AU - Wriggers, Peter

PY - 1982/9

Y1 - 1982/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0019609597&partnerID=8YFLogxK

U2 - 10.1016/0045-7825(82)90092-5

DO - 10.1016/0045-7825(82)90092-5

M3 - Article

AN - SCOPUS:0019609597

VL - 34

SP - 861

EP - 880

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

IS - 1-3

ER -