Accession Number : ADP004904

Title :   Buckled Elastica in Contact - Finite Element Solutions,

Corporate Author : ARMY MATERIALS AND MECHANICS RESEARCH CENTER WATERTOWN MA

Personal Author(s) : Johnson,A. R. ; Quigley,C. J.

Report Date : FEB 1985

Pagination or Media Count : 11

Abstract : The analysis of manufacturing processes for metal sheets, stresses in elastomer bumpers and other geometrically nonlinear problems require numerical techniques which can deal with continuously changing regions of contact. The most common method of dealing with the contact problem is to introduce gap elements in the contact region. These elements provide either zero or very large stiffness between two degrees of freedom. The methods for determining gap element stiffness include computations which determine if contact has been made. In this effort, a revised simplex method of quadratic programming is investigated for treating contact problems. The method allows the contact problem to be treated directly as a minimization problem subject to an inequality constraint without the need to define gap elements. To test the effectiveness of the algorithm the problem of the buckled elastica in contact with itself was solved. An existing finite element formulation for the extensional elastica based on the minimum potential energy principle is used to model the buckled elastica. Solutions to the contact problem are also obtained by a penalty method using gap elements. Results from both numerical methods are compared to theoretical results. (Author)

Descriptors :   *FINITE ELEMENT ANALYSIS, *ELASTIC PROPERTIES, METAL CONTACTS, SIMPLEX METHOD, QUADRATIC PROGRAMMING, ELASTOMERS, BUCKLING

Distribution Statement : APPROVED FOR PUBLIC RELEASE