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FEAP - - A Finite Element Analysis Program

SUMMARY A solution procedure for the analysis of planar and axisymmetric contact problems involving sticking, frictional sliding and separation under large deformations is presented. The contact conditions are imposed using the total potential of the contact forces with the geometric compatibility conditions, which leads to contact system matrices and force vectors. Some key aspects of the procedure arc the contact matrices, the use of distributed tractions on the contact segments for deciding whether a node is sticking, sliding or releasing and the evaluation of the nodal point contact forces. The solutions to various sample problems are presented to demonstrate the applicability of the algorithm. Much progress has been made during recent years in the development of computational capabilities for general analysis of certain nonlinear effects in solids and structures. In each of these developments, quite naturally, the first step was the demonstration of some ideas and possibilities for the analyses under consideration, and then the research and development for reliable and general techniques was undertaken. The second step proved in many cases much more difficult, and in the case of capabilities for analysis of contact problems has yielded few general results. Although some of the first complex contact problems have been solved using the finite element method quite some time ago,'- and much interest exists in the research and solution of contact problems (see, for example, References 4-1 5), there is still a great deaiwf effort necessary for the development of a reliable, general and cost-effective algorithm for the practical analysis of such problems. This is largely due to the fact that the analysis of contact problems is computationally extremely difficult, even for the simplest constitutive relations used. Much of the difficulty lies in that the boundary conditions of the bodies under consideration are not known prior to the analysis, but they depend on the solution variables. The aim in our research is the development of a solution algorithm for analysis of general contact conditions which shall include the possibilities to analyse: contact between flexible-flexible and rigid--flexible bodies; sticking or sliding conditions (with or without friction); large relative motions between bodies; repeated contact and separation between the bodies. Since the large deformation motion of the individual bodies can in many cases be analysed already quite effectively,'6 an algorithm of the above nature will certainly enlarge, very

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A solution method for planar and axisymmetric contact problems

A finite element method for a class of contact-impact problems

A perturbed Lagrangian formulation for the finite element solution of contact problems

A new approach to enforce surface contact conditions in transient non-linear finite element problems is developed in this paper. The method is based on the Lagrange multiplier concept and is compatible with explicit time integration operators. Compatibility with explicit operators is established by referencing Lagrange multipliers one time increment ahead of associated surface contact displacement constraints. However, the method is not purely explicit because a coupled system of equations must be solved to obtain the Lagrange multipliers. An important development herein is the formulation of a highly efficient method to solve the Lagrange multiplier equations. The equation solving strategy is a modified Gauss-Seidel method in which non-linear surface contact force conditions are enforced during iteration. The new surface contact method presented has two significant advantages over the widely accepted penalty function method: surface contact conditions are satisfied more precisely, and the method does not adversely affect the numerical stability of explicit integration. Transient finite element analysis results are presented for problems involving impact and sliding with friction. A brief review of the classical Lagrange multiplier method with implicit integration is also included.

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S.K. Chan

Papers

A finite element method for contact problems of solid bodies—Part I. Theory and validation

A finite element method for contact problems of solid bodies—Part II. Application to turbine blade fastenings