Elasto-plastic analysis for plane stress contact problems using a modified RBSM method

The rigid body-spring model proposed by Kawai (1977, 1978) (called RBSM) can be applied to the contact problem, but it leaves something to be desired as a method of elasto-plastic analysis. Additionally, the results obtained from the RBSM do not agree well with the ones obtained by the FEM. Thus, a modified RBSM is proposed here which uses a more reasonable yielding criterion and a proper stress-strain matrix. A simple example is given, showing that the modified RBSM is effective in elasto-plastic analysis, producing nearly the same approximation as the FEM. Using the modified RBSM and the original RBSM, the elasto-plastic behavior of the cantilever beam with the built-in edge taken as a contact problem is analyzed under the two contact conditions, the sticking friction and the frictionless lubrication. Comparing the results, it is clear that the modified RBSM provides reasonable results but the original RBSM should be used with care.