Mixed Computational Algorithm Based on the Updated Lagrangian Description for Plane Elastic Contact Problems

摘要

A mixed variational formulation and associated finite element model are developed for the stress analysis of plane elastic bodies in contact and undergoing large deformations (large displacements and small strains). The updated Lagrangian formulation is used to develop the incremental equations. The finite element model contains displacements and the components of the second Piola Kirchhoff stress tensor as the nodal degrees of freedom. Two different computational algorithms are developed to analyze the separate cases of rigid pin and elastic pin. The procedure accounts for friction between the contacting bodies and the computational difficulties associated with the unknown contact area. A hybrid technique is also presented that combines the finite element procedure and the moire inteferometry to determine stresses in a pin-loaded plate. The procedure involves the use of the displacements measured in the experiment (moire technique) as boundary conditions at the pin hole interface of the finite element analysis. Then the whole field information of displacements and stresses is obtained using the finite element method. Results of this hybrid technique are compared with those obtained by the numerical algorithm with the results in good agreement.