A consistent tangent stiffness matrix for three‐dimensional non‐linear contact analysis

A consistent tangent stiffness matrix for the analysis of non‐linear contact problems is presented. The associated element has three or four nodes and establishes contact between three‐dimensional structures like solids and shells. It accounts for the non‐linear kinematics of large deformation analysis and guarantees a quadratic convergence rate. Two formulations, the penalty method and the Lagrange multiplier method, are investigated.