Modification of the Lagrange multiplier method with an detached contact boundary for modeling the contact of elastic bodies

A modification of the Lagrange method with detached contact boundary is developed. The modification allows one to construct an approximation of the Lagrange multiplier function independently of the meshes inside the contacting bodies. A method for constructing a contact boundary from a cloud of points belonging to meshes in contacting bodies and marked as having come into contact is presented. A discontinuous piecewise constant approximation of the Lagrange function is considered. The performed test calculations showed the possibility of refining the calculation of the normal stress component at the contact boundary without changing the mesh in the contacting bodies by refining the discretization of the contact boundary.