Discussion on application of piece-wise linear weight functions in 2D contact problems - Klisiński, Marek; Luo, Chouping; Postek, Eligiusz (Computer Assisted Methods in Engineering and Science, 2023)
Standard higher order finite elements often perform unsatisfactory in contact problems. The major difficulties are caused by uneven distribution of nodal forces resulting in oscillating contact pressures. The paper presents a new approach that eliminates this drawback. The weight functions are chosen in such a way that even distributions of nodal forces are obtained. It is achieved by applying piece-wise linear functions. Two new 2D isoparametric quadratic elements are derived: 6-node triangle and 8-node quadrilateral, and tested in many examples. The new elements have unsymmetric stiffness matrices, but the provided examples show their good performance in contact problems.