Non-smooth numerical algorithm for vibration system with dry friction based on linear complementarity principle

Based on the complementarity property of set-valued Coulomb law and velocity-solving Newmark layout, the dry friction vibration problem is transformed into linear complimentary one and the non-smooth Newmark-Linear Complimentary Principle (LCP) numerical algorithm is proposed. Different motion modes of dry friction system were uniformly treated by using LCP and the equality conditions were replaced by complementary ones to monitor motion events. Numerical instability problem in stick zone was solved, and the enumeration amount growth and complication of logical structure in algorithm could be avoided when friction elements increased. Numerical examples show that the Newmark-LCP method can accurately describe dynamic characteristics of the dry friction. Compared with the non-smooth time-stepping method, the proposed method has higher computational efficiency.