On convergence of the penalty method for a static unilateral contact problem with nonlocal friction in electro-elasticity

In this paper, we consider the penalty method to solve the unilateral contact with friction between an electro-elastic body and a conductive foundation. Mathematical properties, such as the existence of a solution to the penalty problem and its convergence to the solution of the original problem, are reported. Then, we present a finite elements approximation for the penalised problem and prove its convergence. Finally, we propose an iterative method to solve the resulting finite element system and establish its convergence.

Analysis of Ultralong Friction Pile Based on Gradient Dependent Nonlocal Friction Model

Based on the gradient theory, the gradient dependent nonlocal friction model is established. It is a new model which can describe the nonlocal friction effect. Based on Mindlin’s solution of displacement, an elastic solution of the lateral frictional resistance for ultralong friction pile is derived. The ultralong friction pile is analyzed by using the gradient dependent nonlocal friction model. Compared with the solution to the local friction law, the results shows that nonlocal friction law is feasible and reliable. The study is helpful for understanding the friction mechanism in geotechnical problems. It is a good attempt to set up the more actual and more accurate friction model.