Study On CUDA-based Parallel Algorithm Of Contact And Impact Problems

Contact-impact problems under large deformation are involved with geometric nonlinearity, material nonlinearity and contact nonlinearity. Because of the complexity, the solution process is very time-consuming. Thus, it is difficult to obtain satisfactory results in traditional serial computers. In order to improve the accuracy and efficiency of the solving, this paper present the CUDA-based parallel algorithm of the contact and impact problems, and research the application on contact-impact problem in transient analysis. Contact-impact problems are generally carried out with finite element method. This paper studies the solution process as follows:1. Establish the format of nonlinear finite element solution of contact-impact problems under the full Lagrange format. In the calculation format, all physical parameters take initial configuration as reference. Therefore, the full Lagrange method takes less amount of calculation compared with updated Lagrange method. The solving process uses explicit integration which avoids the stiffness matrix inversion and thus results in higher solution efficiency compared with the implicit integration.2. Study is conducted on contact searching algorithm and contact force algorithm. In order to compute the contact force, contact search must be implemented. This paper focuses on the application of position code algorithm in which the chain tables are cited and developed in the global search. The technique of chain tables is an effective method to search the contact pairs. Vector which is a kind of container in the language of C++ is introduced to decide the hitting point and establish the appropriate data structure. After contact searching, contact force will be calculated according the check condition and definite condition. Lagrange multiplier method and penalty function method are two basic methods for the computation of contact force. Due to the compatibility and easiness of programming, penalty function is most widely used. This paper also discusses the application of defense node algorithm in the computation of contact force. Defense node algorithm which is compatible with the explicit solution can improve the solution precision. However, due to the complexity of the solution form, it is hard to implement with parallel method.3. CUDA is a kind of new parallel computing architecture software and hardware based on GPU. Threads are used to control the implement of the program. Because of the good parallelism of finite element method, parallel computing technology based on CUDA can be well applied on finite element analysis. What the paper focuses on are as follows: The establishing of CUDA-based parallel computing platform; Parallel generation process of stiffness matrix and mass matrix of the system; Parallel solving of the equation of the system.The optimization of parallel code; Evaluation criteria of parallel solving efficiency. In order to facilitate the interaction between users and the finite element program, interface design based on MFC is also studied to integrate and visualize the finite element program. The interface with simple function of the finite element pre-treatment is concise an easy to use.