Study And Implementation Of The Automatic Contact Algorithm In The Finite Element Method

Contact is widely found in various engineering problems such as car collision,projectile penetration,and punch forming,etc.On one hand,contact is a nonlinear problem,the algorithm is complex and the computation is time consuming.On the other hand,the accuracy of the finite element analysis of engineering problems is seriously affected by the accuracy of the contact algorithm.Therefore,it is significant to study the contact algorithm in depth.Contact interface models can be generally divided into the following three types: the node-to-node model,the node-to-segment model,and the segment-to-segment model.Among them,the node-to-segment model,in which the contact interface is discretized into slave nodes and master element patches,has been widely used in various engineering problems.This thesis is devoted to the study of the automatic contact algorithm which is based on the node-to-segment model.The generation of contact surface,global search,local search and constraint enforcement in this algorithm are carefully investigated and also implemented by coding.The main work of this thesis is as follows:(1)Generation of contact surface is the first step of the contact computation.For this issue,the method of determining the external element patches by judging the external nodes is adopted in this thesis.The algorithm of this method is studied in detail and is implemented by programming.The correctness of the implemented code is validated by numerical examples.(2)The contact search includes the global search and the local search.The major methods for the global search are brute force search method,master-slave algorithm,singlesurface algorithm,hierarchy-territory algorithm,position-code algorithm,NBS algorithm,etc.In this thesis,the bucket sorting algorithm is adopted to implement the global search.The methods for the local search are node-to-segment algorithm,pinball algorithm and smooth curve algorithm,etc.The node-to-segment algorithm is adopted in this thesis to implement the local search.(3)The constraint enforcement is usually computed by the Lagrange multiplier method or the penalty method.The penalty method is straightforward and efficient.In addition,it does not introduce extra degrees of freedom.Therefore,the penalty method is used in this thesis to compute the contact force.The computer program of the penalty method is implemented and its correctness is verified.(4)Based on the above three parts of the work,the finite element automatic contact algorithm is successfully implemented in this thesis.In order to verify the computer code,three examples are computed and they are centering collision of two elastic rods,a block impacting two cantilever beams and multi-block collision.In the example of centering collision of two elastic rods,the contact force and the nodal velocities obtained by this thesis agree well with the theoretical solutions.This demonstrates the correctness of the contact force computation implemented in this thesis.Results of the other two examples show the effectiveness of the computer code of this thesis in handling multiple-surface and random contact problems.