Adaptivity and splitting pinball method in nonlinear structural dynamics with contact-impact

摘要

This dissertation addresses two topics: the splitting pinball contact method and adaptive finite element analysis. Developing an efficient algorithm for transient contact-impact problems in explicit computer programs is the common issue of the two topics. The splitting pinball method has been developed to increase efficiency and provide generality in dealing with contact problems. Adaptive finite element analysis tries to seek the compromise between the accuracy and economical CPU time.;The pinball contact-impact method (Belytschko and Neal(1991)) is extended to the contact between any combination of shell elements and solid elements by the use of splitting. In the splitting pinball adaptation of this algorithm, the parent pinball is split into a hierarchy of descendent pinballs whenever interpenetration of the parent pinballs is detected. The interpenetration check is then applied to the descendent pinballs and contact forces are generated. This provides a better representation of the contact surface for thin shell elements. The implementation of the method with a penalty contact method is described and examples are given. It is shown that the method easily and automatically handles edge-to-edge, edge-to-surface, and self-surface contact without any user specification.;Coulomb friction is added to the pinball contact-impact algorithm so that the frictional contact can be handled by the pinball algorithm. The mathematical basis and numerical implementation for frictional contact are also given. Numerical results which show the effectiveness of the frictional pinball contact-impact algorithm are given.;A simplified, effective h-adaptive algorithm for general purpose explicit FEM program is presented. In this adaptive method, a new data structure is used to handle general 3-dimensional shell structures. An error criterion is developed in terms of the least square projection of the strain invariants. A method is described which estimates the level of refinement which is needed in each element. Applications of the new adaptive algorithm to nonlinear transient shell contact-impact problems are also presented.