Velocity update algorithms for transient impact problems: Consideration of kinematic discontinuities within a conserving framework.

摘要

This dissertation is intended to contribute directly to the growing body of theoretical and algorithmic work in computational solid mechanics, with specific application to systems characterized by dynamic impact. Whereas the current body of research has demonstrated the value of conserving algorithmic integration in the analysis of highly non-linear continuum systems, attempts to extend the numerical benefits of energy and momentum conservation to characteristically disjoint contact systems have generally been compromised by an inability to fully resolve the conservation conditions while simultaneously enforcing the geometric constraints. The contributions herein serve to resolve this discrepancy and thus extend the validity of conserving methods in dynamic impact analysis, for both fully conservative frictionless contact and for physically dissipative frictional contact.; Novel considerations include (1) the introduction of a discrete velocity update vector as a physically motivated algorithmic means of ensuring energy conservation; (2) the design of a framework by which to locally construct the direction of the velocity update such that angular and linear momenta are summarily conserved; (3) the establishment of the algorithmic conditions and means necessary for determining the local magnitudes of the update that ensure conservation of energy; (4) a revised algorithmic description and suitable regularizations of the normal contact constraints that prohibit interpenetration as defined by the contact constraints; (5) a simplified theoretical and algorithmic description of Coulomb friction enabling (6) an algorithmic extension of the conservative method that incorporates frictional dissipation in a manner consistent with physical expectations.; The proposed formulations include details of the discretization process, both temporal and spatial, as well as appropriate Newton-Raphson motivated linearizations of the contact force contributions. The result is a complete presentation of a new robust algorithmic method for the modeling of frictionless and frictional dynamic impact systems, from theoretical development through to supporting numerical examples.