Aspects of computational contact dynamics.
PhD thesis, University of Glasgow.
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This work summarises a computational framework for dealing with dynamic multi-body frictional contact problems. It is in fact a detailed account of an instance of the Contact Dynamics method by Moreau and Jean. Hence the title. Multi-body systems with contact constraints are common. Some of them, such as machines or arrangements of particulate media, need to be predictable. Predictions correspond to approximate solutions of mathematical models describing interactions within such systems. The models are implemented as computational algorithms.
The main contributions of the author are in an improved time integration method for rigid rotations, and in a robust Newton scheme for solving the frictional contact problem. A simple and efficient way of integrating rigid rotations is presented. The algorithm is stable, second order accurate, and in its explicit version involves evaluation of only two exponential maps per time step. The semi-explicit version of the proposed scheme improves upon the long term stability, while it retains the explicitness in the force evaluation. The algebraic structure of both schemes makes them suitable for the analysis of constrained multi-body systems. The explicit algorithm is specifically aimed at the analysis involving small incremental rotations, where its modest computational cost becomes the major advantage. The semi-explicit scheme naturally broadens the scope of possible applications. The semismooth Newton approach is adopted in the context of the frictional contact between three-dimensional pseudo-rigid bodies, proposed by Cohen and Muncaster. The Signorini-Coulomb problem is formulated according to the formalism of Contact Dynamics. Hybrid linearisation, parameter scaling and line search techniques are combined as the global convergence enhancements of the Newton algorithm. Quasi-static simulations of dry masonry assemblies exemplify performance of the presented framework.
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