Open AccessAn algorithm for enforcement of contact constraints in quasistatic applications using matrix-free solution algorithms
Author(s) -
Martin Heinstein
Publication year - 1997
Publication title -
osti oai (u.s. department of energy office of scientific and technical information)
Language(s) - English
Resource type - Reports
DOI - 10.2172/554827
Subject(s) - quasistatic process , convergence (economics) , algorithm , matrix (chemical analysis) , constraint (computer aided design) , conjugate gradient method , relaxation (psychology) , iterative method , mathematics , rate of convergence , finite element method , contact force , stiffness matrix , mathematical optimization , computer science , physics , key (lock) , geometry , classical mechanics , psychology , social psychology , materials science , quantum mechanics , economics , composite material , economic growth , computer security , thermodynamics
A contact enforcement algorithm has been developed for matrix-free quasistatic finite element techniques. Matrix-free (iterative) solution algorithms such as nonlinear Conjugate Gradients (CG) and Dynamic Relaxation (DR) are distinctive in that the number of iterations required for convergence is typically of the same order as the number of degrees of freedom of the model. From iteration to iteration the contact normal and tangential forces vary significantly making contact constraint satisfaction tenuous. Furthermore, global determination and enforcement of the contact constraints every iteration could be questioned on the grounds of efficiency. This work addresses this situation by introducing an intermediate iteration for treating the active gap constraint and at the same time exactly (kinematically) enforcing the linearized gap rate constraint for both frictionless and frictional response
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