Configurational Forces and Variational Mesh Adaption in Solid Dynamics

adaptive mesh refinement;adaptive meshing;arbitrary eulerian lagrangian methods;configurational forces;continuously deforming finite elements;Hamilton Pontryagin principle;Hamilton's principles;material forces;mesh adaption;mixed finite elements;mixed variational principles;moving finite elements;non-linear solid dynamics;r-adaption;thermomechanical variational principles;variational adaptivity;variational integration;variational integrators

Zielonka, Matias Gabriel ; Ortiz, Michael

University:California Institute of Technology

Department:Engineering and Applied Science

关键词: adaptive mesh refinement;    adaptive meshing;    arbitrary eulerian lagrangian methods;    configurational forces;    continuously deforming finite elements;    Hamilton Pontryagin principle;    Hamilton's principles;    material forces;    mesh adaption;    mixed finite elements;    mixed variational principles;    moving finite elements;    non-linear solid dynamics;    r-adaption;    thermomechanical variational principles;    variational adaptivity;    variational integration;    variational integrators;   

Others  :  https://thesis.library.caltech.edu/1724/2/Thesis_Matias_Zielonka_Final.pdf

美国|英语

来源: Caltech THESIS

【 摘 要 】

This thesis is concerned with the exploration and development of a variational finite element mesh adaption framework for non-linear solid dynamics and its conceptual links with the theory of dynamic configurational forces. The distinctive attribute of this methodology is that the underlying variational principle of the problem under study is used to supply both the discretized fields and the mesh on which the discretization is supported. To this end a mixed-multifield version of Hamilton's principle of stationary action and Lagrange-d'Alembert principle is proposed, a fresh perspective on the theory of dynamic configurational forces is presented, and a unifying variational formulation that generalizes the framework to systems with general dissipative behavior is developed. A mixed finite element formulation with independent spatial interpolations for deformations and velocities and a mixed variational integrator with independent time interpolations for the resulting nodal parameters is constructed. This discretization is supported on a continuously deforming mesh that is not prescribed at the outset but computed as part of the solution. The resulting space-time discretization satisfies exact discrete configurational force balance and exhibits excellent long term global energy stability behavior. The robustness of the mesh adaption framework is assessed and demonstrated with a set of examples and convergence tests.