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Title: Variational explicit dynamic integrators for finite element solid mechanics applications
Author: Casals-Roigé, L.
Awarding Body: University of Wales Swansea
Current Institution: Swansea University
Date of Award: 2005
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The goal of this Thesis is the formulation of some new discrete variational integrators, in the sense of the Veselov formulation of discrete mechanics, which will be used to solve dynamic explicit solid mechanics problems with the Finite Element Method. The reason for developing algorithms with this methodology is that when developed in this manner, they preserve the linear and angular momentum, conserve the symplectic form and in addition it has been observed that possess very good energy behaviour. Firstly, a new variational algorithm will be developed in this Thesis that will permit remarkably bigger time steps in nearly incompressible applications. After a detailed development, which takes into account the fractional step method, a stability calculation will suggest that the reason for the increase of the time step can stem from the dependence of the stable time step on the sheer wave speed instead of the slower volumetric wave speed. A pressure stabilization is given for the equal order interpolation. Next an explicit variational Arbitrary Lagrangian-Eulerian formulation is exposed in detail . The equilibrium equation will suggest different possibilities for moving the nodes explicitly. The order into which the operations have to be performed to move the nodes in the material and spatial mesh will be studied giving at the end some examples. Finally a new variational error indicator is proposed, which has been obtained as the residual of the configurational equations. The convergence to zero when the mesh becomes finer and the great agreement between the residual and the more distorted zones of the mesh indicate that it can be an excellent tool to decide which nodes have to be relocated in Arbitrary Lagrangian-Eulerian computations.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available