Isogeometric space-time adaptivity for evolution models of thin shells
| Autor: | Paul, Karsten |
|---|---|
| Přispěvatelé: | Sauer, Roger Andrew, Behr, Marek |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Aachen : RWTH Aachen University 1 Online-Ressource : Illustrationen, Diagramme (2022). doi:10.18154/RWTH-2022-06252 = Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2022 |
| Popis: | Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2022; Aachen : RWTH Aachen University 1 Online-Ressource : Illustrationen, Diagramme (2022). = Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2022 This thesis deals with isogeometric space-time adaptivity for evolution models of thin shells. The surface and the shell theory are formulated within a curvilinear coordinate system, which allows the representation of general surface shapes and deformations. The kinematics follow from Kirchhoff-Love theory. In the first part of this thesis, isotropic viscoelastic material behavior of shell structures is investigated. A multiplicative split of the surface deformation gradient is employed and the evolution laws for the description of the intermediate surface are integrated numerically with the implicit Euler scheme. The implementation of surface and bending viscosity is verified with the help of analytical solutions. Several numerical examples demonstrate the accuracy and convergence of the proposed framework by investigating typical viscoelastic phenomena and boundary viscoelasticity of 3D bodies. The second part of this thesis deals with a thermodynamic consistent and adaptive phase field formulation for dynamic fracture of brittle shells. The phase field evolution equation is determined by minimizing an energy that is based on Griffith's theory. Membrane and bending contributions to the fracture process are modeled separately and thickness integration is established for the latter. The coupled system consists of two nonlinear, fourth-order partial differential equations that are defined on an evolving two-dimensional manifold. The mesh is adaptively refined based on the phase field value and Locally Refinable Non-Uniform Rational B-Splines (LR NURBS) are employed for the local spatial refinement. The temporal integration is based on the generalized-alpha scheme using adaptive time-stepping and the discretized coupled system is solved within a monolithic Newton-Raphson scheme. Several numerical examples investigate the interaction of surface deformation and crack evolution. The third part of this thesis investigates coupled deformation and phase field models on multi-patch surfaces. For multi-patch discretizations, the continuity is not preserved at patch interfaces and thus, needs to be restored. For this, G1- and C1-continuity constraints are formulated within the curvilinear coordinate system and applied to the phase field fracture model. The constraints are either enforced by the Lagrange multiplier or the penalty method using a problem-independent penalty parameter for the phase field model. The accuracy and convergence of the proposed framework are demonstrated by several numerical examples. In the last part of this thesis, a theoretical formulation for topology optimization of thin shell structures is derived. A phase field approach based on the Cahn-Hilliard equation with elastic misfit is employed. The required sensitivities are derived and fully linearized. The shell and phase field model are monolithically coupled and a temporal integration scheme based on the generalized-alpha scheme with adaptive time-stepping is presented. Finally, the complexity of the established formulation is assessed and the feasibility of using the proposed framework in practice is critically discussed. Published by RWTH Aachen University, Aachen |
| Databáze: | OpenAIRE |
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