Numerical approximation of thin structures using stabilized mixed formulations for infinitesimal and finite strain theories, including fluid-structure interaction problem applications
(English) The theories of thin structures can be classified into two main branches depending upon whether shear deformation in the transverse direction is taken into consideration or not. In this context, theories accounting for shear deformations prove suitable for modeling structures with both thi...
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| Format: | doctoral thesis |
| Publication Date: | 2024 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/421448 |
| Online Access: | https://hdl.handle.net/2117/421448 https://dx.doi.org/10.5821/dissertation-2117-421448 |
| Access Level: | Open access |
| Keyword: | 517 624 Àrees temàtiques de la UPC::Enginyeria civil Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Summary: | (English) The theories of thin structures can be classified into two main branches depending upon whether shear deformation in the transverse direction is taken into consideration or not. In this context, theories accounting for shear deformations prove suitable for modeling structures with both thin and thick profiles. In the Finite Element context, they are referred to as C0 theories due to the minimum continuity order of shape functions required to pose a discretized approximation. However, there are space incompatibilities in the standard discrete approximation that exhibits spurious solutions, particularly evident in thin structures. These instabilities, known as numerical locking, result in an artificial stiffening of the structure, whose effect becomes more pronounced for thinner structures. Various forms of numerical locking can be triggered, influenced not only by the slenderness of the structure but also by its shape and the nature of the applied loads. In this context, flat structures are prone to shear locking when exposed to transverse loads. Conversely, curved structures may confront different mechanisms leading to various forms of numerical locking, namely membrane, thickness, and trapezoidal locking. The initial part of the study aims to develop a specialized framework to address instabilities in the context of flat structures in the context of Reissner-Mindlin theory. Subsequently, the second part of the study aims to expand the framework to effectively address instabilities arising in of curved structures in the context of Solid-Shell elements. The locking problem is approached by means of a mixed formulation that considers displacements and stress as unknowns in a curvilinear coordinate framework. This approach allows to isolate the components of the stress tensor in order to study the mechanisms in which every type of numerical locking are triggered. The third part of the thesis is dedicated to integrating the previous advancements into Finite Strain analysis by the inclusion of standard hyperelastic constitutive behavior. With this approach, the problem becomes even more difficult to solve because of the non-linearity and the large deformations the shell is subject to. Lastly, the fourth and final part is dedicated to addressing the Fluid-Structure Interaction problem using an embedded mesh approach, which has consistently been a topic of great research interest in the literature, because of its complexity and wide variety of applications. This problem introduces a variety of challenges that have to be properly addressed: the discontinuous pressure field arising for the structure separating the fluid domain, the computation and imposition of transmission conditions between domains, the coupling strategy, and the algorithmic work needed to join all of these ingredients together. This thesis mainly focuses on overcoming challenges associated with thin structures when employing the conventional Galerkin Finite Element approach. It seeks solutions through stabilized methods, specifically within the Variational Multiscale framework. As result, the formulations developed through the investigations have proven to be robust, allowing to model locking-free thin structures efficiently, and to accurately describe the physics of thin shells immersed in fluid flows and being subject to large deformations. |
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