Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity

Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and devise the hybridizable discontinuous Galerkin (HDG) method. Exact geometry described by non-uniform rational B-splines (NURBS) is integrated into HDG using the framework of the NURBS-enhanced finite element method (NEFEM). Moreover, optimal convergence and superconvergence properties of HDG-Voigt formulation in presence of symmetric second-order tensors are exploited to construct inexpensive error indicators and drive degree adaptive procedures. Applications involving the numerical simulation of problems in electrostatics, linear elasticity and incompressible viscous flows are presented. Moreover, this is done for both high-order HDG approximations and the lowest-order framework of face-centered finite volumes (FCFV).Peer ReviewedPostprint (author's final draft

Proceedings of the FEniCS Conference 2017

Proceedings of the FEniCS Conference 2017 that took place 12-14 June 2017 at the University of Luxembourg, Luxembourg

Otimização topológica evolucionária de problemas com interação fluido-estrutura

Orientador: Renato PavanelloTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: O objetivo desta tese é o desenvolvimento de uma ferramenta computacional para projeto de estruturas considerando interação fluido-estrutura usando otimização topológica. Uma metodologia de otimização estrutural topológica é proposta associada à formulações de elementos finitos em problemas fluido-estrutura acoplados. Nesses tipos de problemas a estrutura sofre carregamentos advindos do meio fluido, ou seja, pressão e/ou forças viscosas. As dificuldades em se projetar estruturas sob carregamentos de fluidos surgem devido à variação da localização, direção e magnitude dos carregamentos quando a forma e topologia da estrutura são alteradas durante a otimização. Isso se torna o principal desafio para os métodos tradicionais baseados na interpolação da densidade do material. Nesses métodos, as superfícies em contato com o fluido não são definidas explicitamente devido à existência de elementos estruturais de densidade intermediária. Neste trabalho é proposta uma metodologia alternativa para esse tipo de carregamento dependente da topologia. Com a extensão do método de otimização estrutural evolucionária bidirecional (BESO) associada à formulações fluido-estrutura acopladas, pressões e forças viscosas podem ser modeladas diretamente para qualquer topologia estrutural devido à natureza discreta dos métodos evolucionários. Assim, o problema é resolvido sem a necessidade de parametrização das superfícies de carregamentos de pressão. A metodologia BESO é estendida considerando os procedimentos de alteração entre elementos fluido-estrutura-vazios, novas análises de sensibilidade e restrições. Problemas em estado estacionário são considerados, incluindo elasticidade linear para a análise estrutural e as equações de Laplace, Helmholtz e escoamento incompressível de Navier-Stokes para a análise do fluido. Carregamentos constantes e não constantes são modelados. Diversos exemplos e aplicações são explorados com a metodologia propostaAbstract: The aim of this thesis is the development of a computational tool for the design of structures considering fluid-structure interaction using topology optimization. A methodology of structural topology optimization is proposed in association with finite element formulations of fluid-structure coupled problems. In this type of problems, the structure undergoes fluid loading, i.e., pressure and/or viscous loads. The difficulties in designing fluid loaded structures arise due to the variation of location, direction and magnitude of the loads when the structural shape and topology change along the optimization procedure. This turns out to be an additional difficulty for the traditional density-based topology optimization methods. In density-based methods, the pressure loaded surfaces are not explicitly defined due to the existence of intermediate density elements. In this thesis, it is suggested an alternative methodology to handle this type of design-dependent loads. With an extended bi-directional evolutionary structural optimization (BESO) method associated with different fluid-structure formulations, pressures and viscous loads can be modelled straightforwardly for any structural topology due to the discrete nature of the method. Thus, the problem is solved without any need for pressure load surfaces parametrization. The BESO methodology is extended considering the procedures of switching fluid-structure-void elements, new sensitivity analyses and constraints. Steady state problems are considered, including linear elasticity for the structural analysis and Laplace, Helmholtz and incompressible Navier-tokes flow equations for the fluid analysis. Constant and non constant loads are modelled. Several examples and applications are explored with the proposed methodologyDoutoradoMecanica dos Sólidos e Projeto MecanicoDoutor em Engenharia Mecânica2011/09730-6FAPES

Well-posedness and Robust Preconditioners for the Discretized Fluid-Structure Interaction Systems

In this paper we develop a family of preconditioners for the linear algebraic systems arising from the arbitrary Lagrangian-Eulerian discretization of some fluid-structure interaction models. After the time discretization, we formulate the fluid-structure interaction equations as saddle point problems and prove the uniform well-posedness. Then we discretize the space dimension by finite element methods and prove their uniform well-posedness by two different approaches under appropriate assumptions. The uniform well-posedness makes it possible to design robust preconditioners for the discretized fluid-structure interaction systems. Numerical examples are presented to show the robustness and efficiency of these preconditioners.Comment: 1. Added two preconditioners into the analysis and implementation 2. Rerun all the numerical tests 3. changed title, abstract and corrected lots of typos and inconsistencies 4. added reference

Structure and pressure drop of real and virtual metal wire meshes

An efficient mathematical model to virtually generate woven metal wire meshes is presented. The accuracy of this model is verified by the comparison of virtual structures with three-dimensional images of real meshes, which are produced via computer tomography. Virtual structures are generated for three types of metal wire meshes using only easy to measure parameters. For these geometries the velocity-dependent pressure drop is simulated and compared with measurements performed by the GKD - Gebr. Kufferath AG. The simulation results lie within the tolerances of the measurements. The generation of the structures and the numerical simulations were done at GKD using the Fraunhofer GeoDict software