Finite Element Simulation of Sheet Metal Forming Processes

In the present study, the survey of research work on finite element analysis of metal forming processes has been carried out. A classification of formulations dealing with geometry and material nonlinearity in the context of finite element simulation of forming operations has been recapitulated. The procedures based upon shell and continuum approaches and methods of dealing withfrictional contact, are described. Topics of current interest on finite element analysis such as error estimation, projection of error, and adaptive mesh refinement have been reviewed

High-fidelity surrogate models for parametric shape design in microfluidics

Nowadays, the main computational bottleneck in computer-assisted industrial design procedures is the necessity of testing multiple parameter settings for the same problem. Material properties, boundary conditions or geometry may have a relevant influence on the solution of those problems. Consequently, the effects of changes in these quantities on the numerical solution need to be accurately estimated. That leads to significantly time-consuming multi-query procedures during decision-making processes. Microfluidics is one of the many fields affected by this issue, especially in the context of the design of robotic devices inspired by natural microswimmers. Reduced-order modelling procedures are commonly employed to reduce the computational burden of such parametric studies with multiple parameters. Moreover, highfidelity simulation techniques play a crucial role in the accurate approximation of the flow features appearing in complex geometries. This thesis proposes a coupled methodology based on the high-order hybridisable discontinuous Galerkin (HDG) method and the proper generalized decomposition (PGD) technique. Geometrically parametrised Stokes equations are solved exploiting the innovative HDG-PGD framework. On the one hand, the parameters describing the geometry of the domain act as extra-coordinates and PGD is employed to construct a separated approximation of the solution. On the other hand, HDG mixed formulation allows separating exactly the terms introduced by the parametric mapping into products of functions depending either on the spatial or on the parametric unknowns. Convergence results validate the methodology and more realistic test cases, inspired by microswimmer devices involving variable geometries, show the potential of the proposed HDG-PGD framework in parametric shape design. The PGD-based surrogate models are also utilised to construct separated response surfaces for the drag force. A comparison between response surfaces obtained through the apriori and the a posteriori PGD is exposed. A critical analysis of the two techniques is presented reporting advantages and drawbacks of both in terms of computational costs and accuracy.Actualmente, el principal obstáculo en los procesos de diseño industrial computarizado es la necesidad de examinar múltiples parámetros para el mismo problema. Las propiedades de los materiales, las condiciones de contorno o la geometría pueden tener una influencia relevante en la solución de esos problemas. Por lo tanto, es necesario estimar con precisión los efectos de las variaciones de esas cantidades en la solución numérica. Esto da origen a procedimientos de consultas múltiples que requieren considerable tiempo durante los procesos de toma de decisión. La microfluídica es uno de los varios campos afectados por esta problemática, especialmente en el contexto del diseño de dispositivos robóticos inspirados en los micronadadores naturales. Generalmente se recurre a procedimientos de reducción de orden de modelo para reducir la complejidad computacional de estos estudios paramétricos basados en múltiples parámetros. Además, los esquemas de alto orden son fundamentales para la aproximación precisa de las particularidades de los flujos que aparecen en las geometrías complejas. Esta tesis propone una metodología acoplada basada en el método de Galerkin discontinuo hibridizable de alto orden (HDG) y la técnica de descomposición propia generalizada (PGD). Las ecuaciones de Stokes geométricamente parametrizadas se resuelven empleando el innovador método HDG-PGD. Por un lado, los parámetros que describen la geometría del dominio actúan como extra-coordinadas y la PGD permite construir una aproximación separada de la solución. Por otra parte, la formulación mixta de HDG admite la separación exacta de los términos introducidos por la descripción paramétrica del dominio en productos de funciones dependientes de las incógnitas espaciales o paramétricas. Los resultados de convergencia validan la metodología y estudios de casos más realistas, inspirados en los dispositivos de micronatación con geometrías variables, muestran el potencial del marco propuesto de HDG-PGD en el diseño de formas parametrizadas. Los modelos reducidos basados en la PGD también permiten construir superficies de respuesta separadas para la fuerza de arrastre. Se realiza una comparación entre las superficies de respuesta obtenidas mediante la PGD a priori y a posteriori. Se exponen una análisis crítica de las dos técnicas reportando las ventajas y desventajas de ambas en términos de costes computacionales y precisión

Computational modelling of some problems of elasticity and viscoelasticity with applications to thermoforming process

Copyright @ 2012 Northwestern Polytechnical University and ISCIThe reliability of computational models of physical processes has received much attention and involves issues such as the validity of the mathematical models being used, the error in any data that the models need, and the accuracy of the numerical schemes being used. These issues are considered in the context of elastic, viscoelastic and hyperelastic deformation, when finite element approximations are applied. Goal oriented techniques using specific quantities of interest (QoI) are described for estimating discretisation and modelling errors in the hyperelastic case. The computational modelling of the rapid large inflation of hyperelastic circular sheets modelled as axisymmetric membranes is then treated, with the aim of estimating engineering QoI and their errors. Fine (involving inertia terms) and coarse (quasi-static) models of the inflation are considered. The techniques are applied to thermoforming processes where sheets are inflated into moulds to form thin-walled structures

Original stopping criteria associated tomultilevel adaptive mesh refinement to dealwith local singularities

International audienceThis paper introduces a local multilevel mesh refinement strat-egy that automatically stops relating to a user-defined tolerance even incase of local singular solutions. Refinement levels are automatically gener-ated thanks to a criterion based on the direct comparison of the a posteriorierror estimate with the prescribed error. Singular solutions locally increase with the mesh step (e.g. load discontinuities, point load or geometric in-duced singularities) and are hence characterized by locally large element-wise error whatever the mesh refinement. Then, the refinement criterionmay not be self-sufficient to stop the refinement process. Additional stop-ping criteria are required to avoid an infinite refinement process while stillrespecting the desired threshold. Two original geometry-based stopping cri-teria are proposed that consist in determining the critical region for whichthe mesh refinement becomes inefficient. Numerical examples show the effi-ciency of the methodology for stress tensor approximation in L 2 -relative orL et8734; -absolute norms

On 3-D inelastic analysis methods for hot section components (base program)

A 3-D Inelastic Analysis Method program is described. This program consists of a series of new computer codes embodying a progression of mathematical models (mechanics of materials, special finite element, boundary element) for streamlined analysis of: (1) combustor liners, (2) turbine blades, and (3) turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain)and global (dynamics, buckling) structural behavior of the three selected components. Three computer codes, referred to as MOMM (Mechanics of Materials Model), MHOST (Marc-Hot Section Technology), and BEST (Boundary Element Stress Technology), have been developed and are briefly described in this report