Size preserving mesh generation in adaptivity processes

It is well known that the variations of the element size have to be controlled in order to generate a high-quality mesh. Hence, several techniques have been developed to limit the gradient of the element size. Although these methods allow generating high-quality meshes, the obtained discretizations do not always reproduce the prescribed size function. Specifically, small elements may not be generated in a region where small element size is prescribed. This is critical for many practical simulations, where small elements are needed to reduce the error of the numerical simulation. To solve this issue, we present the novel size-preserving technique to control the mesh size function prescribed at the vertices of a background mesh. The result is a new size function that ensures a high-quality mesh with all the elements smaller or equal to the prescribed element size. That is, we ensure that the new mesh handles at least one element of the correct size at each local minima of the size function. In addition, the gradient of the size function is limited to obtain a high-quality mesh. Two direct applications are presented. First, we show that we can reduce the number of iterations to converge an adaptive process, since we do not need additional iterations to generate a valid mesh. Second, the size-preserving approach allows to generate quadri- lateral meshes that correctly preserves the prescribed element size.Peer ReviewedPostprint (published version

Template-based geometric transformations of a functionally enriched DMU into FE assembly models

International audiencePre-processing of CAD models derived from Digital Mock-Ups (DMUs) into finite element (FE) models is usually completed after many tedious tasks of model preparation and shape transformations. It is highly valuable for simulation engineers to automate time-consuming sequences of assembly preparation processes. Here, it is proposed to use an enriched DMU with geometric interfaces between components (contacts and interferences) and functional properties. Then, the key concept of template-based transformation can connect to assembly functions to locate consistent sets of components in the DMU. Subsequently, sets of shape transformations feed the template content to adapt components to FE requirements. To precisely monitor the friction areas and the mesh around bolts, the template creates sub-domains into their tightened components and preserves the consistency of geometric interfaces for the mesh generation purposes. From a user-selected assembly function, the method is able to robustly identify, locate and transform groups of components while preserving the consistency of the assembly needed for FE models. To enlarge the scope of the template in the assembly function taxonomy, it is shown how the concept of dependent function enforces the geometric and functional consistency of the transformed assembly. To demonstrate the proposed approach, a business oriented prototype processes bolted junctions of aeronautical structures

Adaptive meshing for finite element analysis of heterogeneous materials

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Automatic sizing functions for unstructured surface mesh generation

Accurate sizing functions are crucial for efficient generation of high-quality meshes, but to define the sizing function is often the bottleneck in complicated mesh generation tasks because of the tedious user interaction involved. We present a novel algorithm to automatically create high-quality sizing functions for surface mesh generation. First, the tessellation of a Computer Aided Design (CAD) model is taken as the background mesh, in which an initial sizing function is defined by considering geometrical factors and user-specified parameters. Then, a convex nonlinear programming problem is formulated and solved efficiently to obtain a smoothed sizing function that corresponds to a mesh satisfying necessary gradient constraint conditions and containing a significantly reduced element number. Finally, this sizing function is applied in an advancing front mesher. With the aid of a walk-through algorithm, an efficient sizing-value query scheme is developed. Meshing experiments of some very complicated geometry models are presented to demonstrate that the proposed sizing-function approach enables accurate and fully automatic surface mesh generation

Tree-based Control Space Structures for Discrete Metric Sources in 3D Meshing

This article compares the different variations of the octree and kd-tree structures used to create a control space based on a set of discrete metric point-sources. The control space thus created supervises the generation of the mesh providing efficient access to the required information on the desired shape and size of the mesh elements at each point of the discretized domain. Structures are compared in terms of computational and memory complexity as well as regarding the accuracy of the approximation of the set of discrete metric sources in the created control space structure

A new approach to automatic and a priori mesh adaptation around circular holes for finite element analysis

Through our research on the integration of finite element analysis in the design and manufacturing process with CAD, we have proposed the concept of mesh pre-optimization. This concept consists in converting shape and analysis information in a size map (a mesh sizing function) with respect to various adaptation criteria (refining the mesh around geometric form features, minimizing the geometric discretization error, boundary conditions, etc.). This size map then represents a constraint that has to be respected by automatic mesh generation procedures. This paper introduces a new approach to automatic mesh adaptation around circular holes. This tool aims at optimizing, before any FEA, the mesh of a CAD model around circular holes. This approach, referred to as “a priori” mesh adaptation, should not be regarded as an alternative to adaptive a posteriori mesh refinement but as an efficient way to obtain reasonably accurate FEA results before a posteriori adaptation, which is particularly interesting when evaluating design scenarios. The approach is based on performing many offline FEA analyses on a reference case and deriving, from results and error distributions obtained, a relationship between mesh size and FEA error. This relationship can then be extended to target user specified FEA accuracy objectives in a priori mesh adaptation for any distribution of circular holes. The approach being purely heuristic, fulfilling FEA accuracy objectives, in all cases, cannot be theoretically guaranteed. However, results obtained using varying hole diameters and distributions in 2D show that this heuristic approach is reliable and useful. Preliminary results also show that extension of the method can be foreseen towards a priori mesh adaptation in 3D and mesh adaptation around other types of 2D features

Ingénierie systèmes basée sur les modèles appliquée à la gestion et l'intégration des données de conception et de simulation : application aux métiers d'intégration et de simulation de systèmes aéronautiques complexes

The aim of this doctoral thesis is to contribute to the facilitation of design, integration and simulation activities in the aeronautics industry, but more generally in the context of collaborative complex product development. This objective is expected to be achieved through the use and improvement of digital engineering capabilities. During the last decade, the Digital Mock-Up (DMU) – supported by Product Data Management (PDM) systems – became a key federating environment to exchange/share a common 3D CAD model-based product definition between co-designers. It enables designers and downstream users(analysts) to access the geometry of the product assembly. While enhancing 3D and 2D simulations in a collaborative and distributed design process, the DMU offers new perspectives for analysts to retrieve the appropriate CAD data inputs used for Finite Element Analysis (FEA), permitting hence to speed-up the simulation preparation process. However, current industrial DMUs suffer from several limitations, such as the lack of flexibility in terms of content and structure, the lack of digital interface objects describing the relationships between its components and a lack of integration with simulation activities and data.This PhD underlines the DMU transformations required to provide adapted DMUs that can be used as direct input for large assembly FEA. These transformations must be consistent with the simulation context and objectives and lead to the concept of “Product View” applied to DMUs andto the concept of “Behavioural Mock-Up” (BMU). A product view defines the link between a product representation and the activity or process (performed by at least one stakeholder) that use or generate this representation as input or output respectively. The BMU is the equivalent of the DMU for simulation data and processes. Beyond the geometry, which is represented in the DMU,the so-called BMU should logically link all data and models that are required to simulate the physical behaviour and properties of a single component or an assembly of components. The key enabler for achieving the target of extending the concept of the established CAD-based DMU to the behavioural CAE-based BMU is to find a bi-directional interfacing concept between the BMU and its associated DMU. This the aim of the Design-Analysis System Integration Framework (DASIF) proposed in this PhD. This framework might be implemented within PLM/SLM environments and interoperate with both CAD-DMU and CAE-BMU environments. DASIF combines configuration data management capabilities of PDM systems with MBSE system modelling concepts and Simulation Data Management capabilities.This PhD has been carried out within a European research project: the CRESCENDO project, which aims at delivering the Behavioural Digital Aircraft (BDA). The BDA concept might consist in a collaborative data exchange/sharing platform for design-simulation processes and models throughout the development life cycle of aeronautics products. Within this project, the Product Integration Scenario and related methodology have been defined to handle digital integration chains and to provide a test case scenario for testing DASIF concepts. These latter have been used to specify and develop a prototype of an “Integrator Dedicated Environment” implemented in commercial PLM/SLM applications. Finally the DASIF conceptual data model has also served as input for contributing to the definition of the Behavioural Digital Aircraft Business Object Model: the standardized data model of the BDA platform enabling interoperability between heterogeneous PLM/SLM applications and to which existing local design environments and new services to be developed could plug.L’objectif de cette thèse est de contribuer au développement d’approches méthodologiques et d’outils informatiques pour développer les chaînes d’intégration numériques en entreprise étendue. Il s’agit notamment de mieux intégrer et d’optimiser les activités de conception, d’intégration et de simulation dans le contexte du développement collaboratif des produits/systèmes complexes.La maquette numérique (DMU) – supportée par un système de gestion de données techniques (SGDT ou PDM) – est devenue ces dernières années un environnement fédérateur clé pour échanger et partager une définition technique et une représentation 3D commune du produit entre concepteurs et partenaires. Cela permet aux concepteurs ainsi qu’aux utilisateurs en aval (ceux qui sont en charge des simulations numériques notamment) d’avoir un accès à la géométrie du produit virtuel assemblé. Alors que les simulations numériques 3D et 2D prennent une place de plus en plus importante dans le cycle de développement du produit, la DMU offre de nouvelles perspectives à ces utilisateurs pour récupérer et exploiter les données CAO appropriées et adaptées pour les analyses par éléments finis. Cela peut ainsi permettre d’accélérer le processus de préparation du modèle de simulation. Cependant, les environnements industriels de maquettes numériques sont actuellement limités dans leur exploitation par : - un manque de flexibilité en termes de contenu et de structure, - l’absence d’artefact numérique 3D permettant de décrire les interfaces des composants de l’assemblage, - un manque d’intégration avec les données et activités de simulation.Cette thèse met notamment l’accent sur les transformations à apporter aux DMU afin qu’elles puissent être utilisées comme données d’entrée directes pour les analyses par éléments finis d’assemblages volumineux (plusieurs milliers de pièces). Ces transformations doivent être en cohérence avec le contexte et les objectifs de simulation et cela nous a amené au concept de « vue produit » appliquée aux DMUs, ainsi qu’au concept de « maquette comportementale » (BMU). Une « vue produit » définit le lien entre une représentation du produit et l’activité ou le processus utilisant ou générant cette représentation. La BMU est l’équivalent de la DMU pour les données et les processus de simulation. Au delà des géométries discrétisées, la dénommée BMU devrait, en principe, lier toutes les données et les modèles qui seront nécessaires pour simuler le comportement d’un ou plusieurs composants. L’élément clé pour atteindre l’objectif d’élargir le concept établi de la DMU (basée sur des modèles CAO) à celui de la BMU (basée sur des modèles CAE), est de trouver un concept d’interface bidirectionnel entre la BMU et sa DMU associée. C’est l’objectif du « Design-Analysis System Integration Framework » (DASIF) proposé dans cette thèse de doctorat. Ce cadre a vise à être implémenté au sein d’environnements PLM/SLM et doit pouvoir inter-opérer à la fois avec les environnements CAD-DMU et CAE-BMU. DASIF allie les fonctionnalités de gestion de données et de configuration des systèmes PDM avec les concepts et formalismes d’ingénierie système basée sur les modèles (MBSE) et des fonctionnalités de gestion des données de simulation (SDM). Cette thèse a été menée dans le cadre d’un projet de recherche européen : le projet CRESCENDO qui vise à développer le « Behavioural Digital Aircraft » (BDA) qui a pour vocation d’être la« colonne vertébrale » des activités de conception et simulation avancées en entreprise étendue. Le concept du BDA doit s’articuler autour d’une plateforme collaborative d’échange et de partage des données de conception et de simulation tout au long du cycle de développement et de vie des produits aéronautiques. [...