Remeshing Process Research Articles

Improved 3D adaptive remeshing scheme applied in high electromagnetic field gradient computation

An improved adaptive remeshing process that allows the accurate control of the numerical solution of a partial differential 3D vectorial equation is introduced. It is applied to compute the electromagnetic intensity around a metallic sphere, which is known to present high gradients in limited zones of space. Thanks to the numerical results of an analytical model, we show that, the precision of the solution being controlled, this improved scheme permits to decrease drastically the computational time as well as the memory requirements by adapting the number and the position of nodes.

An adaptive procedure based on combining finite elements with meshless methods

This paper presents a new method for combining finite elements with meshless methods, which increases the accuracy of computational solutions in a coarse mesh by adding nodes in the domain of interest. The present method shares the features of the finite element and meshless methods such as (a) the meshless interpolation of the MLS type is employed; (b) integration domains are consistent with support domains; and (c) essential boundary conditions can be applied directly. In the present method, a ground mesh with triangular or quadrilateral elements is constructed to define polygonal support domains, and then additional nodes are placed arbitrarily in a domain without the reconstruction of a mesh. The method is very useful in an adaptive calculation, because nodes can be easily added or removed without any remeshing process.

Solution of geometric inverse heat conduction problems by smoothed fixed grid finite element method

This paper presents a methodology for solving the nonlinear inverse geometry heat transfer problems where the observations are temperatures measured at points on the external boundary and the unknowns are the shape and the location of a cavity inside the problem domain. The algorithm is based on the minimization of the squared error between the measured temperatures and those calculated by the proposed smoothed fixed grid finite element method where a non-boundary-fitted mesh is used to solve the direct problem. This eliminates mesh adaptation and re-meshing processes as needed in the standard finite element method and reduces the analysis cost significantly. The proposed method uses the advantages of smoothed finite element method and fixed grid finite element method in which a fixed computational mesh is used to solve the variable domain problem and the numerical integration is performed through gradient smoothing technique. The present method is more accurate and facilitates integration over boundary intersecting elements. The shape gradients of the shape identification problem are obtained by direct differentiation method. The domain parameterization technique with cubic splines is adopted to manipulate the shape variation of the cavity. To stabilize the optimization process, a geometric regularization function is used. Some numerical examples are solved to evaluate the method. In these examples effects of initial guess, measurement errors, cavity shape and cavity size on the results are examined. It is shown that the results are in good agreement with exact solutions.

A spatial warping method for freeform modeling based on a level-set method

Providing an intuitive and effective tool for freeform geometric modeling is important for product design. We introduce in this paper a level-set based spatial warping method for freeform modeling, allowing shape deformation to be initialed by rigid body transformations of volumetric tools. Intuitive user operations including imprinting, deformation and smoothing are developed to shield the user from the underlying geometric complexity. Unlike mesh-based spatial warping methods, the developed method represents a digital model by implicit distance field data and describes its change of geometry by the level-set method. This guarantees the generation of topologically correct triangular mesh models and circumvents the error-prone remeshing and mesh-repairing processes, thus preventing topological errors such as self-intersections. We present this method with algorithm details, numerical experiments and modeling examples.

Online parametric configuration of three-dimensional product visualization based on a triangulation model

This paper proposes a computational scheme for parametric configuration of three-dimensional products based on a triangulation model. This scheme allows real-time change in visualization of a three-dimensional product model without the need of computer-aided design or server-side processing. It simplifies the remeshing process by eliminating Delaunay triangulations. Parametric modification of design features are directly performed on an STL file, where supporting attributes are embedded in the comment fields. This ensures the integrity of the STL format and usage of common rendering tools. An online three-dimensional catalogue is developed for the configuration of a machine tool based on the proposed methods. The prototyping software demonstrates instant shape adjustment and dynamic three-dimensional interactions with the catalogue. As a client-side program, it does not require data transfer from the server during the configuration process or the existence of a B-Rep model. The system responsiveness is thus enhanced. Such a lightweight viewing technology facilitates design communication in a product life cycle as well as mass customization of three-dimensional products in e-commerce.

Finite Element Simulation of Fatigue Life Estimation and Crack Path Prediction of Two-dimensional Structures Components

The main objective of this work is to analyse fatigue crack propagation of two-dimensional structures under constant amplitude loading using the developed adaptive mesh finite element. The finite element mesh is generated using the advancing front method. The adaptive remeshing process is carried out based on the posteriori stress error norm scheme. The stress intensity factors are estimated by employing the displacement extrapolation technique facilitated by construction of singular crack tip elements. The crack propagation is modelled by the splitting node approach and the trajectory follows the successive linear extensions of each crack increment. The propagation process is driven by linear elastic fracture mechanics approach. In the analysis, the resulted stress intensity factor range at each of crack increments is recorded. Fatigue life cycle can be predicted immediately after completion of the recording by integrating the generalized Paris’ equation. The procedure is applied to the fatigue analysis ...

Finite element model for linear-elastic mixed mode loading using adaptive mesh strategy

An adaptive mesh finite element model has been developed to predict the crack propagation direction as well as to calculate the stress intensity factors (SIFs), under linear-elastic assumption for mixed mode loading application. The finite element mesh is generated using the advancing front method. In order to suit the requirements of the fracture analysis, the generation of the background mesh and the construction of singular elements have been added to the developed program. The adaptive remeshing process is carried out based on the posteriori stress error norm scheme to obtain an optimal mesh. Previous works of the authors have proposed techniques for adaptive mesh generation of 2D cracked models. Facilitated by the singular elements, the displacement extrapolation technique is employed to calculate the SIF. The fracture is modeled by the splitting node approach and the trajectory follows the successive linear extensions of each crack increment. The SIFs values for two different case studies were estimated and validated by direct comparisons with other researchers work.

Crack growth analysis using mesh superposition technique and X‐FEM

AbstractIn this paper, a new approach to crack propagation analysis for large scale or complicated geometry structures is presented. That is the connection of mesh superposition technique and the extended finite element method. The former is a technique that increases the accuracy of analysis locally by superimposing additional mesh of higher resolution onto the mesh that represents the rough deformation of the structure. In this technique, the boundaries and nodes of both meshes do not have to coincide with each other. In the latter technique, the discontinuity across the crack segment and singularity around the crack tips are represented in the approximation by enriching the nodal degrees using partition of unity condition. This technique does not require meshes to conform to the crack geometry and this enables crack propagation procedure with no re‐meshing process by connecting both techniques, it becomes possible to analyse crack growth models of large scale and complicated shape with highly flexible modelling and no remeshing process. By using this approach, some numerical examples are analysed and appropriate results are obtained. Copyright © 2007 John Wiley & Sons, Ltd.

Integrated topology and shape optimization software for compliant MEMS mechanism design

The objective of this work is to develop a specialized integrated design tool for MEMS compliant mechanisms from topology to shape optimization. We use the topology optimization technology to obtain an optimal mechanism layout achieving the best overall system performance. This design process is followed by shape optimization to improve stress-based local performance around hinges of the mechanism. Numerical instabilities in topology optimization such as checkerboard layout are overcome by use of nonconforming finite elements. To avoid the cumbersome remeshing process required to handle boundary shape changes, we employ the remesh-free shape optimization method based on the wavelet-Galerkin analysis. A few examples are considered to illustrate the integrated design procedure from topology to shape optimization and to demonstrate the effectiveness of the present approach.

An adaptive remeshing strategy for flows with moving boundaries and fluid–structure interaction

AbstractThe primary objective of this work is to extend the capability of the arbitrary Lagrangian–Eulerian (ALE)‐based strategy for solving fluid–structure interaction problems. This is driven by the fact that the ALE mesh movement techniques will not be able to treat problems in which fluid–structure interface experiences large motion. In addition, for certain problems the need arises to capture accurately flow features, such as a region with high gradients of the solution variables. This can be achieved by incorporating an adaptive remeshing procedure into the solution strategy.As in our previous works (Comput. Methods Appl. Mech. Eng. 2006; 195:1633–1666; Comput. Methods Appl. Mech. Eng. 2006; 195:5754–5779), here, the fluid flow is governed by the incompressible Navier–Stokes equations and modelled by using stabilized low order velocity–pressure finite elements. The motion of the fluid domain is accounted for by an arbitrary Lagrangian–Eulerian (ALE) strategy. The flexible structure is represented by means of appropriate standard finite element formulations while the motion of the rigid body is described by rigid body dynamics. For temporal discretization of both fluid and solid bodies, the discrete implicit generalized‐α method is employed. The resulting strongly coupled set of non‐linear equations is then solved by means of a novel partitioned solution procedure, which is based on the Newton–Raphson methodology and incorporates full linearization of the overall incremental problem.Within the adaptive solution strategy, the quality of fluid mesh and the solution quality indicator are evaluated regularly and compared against the appropriate remeshing criteria to decide whether a remeshing step is required. The adaptive remeshing procedure follows closely the standard computational procedure in which the adaptive remeshing process produces a mesh that can capture salient features of the flow field. For the problems under consideration in this work the motion of the fluid boundary very often results in boundaries with very high curvatures and a fluid domain that contain areas with small cross‐sections. To be able to generate meshes that give result with acceptable accuracy these local geometrical features need to be included in determining the element density distribution. The numerical examples demonstrate the robustness and efficiency of the methodology. Copyright © 2007 John Wiley & Sons, Ltd.

Automatic remeshing by mapping a 2D grid on 3D genus- [formula omitted] meshes based on topological analysis

Remeshing of 3D meshes is important for many CAD, visualization and analysis applications. Current remeshing methods for closed manifold genus- g meshes usually involve 3D mesh operations, such as splitting and merging the mesh edges, in order to construct a new mesh that will satisfy given geometrical criteria. These 3D operations are local and usually do not lead to the desired new mesh. Indeed, the remeshed model usually does not satisfy regular criteria. Moreover, changing one of the criteria will lead to reactivating the remeshing process from scratch. In this paper, we propose a novel remeshing approach which overcomes the above problems. It can be applied on 3D genus- g meshes ( g > 0 ) which are 2D manifold and triangular. The proposed approach is based on continuously mapping a 2D grid on the 3D genus- g meshes. The criteria of the new mesh can be defined directly on the 2D grid. The remeshing is invariant to the original triangular mesh. The mapping is based on a new parameterization technique, also developed by the authors, which utilizes the topologic analysis of the object. As a result, the mapping of the 2D grid into a 3D mesh minimizes distortion and guarantees continuity. In addition, the 2D grid, element shapes and density can be modified straightforwardly, thus making the approach modular. In the paper, the remeshing approach and the parameterization (mapping) technique are described in detail, and the feasibility of the remeshing method is demonstrated on complex 3D genus- g objects.

2020 Bスプラインウェーブレットガラーキン法を用いたアダプティブ解析に関する研究(S04-3 FEM/メッシュフリー法/粒子法とその関連技術(3),S04 FEM/メッシュフリー法/粒子法とその関連技術)

An adaptive B-spline wavelet Galerkin method is adopted to the solid and structural analyses. The B-spline scaling function and wavelets used as the basis functions have simple forms and are relatively easy to integrate and differentiate. The basis functions have the so called multiresolution properties. High gradient region of stresses and strains can be refined by the superposition of the different length scale basis functions. As the wavelet Galerkin method is discretized based on structured cells, there are no re-meshing processes for the refinement of the solution. Due to control the spatial resolution of the wavelet Galerkin solution based on the posteriori estimate of its discretization error, an adaptive analysis is adopted. In this paper, adaptive B-spline wavelet Galerkin analyses to the stress concentration problems are performed.

Optimum Shape Design of Composite Structures Using Boundary-Element Method.

The boundary-element method, combined with a numerical optimization algorithm, has been employed for the shape optimization of two-dimensional anisotropic structures. To find the optimum shape of a structure with the highest stiffness, the elastic compliance of the structure has been minimized subject to constraints upon stresses, weight, and geometry. The optimum shapes of a series of anisotropic structures are obtained for maximum stiffness and minimum weight and stress, for specified loading conditions. The results are compared with the optimum shapes, that were already created by the minimization of the structural weight while satisfying certain constraints upon stresses and geometry. A directly differentiated form of boundary integral equation with respect to geometric design variables is used to calculate shape design sensitivities of anisotropic materials. Because of the nonlinear nature of the mean compliance, weight, and stresses, the numerical optimization algorithm used is the feasible direction method, together with the golden section method for the one-dimensional search. Hermitian cubic spline functions are used to represent boundary shapes that offer considerable advantages in fitting a wide range of curves and in the automatic remeshing process. Five example problems with anisotropic material properties are presented to demonstrate the applications of this general-purpose program.

Re-etched grids for large-strain measurement in fine-blanking

This paper presents an experimental remeshing process for the large strain analysis of fine-blanking. The research is to be carried out mainly because the severe and localized deformation of fine-blanking greatly obstructs the measurement of strains. In order to solve this problem, a new experimental remeshing process was developed to measure the strain in the major deformation areas of fine-blanking. Without this newly developed process, a more intensive and practical strain analysis of fine-blanking could not have been achieved. Therefore, a study of this remeshing process, with a step increment of 20 per cent, until the total punch penetration is 80 per cent of the material's thickness, is to be performed to verify its effectiveness. Low-carbon steel sheets of JISG3101 were used to split blanks. As a consequence, findings showed that an increase in the total punch penetration will clearly induce an exponential increase in the effective strain, and the severity of deformation will be augmented with the increase in the total punch penetration.

Remesh-free shape optimization using the wavelet-Galerkin method

The objective of this investigation is to develop a new remesh-free shape optimization method based on the adaptive wavelet-Galerkin analysis. To avoid cumbersome remeshing processes, we embed the original analysis design domain inside a simple fictitious domain and use the predetermined analysis grid points. For efficient adaptive analysis, we utilize the multiscale multiresolution characteristics of the hat interpolation wavelets that are associated with predetermined grid points. Furthermore, we approximate the design boundary curve by oblique lines that do not necessarily pass through the analysis grid points and develop an accurate stress evaluation technique based on the proposed boundary approximation. The validity of the proposed remesh-free shape optimization formulation based on the wavelet-Galerkin method is verified through benchmark shape optimization problems.

Element-free Galerkin method in pulsed eddy currents

Compared with the conventional finite element method that relies on an underlying mesh and element-node connectivity to describe the geometry, meshless method shows its advantage in mesh simplification, tight crack representation and re-meshing process. An effective numerical implementation of the meshless method uses the Galerkin technique and is referred to as the element-free Galerkin (EFG) method. In this paper, the EFG method is applied to a field of electromagnetic computation, namely, simulation of pulsed eddy current testing. The model is validated against analytical solutions.

Crack growth analysis using mesh superposition method and X-FEM

In this paper, a new approach to crack propagation analysis for large-scale or complicated geometry structures is presented. That is the connection of mesh superposition method and extended finite element method. In the former technique, two types of meshes are used and displacement is represented as the sum of them. And in the latter technique, discontinuity across the crack segment and singularity around the crack tips are represented in the approximation by enriching the nodal degrees. This technique does not require meshes to conform to the crack geometry. This enables crack propagation procedure with no re-meshing process. By using this approach, some numerical examples are presented.

Anisotropic polygonal remeshing

In this paper, we propose a novel polygonal remeshing technique that exploits a key aspect of surfaces: the intrinsic anisotropy of natural or man-made geometry. In particular, we use curvature directions to drive the remeshing process, mimicking the lines that artists themselves would use when creating 3D models from scratch. After extracting and smoothing the curvature tensor field of an input genus-0 surface patch, lines of minimum and maximum curvatures are used to determine appropriate edges for the remeshed version in anisotropic regions, while spherical regions are simply point sampled since there is no natural direction of symmetry locally. As a result our technique generates polygon meshes mainly composed of quads in anisotropic regions, and of triangles in spherical regions. Our approach provides the flexibility to produce meshes ranging from isotropic to anisotropic, from coarse to dense, and from uniform to curvature adapted.

A methodology for adaptive finite element analysis: Towards an integrated computational environment

This work introduces a methodology for self-adaptive numerical procedures, which relies on the various components of an integrated, object-oriented, computational environment involving pre-, analysis, and post-processing modules. A basic platform for numerical experiments and further development is provided, which allows implementation of new elements/error estimators and sensitivity analysis. A general implementation of the Superconvergent Patch Recovery (SPR) and the recently proposed Recovery by Equilibrium in Patches (REP) is presented. Both SPR and REP are compared and used for error estimation and for guiding the adaptive remeshing process. Moreover, the SPR is extended for calculating sensitivity quantities of first and higher orders. The mesh (re-)generation process is accomplished by means of modern methods combining quadtree and Delaunay triangulation techniques. Surface mesh generation in arbitrary domains is performed automatically (i.e. with no user intervention) during the self-adaptive analysis using either quadrilateral or triangular elements. These ideas are implemented in the Finite Element System Technology in Adaptivity (FESTA) software. The effectiveness and versatility of FESTA are demonstrated by representative numerical examples illustrating the interconnections among finite element analysis, recovery procedures, error estimation/adaptivity and automatic mesh generation.

2D Mesh Generation Scheme for Adaptive Remeshing Process in Finite Element Method

The discretization of a whole domain is a prerequisite process for Finite Element Method (FEM). Since manual mesh generation is tedious, mesh generation schemes have been studied in recent years. In iterative analyses, the geometry of the domain is drastically changed by each iteration. It is known that mesh regeneration eliminates mesh distortion caused by the geometry change, which greatly affects the convergence of the whole analysis. If error control in the analysis is additionally considered in the mesh regeneration, such a process should be adaptive ; adaptive remeshing is required for a reliable solution. There are many mesh generators available, however, most of them require interaction with the user, and thus cannot be used for adaptive remeshing. In this paper, a sophisticated mesh generation scheme for the adaptive remeshing in the 2D FEM is discussed in detail. After comparison with other schemes, it is concluded that our scheme is superior to the others in terms of flexibility and time complexity.