Adaptive Remeshing Method Research Articles

A Quasi-Optimal Shape Design Method for Electromagnetic Scatterers Based on NURBS Surfaces and Filter-Enhanced GWO

This paper presents a quasi-optimal and efficient method for designing the shape of electromagnetic (EM) scatterers. Optimizing the EM scatterer shape to achieve satisfactory scattering properties is a crucial, yet challenging problem due to the complex geometry involved and the high non-linearity in the optimization. In this paper, the geometric complexity is to be handled by modeling EM scatterer shapes as non-uniform rational basis spline (NURBS) surfaces, which enables an easy and intuitive shape control. Using the surfaces’ control points as optimization variables, the shape optimization problem is to be solved with the heuristic optimization strategy, which can effectively handle non-linearity and the associated local optima. Specifically, the recently developed grey wolf optimizer (GWO) is employed. Although GWO can effectively avoid local optima and achieve quasi-optimal results, it requires repeated calls to time-consuming EM simulations. To solve this efficiency issue, a filter-enhanced version of GWO is proposed to reduce the times of calling EM simulations, and an efficient, adaptive remeshing method is proposed to accelerate the numerical analysis process within each EM simulation call. Altogether, they lead to a quasi-optimal and efficient method for optimizing EM scatterers. Its effectiveness has also been validated by several examples.

A geometrically and locally adaptive remeshing method for finite difference modeling of mining-induced surface subsidence

Surface subsidence induced by underground mining is a typical serious geohazard. Numerical approaches such as the discrete element method (DEM) and finite difference method (FDM) have been widely used to model and analyze mining-induced surface subsidence. However, the DEM is typically computationally expensive, and is not capable of analyzing large-scale problems, while the mesh distortion may occur in the FDM modeling of largely deformed surface subsidence. To address the above problems, this paper presents a geometrically and locally adaptive remeshing method for the FDM modeling of largely deformed surface subsidence induced by underground mining. The essential ideas behind the proposed method are as follows: (i) Geometrical features of elements (i.e. the mesh quality), rather than the calculation errors, are employed as the indicator for determining whether to conduct the remeshing; and (ii) Distorted meshes with multiple attributes, rather than those with only a single attribute, are locally regenerated. In the proposed method, the distorted meshes are first adaptively determined based on the mesh quality, and then removed from the original mesh model. The tetrahedral mesh in the distorted area is first regenerated, and then the physical field variables of old mesh are transferred to the new mesh. The numerical calculation process recovers when finishing the regeneration and transformation. To verify the effectiveness of the proposed method, the surface deformation of the Yanqianshan iron mine, Liaoning Province, China, is numerically investigated by utilizing the proposed method, and compared with the numerical results of the DEM modeling. Moreover, the proposed method is applied to predicting the surface subsidence in Anjialing No. 1 Underground Mine, Shanxi Province, China.

A two-dimensional adaptive remeshing method for solving melting and solidification problems with convection

Melting and solidification problems in presence of natural convection are known to require high computational resources. Very fine meshes are essential to accurately determine the flow structure and interface position between the different phases. In this work, a time-dependent adaptive remeshing method based on an efficient error estimator is presented. The proposed method greatly reduces the number of mesh elements while maintaining and even enhancing the efficiency of the simulations. A variant of the enthalpy-porosity formulation is used where the different thermo-physical properties between the solid–liquid phases are easily taken into account. A second order mixed finite element formulation for both space and time is employed for solving the momentum and energy equations. The efficiency of the proposed methodology is established by comparing solutions on very fine meshes with those obtained on adapted meshes and with existing experimental and numerical results found in the literature.

Simulation of a two-slope pyramid made by SPIF using an adaptive remeshing method with solid-shell finite element

Single point incremental forming (SPIF) is an emerging application in sheet metal prototyping and small batch production, which enables dieless production of sheet metal parts. This research area has grown in the last years, both experimentally and numerically. However, numerical investigations into SPIF process need further improvement to predict the formed shape correctly and faster than current approaches. The current work aims the use of an adaptive remeshing technique, originally developed for shell and later extended to 3D “brick” elements, leading to a Reduced Enhanced Solid-Shell formulation. The CPU time reduction is a demanded request to perform the numerical simulations. A two-slope pyramid shape is used to carry out the numerical simulation and modelling. Its geometric difficulty on the numerical shape prediction and the through thickness stress behaviour are the main analysis targets in the present work. This work confirmed a significant CPU time reduction and an acceptable shape prediction accuracy using an adaptive remeshing method combined with the selected solid-shell element. The stress distribution in thickness direction revealed the occurrence of bending/unbending plus stretching and plastic deformation in regions far from the local deformation in the tool vicinity.

Comparison between an Advanced Numerical Simulation of Sheet Incremental Forming Using Adaptive Remeshing and Experimental Results

Recently, new sheet metal forming technique, incremental forming has been introduced. It is based on using a single spherical tool, which is moved along CNC controlled tool path. During the incremental forming process, the sheet blank is fixed in sheet holder. The tool follows a certain tool path and progressively deforms the sheet. Nowadays, numerical simulations of metal forming are widely used by industry to predict the geometry of the part, stresses and strain during the forming process. Because incremental forming is a dieless process, it is perfectly suited for prototyping and small volume production [1, 2]. On the other hand, this process is very slow and therefore it can only be used when a slow series production is required. As the sheet incremental forming process is an emerging process which has a high industrial interest, scientific efforts are required in order to optimize the process and to increase the knowledge of this process through experimental studies and the development of accurate simulation models. In this paper, a comparison between numerical simulation and experimental results is realized in order to assess the suitability of the numerical model. The experimental investigation is realized using a three-axis CNC milling machine. The forming tool consists in a cylindrical rotating punch with a hemispherical head. A subroutine has been developed to describe the tool path from CAM procedure. A numerical model has been developed to simulate the sheet incremental forming process. The finite element code Abaqus explicit has been used. The simulation of the incremental forming process stays a complex task and the computation time is often prohibitive for many reasons. During this simulation, the blank is deformed by a sequence of small increments that requires many numerical increments to be performed. Moreover, the size of the tool diameter is generally very small compared to the size of the metal sheet and thus the contact zone between the tool and the sheet is limited. As the tool deforms almost every part of the sheet, small elements are required everywhere in the sheet resulting in a very high computation time. In this paper, an adaptive remeshing method has been used to simulate the incremental forming process. This strategy, based on adaptive refinement and coarsening procedures avoids having an initially fine mesh, resulting in an enormous computing time. Experiments have been carried out using aluminum alloy sheets. The final geometrical shape and the thickness profile have been measured and compared with the numerical results. These measurements have allowed validating the proposed numerical model.

Numerical Simulation of the Deformation of Drops under Simple Shear Flow

In this paper, we perform a numerical simulation of the deformation of a drop under simple shear flow. The drop and the fluid matrix can be Newtonian or viscoelastic fluids. For viscoelastic fluids, the Oldroyd-B model is used in a log-conformation formulation as in Fattal et al. /I/ and Guenette et al./2/. An anisotropic adaptive remeshing method is used and combined with a level set method for the computation of the free surfaces. Comparisons are made with similar simulations presented by Chung et al. /3/ and Chinyoka et al. /4/.

Thermo‐mechanically coupled modeling and simulation of hot metal‐forming processes using adaptive remeshing method

AbstractThe purpose of this work is to model and simulate hot metal forming processes in which material undergoes large deformations with help of the Finite Element (FE) software ABAQUS using Lagrangian formulation. Extrusion of aluminum alloys and forging of steels as two examples are taken into account in this work. To this end, a material model based on thermoelastic viscoplasticity is formulated for each case. The microstructural evolution is modeled effectively with the help of internal state variables. Element distortion and contact during the simulation of large deformation processes is controlled with the help of a custom adaptive remeshing system based on Python scripting and utilizable in commercial programs such as Abaqus. Simulation results for the microstructural development during extrusion as a func‐tion of process conditions demonstrate the sensitivity of microstructure development to these conditions. Comparison of the simulation results for the microstructure evolution with corresponding experimental results show good qualitative agreement (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A 3-D indirect boundary element method for bounded creeping flow of drops

The simulation of the flow of emulsions in porous media presents formidable challenges, due to the extremely complex evolving geometry. Methods based on boundary integral equations, suitable for creeping flows, reduce the effort dedicated to geometry representation, but can become computationally expensive. An efficient indirect boundary integral formulation representing deformable drops in a bounded Stokes flow, resulting in a set of Fredholm integral equations of the second kind, is presented. The boundary element method (BEM) based on the formulation employs an accurate numerical integration scheme for the singular kernels involved, an effective and accurate curvature and normal calculation method, and an adaptive remeshing method to simulate interfacial deformation of drops. Two benchmark problems are used to assess the accuracy of the method, and to investigate its behavior for large problems. The method is found to provide accurate results combined with well-posedness, making it suitable for use in accelerated fast multipole method algorithms.

Remaillage adaptatif pour la mise en forme des tôles minces

Problems associated with finite element simulation of the forming processes are characterized by large elastoplastic deformations, evolutive contact with friction, geometrical nonlinearities inducing a severe distortion of the computational mesh of the domain. In this case, frequent remeshing of the deformed domain during computation are necessary to obtain an accurate solution and complete the computation until the termination of the numerical simulation process. This Note presents a new adaptive remeshing method of thin sheets for numerical simulation of metal forming processes. The proposed method is based on geometrical criteria and does not use the geometry of the forming tools. It is integrated in a computational environment using the ABAQUS solver. Numerical examples are given to show the efficiency of our approach. To cite this article: L. Moreau et al., C. R. Mecanique 333 (2005).

Adaptive computation for elastic wave propagation in plate/shell structures under moving loads

An adaptive remeshing method tailored to computations for elastic wave propagation is proposed and its application to the elastic wave propagation in plates or shells under moving loads is presente...

Error estimators for viscoplastic materials: application to forming processes

The analysis of error estimation is addressed in the framework of viscoplasticity problems, this is to say, of incompressible and non‐linear materials. Firstly, Zienkiewicz—Zhu (Z2) type error estimators are studied. They are based on the comparison between the finite element solution and a continuous solution which is computed by smoothing technique. From numerical examples, it is shown that the choice of a finite difference smoothing method (Orkisz’ method) improves the precision and the efficiency of this type of estimator. Then a Δ estimator is introduced. It makes it possible to take into account the fact that the smoothed solution does not verify the balance equations. On the other hand, it leads us to introduce estimators for the velocity error according to the L2 and L∞norms, since in metal forming this error is as important as the energy error. These estimators are applied to an industrial problem of extrusion, demonstrating all the potential of the adaptive remeshing method for forming processes.

An adaptive remeshing method in the simulation of Resin Transfer Molding (RTM) process

In this paper, an adaptive remeshing method for the numerical analysis of a mold filling process is presented. After a brief discussion of the derivation, of governing equations using the homogenization method, the adaptive remeshing method is developed which incorporates error measures and an automatic mesh generator. The method is successfully combined with the finite element/control volume method to solve the governing equations. Two model problems are provided to examine the performance of the method.

Adaptive boundary-type finite element method for wave diffraction-refraction in harbors

Abstract This paper presents an adaptive boundary-type finite element method for wave diffraction-refraction in harbors. The present method consists of three parts; the automatic mesh generation method, the boundary type finite element method and the adaptive remeshing method. The present model is based on the mild-slope equation and an arbitrary reflection condition is introduced. The computed results are compared with the existing analytical and experimental results. This method is shown to be a useful and powerful tool for the analysis of wave diffractionrefraction in harbors.

Structured and unstructured remeshing method for high-speed flows

An adaptive remeshing method using both triangular and quadrilateral elements suitable for high speed flows is presented. For inviscid flows the method generates completely unstructured meshes. For viscous flows the boundary layer edge is identified adaptively and a structured mesh is generated in the boundary layer, and an unstructured mesh is generated in the inviscid region. Examples of inviscid and viscous mesh adaptations for high speed flows are presented. A comparison is made between first order and higher order finite element algorithms when used in association with the remeshing method.

Adaptive remeshing method for finite-element thermal analysis

A finite element remeshing approach that makes use of quadrilateral and triangular elements is described. The approach uses the solution on a previous mesh to create a new mesh. Meshes are completely unstructured with highly refined elements in regions of steep gradients and larger elements where gradients are smaller. Studies of convergence rates for heat conduction problems with exact solutions show that for problems with highly localized solution variations, the remeshing approach gives smaller solution errors with fewer unknowns than refinement of uniform, structured meshes.