Adaptive analysis thin-walled structures using three dimensional solid elements

Mesh refinement for anisotropic diffusion in magnetized plasmas

It is important to establish an integrated CAD system for mechanical engineering. The geometric model is constructed with primitives, such as wire frame, surface and solid on this system. The finite element model is induced from the substructure, which is a component of the geometric model. After the extraction of the substructure from the model, the mesh for the finite element analyses is automatically generated against the substructure. An approach to automatic mesh generation is discussed on this paper, based upon the techniques of interpolation with the blending function, originally developed for geometric modeling. But, the blending function may produce unexpected results when the mesh is generated, due to the nature of the algorithm. In order to conclude with expected results for automatic mesh generation, and accuracy-fitting method is introduced.

The finite element method has recently been employed in investigating magnetization processes in materials with an irregular microstructure. In order to improve the accuracy of the solution, a method based on an adaptive refinement scheme is clearly desirable. Error control is essential if accuracy of results is to be optimal. We have applied an adaptive scheme to a system of interacting two-dimensional polycrystalline grains. The error estimator is based on the divergence and curl of both the magnetization and demagnetizing field. It is shown that increasing levels of discretization improve the micromagnetic solution, and the spatial localization of the additional nodes demonstrates the importance of the adaptive meshing technique.

An automatic adaptive refinement procedure for the analysis of shell structures using the nine-node degenerated solid shell element is suggested. The basic adaptive refinement principle and the effects of singularities and boundary layers on the convergence rate of the nine-node element used are discussed. A new stress recovery procedure based on the patch convective co-ordinate system concept is developed for the construction of a continuous smoothed stress field over the shell domains. The stress recovery procedure is easy to implement, requires a modest computational effort and needs only local patch information. It can be applied to shells with non-uniform thickness as well as to multi-layered shell structures. The smoothed recovered stress obtained is then used with the Zienkiewicz and Zhu error estimator for a posteriori error estimation during the adaptive refinement analysis. Numerical results which are in good agreement with theoretical predictions are obtained and they indicate that the current adaptive refinement procedure can eliminate the effect of singularities inside the problem domains so that a near-optimal convergence rate is achieved in all the numerical examples. This also indicates that the stress recovery procedure can produce an accurate stress field and as a result the error estimator can reflect the error distribution of the finite element solution. Even though in the current study only one type of element is used in the analysis, the whole adaptive refinement scheme can be readily applied to any other types of degenerated solid element. © 1997 John Wiley & Sons, Ltd.

Functionally graded materials provide versatility in adjusting the volume fractions of constituent materials to meet specific design requirements. However, this customization often introduces mode-mixity at the crack tip, posing challenges in predicting fracture under cyclic loading with discrete approaches and computationally expensive with conventional phase-field fracture models. To address these issues, this paper introduces an adaptive phase-field fracture formulation with cycle jump scheme to elegantly predict fatigue crack nucleation and growth in functionally graded materials. Within this framework, the effective properties at a point are estimated using the Mori–Tanaka homogenization scheme, while the crack growth due to cyclic load is captured by incorporating an additional fatigue degradation parameter. Moreover, the computational efficiency of the proposed framework is improved through an adaptive mesh refinement and explicit cycle jump scheme. The adaptive refinement scheme utilizes an error indicator derived from both the displacement solution and phase-field variable. The adaptive refinement scheme is integrated with efficient quadtree decomposition, which generates a hierarchical mesh structure. Hanging nodes resulting from the quadtree decomposition are efficiently handled using a polygonal finite element method. The proposed framework is validated against experimental and numerical results reported in the literature. Furthermore, we investigate the fatigue crack growth resistance across a broad range of material gradation directions, gaining valuable insights and identifying functionally graded materials with high fatigue resistance.

2D automatic body-fitted structured mesh generation using advancing extraction method

An electromagnetic wave propagation problem can be formulated according to a pair of complementary formulations, called the ${e}$ -formulation and the ${h}$ -formulation. The two formulations are linked to each other by Maxwell’s curl equations, and, in the continuous setting, they are perfectly equivalent in describing the wave propagation phenomenon. However, this is not true in the discrete setting, where the two formulations, in general, give different solutions. In the past decades, complementary formulations were widely studied for static problems and eddy-current problems, where they were exploited as error estimators for adaptive refinement schemes. Moreover, the so-called bilateral energy bounds arise for some problems whether theoretically or at least numerically. However, to the best of our knowledge, little attention has been given to complementarity in the wave propagation problems. In this paper, we propose an adaptive refinement scheme using the constitutive error as an estimator, and then, we investigate the behavior in terms of bilateral energy bounds.

A methodology for the automatic mesh generation of quadrilateral elements is proposed. The methodology is based on the facts that (i) a region can always be subdivided entirely into quadrilaterals if the polygon which forms the boundary of the region has an even number of sides, (ii) a quadrilateral can be formed by two triangles which share a common side. By taking advantage of the techniques developed in an existing automatic triangular mesh generator, quadrilateral meshes can be generated according to the distribution of user specified element size over the domain of interest. In particular, an automatic quadrilateral mesh generator based on the advancing front technique for triangular mesh generation1 is described. Techniques to improve the quality of the generated quadrilateral meshes are introduced. The robustness and versatility of the mesh generator are demonstrated by a variety of examples.

<div class="section abstract"><div class="htmlview paragraph">Prediction of in-cylinder flows and fuel-air mixing are two fundamental pre-requisites for a successful simulation of direct-injection engines. Over the years, many efforts were carried out in order to improve available turbulence and spray models. However, enhancements in physical modeling can be drastically affected by how the mesh is structured. Grid quality can negatively influence the prediction of organized charge motion structures, turbulence generation and interaction between in-cylinder flows and injected sprays. This is even more relevant for modern direct injection engines, where multiple injections and control of charge motions are employed in a large portion of the operating map. Currently, two different approaches for mesh generation exist: manual and automatic. The first makes generally possible to generate high-quality meshes but, at the same time, it is very time consuming and not completely free from user errors. Automatic mesh generation is very fast, but does not easily allow to align grid with flow and spray in regions of interest, for instance where fuel is injected or where the air flow is confined between pipe walls and thigh gaps (intake and exhaust head ducts and valve gaps). Within this context, the authors have developed a novel approach for automatic mesh generation, where both mesh quality and flow alignment are taken into account. Such methodology has been incorporated into the Lib-ICE code, which is based on the OpenFOAM technology. On the basis of combustion chamber details and/or user specified parameters (piston bowl points, injector direction, squish height, valve lift diagram,…), body fitted, high quality grids are automatically generated to perform full-cycle or compression/combustion simulations. To assess the proposed approach, two direct-injection engines were simulated. The first is Diesel fueled and only compression and combustion phases are simulated, showing the advantages of a spray-oriented grid, compared to a conventional Cartesian one, in terms of prediction of fuel-air mixing and combustion process. The second one is a gasoline, direct-injection engine. In this case full-cycle simulations were performed and computed flow field data were compared with optical experimental ones.</div></div>

A novel approach to implicit residual‐type error estimation in mesh‐free methods and an adaptive refinement strategy are presented. This allows computing upper and lower bounds of the error in energy norm with the ultimate goal of obtaining bounds for outputs of interest. The proposed approach precludes the main drawbacks of standard residual‐type estimators circumventing the need of flux‐equilibration and resulting in a simple implementation that avoids integrals on edges/sides of a domain decomposition (mesh). This is especially interesting for mesh‐free methods. The adaptive strategy proposed leads to a fast convergence of the bounds to the desired precision. Copyright © 2008 John Wiley & Sons, Ltd.

The current state of the art of Finite Element Methods in Computational Fluid Dynamics is reviewed. The aim of this review is to point out what appear currently as the main shortcomings of Finite Element Methods, so as to concentrate the efforts to remove them. The analysis of flows using Finite Elements will only be successful if all steps involved in it are optimized. Therefore, I deem it necessary to describe explicit and implicit flow solvers, unstructured multigrid methods, adaptive refinement schemes, grid generation and graphics in 3‐D, the effective use of supercomputer hardware and memory, as well as the combination of structured and unstructured grids.

SummaryThis article proposes an efficient approach for solving three‐dimensional (3D) topology optimization problem. In this approach, the number of design variables in optimization as well as the number of degrees of freedom in structural response analysis can be reduced significantly. This is accomplished through the use of scaled boundary finite element method (SBFEM) for structural analysis under the moving morphable component (MMC)‐based topology optimization framework. In the proposed method, accurate response analysis in the boundary region dictates the accuracy of the entire analysis. In this regard, an adaptive refinement scheme is developed where the refined mesh is only used in the boundary region while relating coarse mesh is used away from the boundary. Numerical examples demonstrate that the computational efficiency of 3D topology optimization can be improved effectively by the proposed approach.

A novel adaptive isogeometric digital height correlation (DHC) technique has been developed in which the set of shape functions, needed for discretization of the ill‐posed DHC problem, is autonomously optimized for each specific set of profilometric height images, without a priori knowledge of the kinematics of the experiment. To this end, an adaptive refinement scheme is implemented, which refines the shape functions in a hierarchical manner. This technique ensures local refinement, only in the areas where needed, which is beneficial for the noise robustness of the DHC problem. The main advantage of the method is that it can be applied in experiments where the deformation mechanisms are unknown in advance, thereby complicating the choice of suitable shape functions. The method is applied to a virtual experiment in order to provide a proof of concept. A second virtual experiment is executed with stretchable electronics interconnects, which entail localized buckles upon deformation with complex kinematics. In both cases, accurate results were obtained, demonstrating the beneficial aspects of the proposed method. Moreover, the technique performance on profilometric images of a real experiment with stretchable interconnects was demonstrated.

SUMMARYThis paper presents a numerical formulation for computation of collapse load of Mindlin–Reissner plates that uses stabilized discrete shear gap finite elements and second‐order cone programming. Displacement fields are approximated using the discrete shear gap in combination with a stabilized strain smoothing technique, ensuring that shear‐locking problem can be avoided and that accurate solutions can be obtained. The underlying optimization problem is formulated in the form of a standard second‐order cone programming, so that it can be solved using highly efficient primal‐dual interior‐point algorithm. An error indicator based on plastic dissipation will be used in the adaptive refinement scheme. Various plates with arbitrary geometries and boundary conditions are examined to illustrate the performance of the proposed procedure. Copyright © 2013 John Wiley & Sons, Ltd.

Winding number based automatic mesh generation algorithm for hydrogen analysis code GASFLOW-MPI