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Traditional adaptive analysis based on a coarse mesh, using finite element method (FEM) analysis, produces the original solution. Then post-processing the result and figuring out the regions should be refined and these regions refined once. Finally, this new mesh is used to get the solution of first refinement. After several iterations of above procedures, we can achieve the last result that is closer to the true solution, which takes time, making adaptive scheme inpractical to engineering application. The paper aims to discuss these issues.

This paper based on FEM proposes a multi-level refinement strategy with a refinement strategy and an indicator. The proposed indicator uses value of the maximum difference of strain energy density among the elements that associated with one node, and divides all nodes into several categories based on the value. A multi-level refinement strategy is proposed according to which category the node belongs to refine different elements to different times rather than whether refine or not.

Multi-level refinement strategy takes full use of the numerical calculation, resulting in the whole adaptive analysis that only need to iterate twice while other schemes must iterate more times. Using much less times of numerical calculation and approaches, more accurate solution, making adaptive analysis more practical to engineering.

Multi-level refinement strategy takes full use of the numerical calculation, resulting in the whole adaptive analysis only need iterate twice while other schemes must iterate more times. using much less times of numerical calculation and approaches more accurate solution, making adaptive analysis more practical to engineering.

Presents an efficiency study of different refinement procedures for the p‐version of the adaptive finite element method in two‐dimensional elasticity problems. The refinement strategy, based on the estimated error in energy norm, attempts an optimal distribution of the nodeless degrees of freedom associated with the basic approximation parameter of the order p of the hierarchical shape functions. This procedure is combined with appropriate matrix‐handling techniques and equation solvers in order to achieve a solution of a given accuracy with the minimum computational resources in terms of computing time and storage. To this extent, convergence studies are performed with constant and variable adaptivity indices, with error estimators based on global and elemental approaches and with domain decomposition matrix‐handling techniques and the preconditioned conjugate gradient solver.

A new h‐refinement adaptive tetrahedral mesh generation algorithm is presented. Three‐dimensional domains, to be analysed by the finite element method, are initially modelled by a coarse background mesh of tetrahedral elements. This mesh forms the input for finite element analysis and error estimation by the Zienkiewicz‐Zhu simple error estimator. Adaptive mesh refinement proceeds by selecting an element for remeshing whose longest edge is shared by elements that also require refinement. This group of elements is refined by inserting a new node at the mid‐point of the shared edge thereby bisecting all elements within the group. Adaptive parameters are calculated for the new node and elements. Refinement then proceeds until no further group of elements can be found for refinement or no elements within the current mesh require further refinement. The shape quality of the current mesh is then enhanced by the iterative application of nodal relaxation plus three topological transformations. The entire refinement process is repeated iteratively until the required degree of mesh refinement is reached. Ten‐noded linear strain tetrahedral finite element meshes have been used for the finite element and error estimation analyses. Four examples of adaptive tetrahedral mesh generation for linear elastic stress/displacement analysis are presented which show that this algorithm is robust and efficient in terms of reduction of the domain error with a minimum number of degrees of freedom being generated, number of iterations, and therefore finite element analyses, required and computational time for refinement when compared to the advancing front method and Delaunay triangulation.

This study aims to propose a general and efficient adaptive strategy with local mesh refinement for two-dimensional (2D) finite element (FE) analysis based on the element energy projection (EEP) technique.

In view of the inflexibility of the existing global dimension-by-dimension (D-by-D) recovery method via EEP technique, in which displacements are recovered through element strips, an improved element D-by-D recovery strategy was proposed, which enables the EEP recovery of super-convergent displacements to be implemented mostly on a single element. Accordingly, a posteriori error estimate in maximum norm was established and an EEP-based adaptive FE strategy of h-version with local mesh refinement was developed.

Representative numerical examples, including stress concentration and singularity problems, were analyzed; the results of which show that the adaptively generated meshes reasonably reflect the local difficulties inherent in the physical problems and the proposed adaptive analysis can produce FE displacement solutions satisfying the user-specified tolerances in maximum norm with an almost optimal adaptive convergence rate.

The proposed element D-by-D recovery method is a more efficient and flexible displacement recovery method, which is implemented mostly on a single element. The EEP-based adaptive FE analysis can produce displacement solutions satisfying the specified tolerances in maximum norm with an almost optimal convergence rate and thus can be expected to apply to other 2D problems.

Two mesh refinement indicators based on the gradients of effective stress (GSIG) and effective plastic strain (GEPS), respectively, are proposed for adaptive finite element analysis of the large deformation, quasi‐static or dynamic response of shell structures. The mesh refinement indicators are based on equi‐distributing the variation of stresses or plastic strains over the elements of the mesh. A program module is developed and implemented in the non‐linear explicit finite element code LS‐DYNA. This module provides element‐wise refinement evaluations so that selective mesh refinements are carried out in regions of the mesh where the values of local indicators exceed a user‐specified tolerance. The FE model of a conventional deep drawing process is used as a numerical model, including both material and geometrical non‐linearities, in order to demonstrate the versatility of the two refinement indicators. Four different refinement indicators, based on angle change, thickness change, GSIG and GEPS, are applied in this investigation. The numerical results are compared with experimental results regarding the thickness distribution versus cup height, cup height variation versus circumference angle, effective plastic strain in the deformed sheet and punch force. It is shown that the proposed indicators can identify finite elements which have high gradients of effective stress or effective plastic strain so that the mesh is refined in the regions undergoing the most severe deformations and the numerical results are improved.

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for meshing and remeshing, parallel processing in the finite element modelling, etc. are also included. The bibliography at the end of this paper contains 1,727 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1990 and 2001.

Numerical simulation of the single point incremental forming (SPIF) processes can be very demanding and time consuming due to the constantly changing contact conditions between the tool and the sheet surface, as well as the nonlinear material behaviour combined with non-monotonic strain paths. The purpose of this paper is to propose an adaptive remeshing technique implemented in the in-house implicit finite element code LAGAMINE, to reduce the simulation time. This remeshing technique automatically refines only a portion of the sheet mesh in vicinity of the tool, therefore following the tool motion. As a result, refined meshes are avoided and consequently the total CPU time can be drastically reduced.

SPIF is a dieless manufacturing process in which a sheet is deformed by using a tool with a spherical tip. This dieless feature makes the process appropriate for rapid-prototyping and allows for an innovative possibility to reduce overall costs for small batches, since the process can be performed in a rapid and economic way without expensive tooling. As a consequence, research interest related to SPIF process has been growing over the last years.

In this work, the proposed automatic refinement technique is applied within a reduced enhanced solid-shell framework to further improve numerical efficiency. In this sense, the use of a hexahedral finite element allows the possibility to use general 3D constitutive laws. Additionally, a direct consideration of thickness variations, double-sided contact conditions and evaluation of all components of the stress field are available with solid-shell and not with shell elements. Additionally, validations by means of benchmarks are carried out, with comparisons against experimental results.

It is worth noting that no previous work has been carried out using remeshing strategies combined with hexahedral elements in order to improve the computational efficiency resorting to an implicit scheme, which makes this work innovative. Finally, it has been shown that it is possible to perform accurate and efficient finite element simulations of SPIF process, resorting to implicit analysis and continuum elements. This is definitively a step-forward on the state-of-art in this field.

The authors' objective in this paper is to find the numerical solutions of obstacle, unilateral and contact second‐order boundary‐value problems.

To achieve this, the authors formulate a spatially adaptive grid refinement scheme following Galerkin's finite element method based on a weighted‐residual. A residual based a‐posteriori error estimation scheme has been utilized for checking the approximate solutions for various finite element grids. The local element balance has been considered as an error assessment criterion. The approach utilizes piece‐wise linear approximations utilizing linear Langrange polynomials. Numerical experiments indicate that local errors are large in regions where the gradients are large.

A comparison of the spatially adaptive grid refinement with that of uniform meshing for second order obstacle boundary value problems confirms the superiority of the scheme without increasing the number of unknown coefficients.

The authors believe the work has merit not only in terms of the approach but also of the problem solved in the paper.

A combination of both time step adaptivity and spatial mesh adaptivity is presented for transient magneto‐quasistatic fields.

Error controlled time step adaptivity is achieved using an implicit integration scheme and the spatial mesh resolution is adapted in each time step in order to effectively resolve the appearing and disappearing local transient saturation effects and eddy current layers. Two spatial refinement strategies are considered, the red‐green refinement leading to a regular mesh and the red refinement leading to an irregular mesh. Numerical results for 2d nonlinear magneto‐dynamic problems are presented.

An algorithm is proposed which computes the solution of a transient magnetostatic problem given a user prescribed error tolerance for the time stepping and the spatial refinement. The red refinement leading to irregular meshes requires projection techniques in the iterative conjugate gradient solver. However, the algorithm with red‐green refinement turns out to perform faster since the projection is too expensive.

The combination of error controlled time stepping and spatial adaptivity is firstly established in electromagnetic field computation.