Search results

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.

Two different ‘a posteriori’ error estimation techniques are proposed in this paper. The effectiveness of the error estimates in adaptive mesh refinement for 2D and 3D electrostatic problems are also analyzed with numerical test results. The post‐processing method employs an improved solution to estimate the error, whereas the gradient of field method utilizes the gradient of the field solution for estimating the ‘a posterior’ error. The gradient of field method is computationally inexpensive, since it solves a local problem on a patch of elements. The error estimates are tested by solving a set of self‐adjoint boundary value problems in 2D and 3D using a hierarchical minimal tree based mesh refinement algorithm. The numerical test results and the performance evaluation establish the effectiveness of the proposed error estimates for adaptive mesh refinement.

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.

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.

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.

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.

Proposes an automatic adaptive meshing scheme. Error in strain energy is directly obtained through strain energy density function (SED). Versatility of this function, in comparison with that of others, is looked at in detail. Mesh enrichment method consists of a series of h‐refinement steps and concludes with a single p‐refinement step. Adds that an examination of the accuracy of the element used in the refinement procedure is made. This scheme has been implemented in ZATILAN, a FE code developed in the Department of the Mechanical Engineering of the University of the Basque Country.

The concepts of solution error and optimal mesh in adaptive finite element analysis are revisited. It is shown that the correct evaluation of the convergence rate of the error norms involved in the error measure and the optimal mesh criteria chosen are essential to avoid oscillations in the refinement process. Two mesh optimality criteria based on: (a) the equal distribution of global error, and (b) the specific error over the elements are studied and compared in detail through some examples of application.

This study aimed to overcome the challenging issues involved in providing high-precision eigensolutions. The accurate prediction of the buckling load bearing capacity under different crack damage locations, sizes and numbers, and analysing the influence mechanism of crack damage on buckling instability have become the needs of theoretical research and engineering practice. Accordingly, a finite element method was developed and applied to solve the elastic buckling load and buckling mode of curved beams with crack damage. However, the accuracy of the solution depends on the quality of mesh, and the solution inevitably introduces errors due to mesh. Therefore, the adaptive mesh refinement method can effectively optimise the mesh distribution and obtain high-precision solutions.

For the elastic buckling of circular curved beams with cracks, the section damage defect analogy scheme of a circular arc curved beam crack was established to simulate the crack size (depth), position and number. The h-version finite element mesh adaptive analysis method of the variable section Euler–Bernoulli beam was introduced to solve the elastic buckling problem of circular arc curved beams with crack damage. The optimised mesh and high-precision buckling load and buckling mode solutions satisfying the preset error tolerance were obtained.

The results of testing typical examples show that (1) the established section damage defect analogy scheme of circular arc curved beam crack can effectively realise the simulation of crack size (depth), position and number. The solution strictly satisfies the preset error tolerance; (2) the non-uniform mesh refinement in the algorithm can be adapted to solve the arbitrary order frequencies and modes of cracked cylindrical shells under the conditions of different ring wave numbers, crack positions and crack depths; and (3) the change in the buckling mode caused by crack damage is applicable to the study of elastic buckling under various curved beam angles and crack damage distribution conditions.

This study can provide a novel strategy for the adaptive mesh refinement for finite element analysis of elastic buckling of circular arc curved beams with crack damage. The adaptive mesh refinement method established in this study is fundamentally different from the conventional finite element method which employs the user experience to densify the meshes near the crack. It can automatically and flexibly generate a set of optimised local meshes by iteratively dividing the fine mesh near the crack, which can ensure the high accuracy of the buckling loads and modes. The micro-crack in curved beams is also characterised by weakening the cross-sectional stiffness to realise the characterisation of locations, depths and distributions of multiple crack damage, which can effectively analyse the disturbance behaviour of different forms of micro-cracks on the dynamic behaviour of beams.