• Structural Engineering and Mechanics
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• v.3 no.4
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• pp.391-410
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• 1995

The application of adaptive finite element method to dynamic problems is investigated. Both the kinetic and strain energy errors induced by space and time discretization were estimated in a consistent manner and controlled by the simultaneous use of the adaptive mesh generation and the automatic time stepping. Also an optimal ratio of spatial discretization error to temporal discretization error was discussed. In this study it was found that the best performance can be obtained when the specified spatial and temporal discretization errors have the same value. Numerical examples are carried out to verify the performance of the procedure.

• Structural Engineering and Mechanics
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• v.39 no.6
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• pp.767-793
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• 2011

An efficient edge-based smoothed finite element method (ES-FEM) has been recently developed for solving solid mechanics problems. The ES-FEM uses triangular elements that can be generated easily for complicated domains. In this paper, the complexity study of the ES-FEM based on triangular elements is conducted in detail, which confirms the ES-FEM produces higher computational efficiency compared to the FEM. Therefore, the ES-FEM offers an excellent platform for adaptive analysis, and this paper presents an efficient adaptive procedure based on the ES-FEM. A smoothing domain based energy (SDE) error estimate is first devised making use of the features of the ES-FEM. The present error estimate differs from the conventional approaches and evaluates error based on smoothing domains used in the ES-FEM. A local refinement technique based on the Delaunay algorithm is then implemented to achieve high efficiency in the mesh refinement. In this refinement technique, each node is assigned a scaling factor to control the local nodal density, and refinement of the neighborhood of a node is accomplished simply by adjusting its scaling factor. Intensive numerical studies, including an actual engineering problem of an automobile part, show that the proposed adaptive procedure is effective and efficient in producing solutions of desired accuracy.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.73-79
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• 2006

In this paper, we propose a new triangular finite element mesh generation method based on simplification of high-density mesh and adaptive Level-of-Detail (LOD) methods for efficient CAE. In our method, mesh simplification is used to control the mesh properties required for FE mesh, such as the number of triangular elements, element shape quality and size while keeping the specified approximation tolerance. Adaptive LOD methods based on vertex hierarchy according to curvature and region of interest, and global LOD method preserving density distributions are also proposed in order to construct a mesh more appropriate for CAE purpose. These methods enable efficient generation of FE meshes with properties appropriate for analysis purpose from a high-density mesh. Finally, the effectiveness of our approach is shown through evaluations of the FE meshes for practical use.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.271-274
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• 2007

The finite element linear buckling analysis of folded plate structures using adaptive h-refinement methods is presented in this paper. The variable-node flat shell element used in this study possesses the drilling D.O.F. which, in addition to improvement of the element behavior, permits an easy connection to other elements with six degrees of freedom per node. The Box-typed structures can be analyzed using these developed flat shell elements. By introducing the variable node elements some difficulties associated with connecting the different layer patterns, which are common in the adaptive h-refinement on quadrilateral mesh, can be overcome. To obtain better stress field for the error estimation, the super-convergent patch recovery is used. The convergent buckling modes and the critical loads associated with these modes can be obtained.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.7 s.178
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• pp.1763-1770
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• 2000

A finite element interface system for the design of optimal spot welding locations has been developed. In order to find out the optimal locations of spot welding points, iterative finite element an alyses are necessary, and thus automatic generation of finite element model for the structures with spot welded pointsis required. In this interface system, quadrilateral shell elements are automatically generated for finite element analysis of spot welded structured, which employs a domain decomposition methodand adaptive mesh(h-method).

• Journal of the korean Society of Automotive Engineers
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• v.10 no.6
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• pp.54-60
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• 1988

During recent years, a great deal of interest has emerged on the use of adaptive approaches and a posteriori estimates in finite element method. The results are intended to be used to improve the quality of finite element solution by changing the location of the nodes within a fixed number of degrees of freedom-so called r method-, and by increasing the order of polynomial approximation with the new degrees of freedom-p method. This paper deals with error analysis that contains the basic theory and method of deriving error estimates and adaptive processes applied to finite element solutions underlying the rpm method that is the combination of r and p method of finite element. It is shown that we can obtain more accurate solution by applying the method to the 2-dimensional heat transfer problem.

• Structural Engineering and Mechanics
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• v.83 no.3
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• pp.353-361
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• 2022

Linear Elastic Fracture Mechanics (LEFM) has been developed by applying stress analysis to determine the stress intensity factor (SIF, K). The finite element method (FEM) is widely used as a standard tool for evaluating the SIF for various crack configurations. The prediction accuracy can be achieved by applying an adaptive Delaunay triangulation combined with a FEM. The solution can be solved using either direct or iterative solvers. This work adopts the element-by-element preconditioned conjugate gradient (EBE-PCG) iterative solver into an adaptive FEM to solve the solution to heal problem size constraints that exist when direct solution techniques are applied. It can avoid the formation of a global stiffness matrix of a finite element model. Several numerical experiments reveal that the present method is simple, fast, and efficient compared to conventional sparse direct solvers. The optimum convergence criterion for two-dimensional LEFM analysis is studied. In this paper, four sample problems of a two-edge cracked plate, a center cracked plate, a single-edge cracked plate, and a compact tension specimen is used to evaluate the accuracy of the prediction of the SIF values. Finally, the efficiency of the present iterative solver is summarized by comparing the computational time for all cases.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.9 no.5
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• pp.50-56
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• 2010

Meshfree methods show many advantages over finite element method(FEM) in the class of problems for which the remeshing process is inevitable when the conventional FEM used, such as propagating crack problems, large deformation and so on. One of the promising applications of meshfree methods is the adaptive refinement for problems having multi-scale nature. In this study, an adaptive node generation procedure is proposed and several numerical examples are also presented to illustrate the efficiency of proposed method.

• Structural Engineering and Mechanics
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• v.15 no.5
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• pp.563-578
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• 2003

Delaunay triangulation is combined with an adaptive finite element method for analysis of two-dimensional crack propagation problems. The content includes detailed descriptions of the proposed procedure which consists of the Delaunay triangulation algorithm and an adaptive remeshing technique. The adaptive remeshing technique generates small elements around the crack tips and large elements in the other regions. Three examples for predicting the stress intensity factors of a center cracked plate, a compact tension specimen, a single edge cracked plate under mixed-mode loading, and an example for simulating crack growth behavior in a single edge cracked plate with holes, are used to evaluate the effectiveness of the procedure. These examples demonstrate that the proposed procedure can improve solution accuracy as well as reduce total number of unknowns and computational time.

• Journal of the Korean Society of Hazard Mitigation
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• v.10 no.1
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• pp.23-28
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• 2010

Reliable dynamic analysis is essential in order to properly maintain structures so that structural hazards may be minimized. The finite element method (FEM) is proven to be an affective approximate method of structural analysis if proper element types and meshes are chosen. When the method is applied to dynamics analyzed in time domain, the meshes may need to be modified at each time step. As many meshes need to be generated, adaptive mesh generation schemes have become an important part in complex time domain dynamic finite element analyses of structures. In this paper, an adaptive mesh generation scheme for dynamic finite element analyses of structures is described. The concept of representative strain value is used for error estimates and the refinements of meshes use combinations of the h-method (node movement) and the r-method (element division). The validity of the scheme is shown through a cantilever beam example under a concentrated load with varying values. The example shows reasonable accuracy and efficient computing time. Furthermore, the study shows the potential for the scheme's effective use in complex structural dynamic problems such as those under seismic or erratic wind loads.