• Structural Engineering and Mechanics
• /
• v.74 no.4
• /
• pp.547-557
• /
• 2020

In this paper, an automatic adaptive mesh refinement procedure is presented for two-dimensional problems on the basis of a new probabilistic error estimator. First-order perturbation theory is employed to determine the lower and upper bounds of the structural displacements and stresses considering uncertainties in geometric sizes, material properties and loading conditions. A new probabilistic error estimator is proposed to reduce the mesh dependency of the responses dispersion. The suggested error estimator neglects the refinement at the critical points with stress concentration. Therefore, the proposed strategy is combined with the classic adaptive mesh refinement to achieve an optimal mesh refined properly in regions with either high gradients or high dispersion of the responses. Several numerical examples are illustrated to demonstrate the efficiency, accuracy and robustness of the proposed computational algorithm and the results are compared with the classic adaptive mesh refinement strategy described in the literature.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.11
• /
• pp.2932-2943
• /
• 1994

An efficient approach to the automatic construction of effective quadrilateral finite element meshes for two-dimensional analysis is presented. The procedure is composed of, firstly, an initial mesh generation and, secondly, an h-version of adaptive refinement based on error analysis. As for an initial mesh generation scheme, a modified looping algorithm has been employed. For the adaptive refinement process, an error indicator obtained by computing the residual error of the equilibrium equations in the energy norm with a relaxation factor has been employed. Examples of mesh generation and self-adaptive mesh improvements are given. These example solutions demonstrate that an effective mesh for a given error tolerance can be obtained in a few steps of the analysis processes.

• Structural Engineering and Mechanics
• /
• v.75 no.6
• /
• pp.685-699
• /
• 2020

Polygonal finite element provides a great flexibility in mesh generation of crack propagation problems where the topology of the domain changes significantly. However, the control of the discretization error in such problems is a main concern. In this paper, a polygonal-FEM is presented in modeling of crack propagation problems via an automatic adaptive mesh refinement procedure. The adaptive mesh refinement is accomplished based on the Zienkiewicz-Zhu error estimator in conjunction with a weighted SPR technique. Adaptive mesh refinement is employed in some steps for reduction of the discretization error and not for tracking the crack. In the steps that no adaptive mesh refinement is required, local modifications are applied on the mesh to prevent poor polygonal element shapes. Finally, several numerical examples are analyzed to demonstrate the efficiency, accuracy and robustness of the proposed computational algorithm in crack propagation problems.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1990.10a
• /
• pp.9-15
• /
• 1990

In this study, an adaptive mesh h-refinement procedure was presented in plate bending problems. By introducing the transition elements for the procedure, same drawbacks due to the irregular nodes are eliminated which are generated in the consequence of local mesh refinement in common adaptive h-version performed by single type of quadrilateral elements. For the above objective, compatible 5-node through 7-node transition plate bending elements are developed by including variable number of midside nodes. Using the Zienkiewicn-Zhu error estimator, some numerical examples are presented to show the effectiveness of the adaptive h-refinement using the transition elements.

• Structural Engineering and Mechanics
• /
• v.17 no.3_4
• /
• pp.379-391
• /
• 2004

This paper deals with the development of h-version adaptive mesh refinement and recovery strategy using variable-node elements and its application to various engineering field problems with 2D quadrilateral and 3D hexahedral models. The variable-node elements which have variable mid-side nodes on edges or faces are effectively used in overcoming some problems in connecting the different layer patterns of the transition zone between the refined and coarse mesh. A modified recovery technique of gradients adequate for variable-node elements and proper selection of error norms for each engineering field problems are proposed. In the region in which the error is greater than the permissible refinement error, the mesh is locally refined by subdivision. Reversely, in some parts of the domain having the error smaller than the permissible recovery error, the mesh is locally recovered (coarsened) by combination. Hierarchical structures (e.g. quadtrees and octrees) and element-based storage structures are composed to perform this adaptive process of refinement and recovery. Some numerical examples of a 3D heat conduction analysis of the concrete with hydration heat and a 2D flow analysis of vortex shedding show effectiveness and validity of the proposed scheme.

• Structural Engineering and Mechanics
• /
• v.11 no.4
• /
• pp.443-460
• /
• 2001

This paper presents an effective application of a variable-node axisymmetric solid element designated as AQV (Axisymmetric Quadrilateral Variable-node element). The variable-node element with physical midside nodes helps to overcome some problems in connecting the different layer patterns on a quadrilateral mesh in the adaptive h-refinement. This element alleviates the necessity of imposing displacement constraints on irregular (hanging) nodes in order to enforce the inter-element compatibility. Therefore, the elements with variable mid-side nodes can be used effectively in the local mesh refinement for the axisymmetric structures which have stress concentrations. A modified Gaussian quadrature should be adopted to evaluate the stiffness matrices of the variable-node elements mainly because of the slope discontinuity of assumed displacement within the elements. Some numerical examples show the usefulness of variable-node axisymmetric elements in the practical application.

• 한국전산유체공학회:학술대회논문집
• /
• 2010.05a
• /
• pp.534-541
• /
• 2010

A high-order accurate Euler flow solver based on a discontinuous Galerkin method has been developed for the numerical simulation of unsteady flows on unstructured meshes. A multi-level solution-adaptive mesh refinement/coarsening technique was adopted to enhance the resolution of numerical solutions efficiently by increasing mesh density in the high-gradient region. An acoustic wave scattering problem was investigated to assess the accuracy of the present discontinuous Galerkin solver, and a supersonic flow in a wind tunnel with a forward facing step was simulated by using the adaptive mesh refinement technique. It was shown that the present discontinuous Galerkin flow solver can capture unsteady flows including the propagation and scattering of the acoustic waves as well as the strong shock waves.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 2004.10a
• /
• pp.79-82
• /
• 2004

In this study, a new refinement technique for 3-dimensional hexahedral element mesh is proposed, which is aimed at the control of mesh density. With the proposed scheme the mesh is refined adaptively to the elemental error which is estimated by 'a posteriori' error estimator based on the energy norm. A desired accuracy of an analysis i.e. a limit of error defines the new desired mesh density map on the current mesh. To obtain the desired mesh density, the refinement procedure is repeated iteratively until no more elements to be refined exist. In the algorithm, at first the regions of mesh to be refined are defined and, then, the zero-thickness element layers are inserted into the interfaces between the regions. All the meshes in the regions, in which the zero-thickness layers are inserted, are to be regularized in order to improve the shape of the slender elements on the interfaces. This algorithm is tested on a simple shape of 2-d quadrilateral element mesh and 3-d hexahedral element mesh. A numerical example of elastic deformation of a plate with a hole shows the effectiveness of the proposed refinement scheme.

• Proceedings of the KSME Conference
• /
• 2007.05a
• /
• pp.632-635
• /
• 2007

Automobile tire has very complicated shape and is composed of rubber, steel cord and ply cord, Tread pattern of tire is very essential for the basic characteristics of tire, such as braking, acceleration and comfortableness. Tire components such as tread, sidewall, and spex are prepared by forcing uncured rubber compound through an extruder to shape during curing process. Because of its complexity of shape, adaptive mesh refinement was used for the analysis of tire tread. Effects of forming variables were evaluated.

• Wind and Structures
• /
• v.1 no.1
• /
• pp.111-125
• /
• 1998

This paper deals with the development of variable-node element and its application to the adaptive h-version mesh refinement-recovery for the incompressible viscous flow analysis. The element which has variable mid-side nodes can be used in generating the transition zone between the refined and unrefined element and efficiently used for the construction of a refined mesh without generating distorted elements. A modified Guassian quadrature is needed to evaluate the element matrices due to the discontinuity of derivatives of the shape functions used for the element. The penalty function method which can reduce the number of the independent variables is adopted for the purpose of computational efficiency and the selective reduced integration is carried out for the convection and pressure terms to preserve the stability of solution. For the economical analysis of transient problems in which the locations to be refined are changed in accordance with the dynamic distribution of velocity gradient, not only the mesh refinement but also the mesh recovery is needed. The numerical examples show that the optimal mesh for the finite element analysis of a wind around the structures can be obtained automatically by the proposed scheme.