scholarly journals Approaches to the Automatic Generation and Control of Finite Element Meshes

1988 ◽  
Vol 41 (4) ◽  
pp. 169-185 ◽  
Author(s):  
Mark S. Shephard
Keyword(s):  
Finite Element ◽  
Geometric Modeling ◽  
A Priori ◽  
Automatic Generation ◽  
Element Mesh ◽  
Algorithmic Approaches ◽  
Automatic Mesh ◽  
And Control ◽  
Mesh Generators ◽  
User Intervention

This review paper discusses the algorithmic approaches being taken to the development of finite element mesh generators capable of automatically discretizing general domains without the need for user intervention. The paper demonstrates that because of the modeling demands placed on an automatic mesh generator, all the approaches taken to date produce unstructured meshes. Consideration is also given to both a priori and a posteriori mesh control devices for automatic mesh generators as well as their integration with geometric modeling and adaptive analysis procedures.

A Constrained Optimization Approach to Finite Element Mesh Smoothing

1991 ◽  
Author(s):  
V. N. Parthasarathy ◽  
Srinivas Kodiyalam
Keyword(s):  
Finite Element ◽  
Constrained Optimization ◽  
Finite Element Mesh ◽  
Optimization Approach ◽  
Element Mesh ◽  
Initial Mesh ◽  
Nodal Coordinates ◽  
Automatic Mesh ◽  
Mesh Generators

Abstract The quality of a finite element solution has been shown to be affected by the quality of the underlying mesh. A poor mesh may lead to unstable and lor inaccurate finite element approximations. Mesh quality is often characterized by the “smoothness” or “shape” of the elements (triangles in 2-D or tetrahedra in 3-D). Most automatic mesh generators produce an initial mesh where the aspect ratio of the elements are unacceptably high. In this paper, a new approach to produce acceptable quality meshes from an initial mesh is presented. Given an initial mesh (nodal coordinates and element connectivity), a “smooth” final mesh is obtained by solving a constrained optimization problem. The variables for the iterative optimization procedure are the nodal coordinates (excluding, the boundary nodes) of the finite element mesh, and appropriate bounds are imposed on these to prevent an unacceptable finite element mesh. Examples are given of the application of the above method for 2/3-D triangular meshes generated using a QUADTREE | OCTREE automatic mesh generators. Results indicate that the new method not only yields better quality elements when compared with the traditional Laplacian smoothing, but also guarantees a valid mesh unlike the Laplacian method.

Automatic Finite Element Mesh Generation Over Intersecting Rigid Body-Movable Subdomains for the Automation of Parametric Conceptual Design

1994 ◽  
Vol 116 (4) ◽  
pp. 1049-1057 ◽  
Author(s):  
H. Yang ◽  
D. A. Hoeltzel
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Computer Aided Design ◽  
Geometric Modeling ◽  
Combustion Engine ◽  
Three Dimensional ◽  
Automatic Generation ◽  
Element Mesh ◽  
Geometric Primitives ◽  
Dimensional Domain

An approach for the automatic generation and refinement of three-dimensional finite element meshes subdivided by multiply connected, rigid body movable subdomains has been developed. A combination of computational geometry and geometric modeling techniques have been employed to implement parametric computer-aided design based on the finite element method. Nonconvexity of an overall three-dimensional domain has been handled by combining convex geometric primitives as subdomains for the construction of a three-dimensional domain. A clipping technique is employed for determining intersection points between subdomains bounded by traingulated surface, following their rigid body movements. To demonstrate the utility of this approach to parametric redesign, a series of meshes that model a hip joint prosthesis and a reciprocating internal combustion engine, as assemblies of parametrically-defined geometric primitives, has been developed.

Update to: Approaches to the Automatic Generation and Control of Finite Element Meshes

1996 ◽  
Vol 49 (10S) ◽  
pp. S5-S14 ◽  
Author(s):  
Mark S. Shephard
Keyword(s):  
Mesh Generation ◽  
Three Dimensional ◽  
Automatic Generation ◽  
Tetrahedral Mesh ◽  
Hexahedral Mesh ◽  
Automatic Mesh Generation ◽  
The Status ◽  
Automatic Mesh ◽  
And Control ◽  
Mesh Generators

This paper updates the status of efforts on the development of automatic mesh generation techniques for general three-dimensional domains. The technical areas reviewed include: (i) issues associated with automatic mesh generation of CAD geometric models, (ii) local mesh modification procedures for improving mesh quality, (iii) advances in tetrahedral mesh generators, (iv) generation of anisotropic meshes, (v) hexahedral mesh generators, and (vi) implementation of automatic mesh generators on parallel computers.

Automatic Finite Element Mesh Generation Over Intersecting Rigid Body-Movable Subdomains for the Automation of Parametric Conceptual Design

1991 ◽  
Author(s):  
Hyunik Yang ◽  
David A. Hoeltzel
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Computer Aided Design ◽  
Geometric Modeling ◽  
Combustion Engine ◽  
Three Dimensional ◽  
Automatic Generation ◽  
Triangulated Surfaces ◽  
Geometric Primitives ◽  
Dimensional Domain

Abstract An approach for the automatic generation and refinement of three dimensional finite element meshes subdivided by multiply connected, rigid body movable subdomains has been developed. A combination of computational geometry and geometric modeling techniques have been employed to implement parametric computer-aided design based on the finite element method. Nonconvexity of an overall three dimensional domain has been handled by combining convex geometric primitives as subdomains for the construction of a three dimensional domain. A clipping technique is employed for determining intersections points between subdomains bounded by triangulated surfaces, following their rigid body movements. To demonstrate the utility of this approach to parametric redesign, a series of meshes that model a hip joint prosthesis and a reciprocating internal combustion engine, as assemblies of parametrically-defined geometric primitives, have been developed.

Requirements for a solid modeler coupled to finite-element mesh generators

1998 ◽  
Vol 34 (5) ◽  
pp. 3447-3450 ◽  
Author(s):  
A. Liddy ◽  
C. De Castro Magaihaes ◽  
R.C. Mesquita
Keyword(s):  
Finite Element ◽  
Finite Element Mesh ◽  
Element Mesh ◽  
Solid Modeler ◽  
Mesh Generators

A GENETIC ALGORITHM BASED PROCEDURE FOR AUTOMATIC CRACK PROFILE IDENTIFICATION

2005 ◽  
Vol 02 (03) ◽  
pp. 401-417 ◽  
Author(s):  
YUNHUA LUO ◽  
ARVIND SHAH
Keyword(s):  
Genetic Algorithm ◽  
Finite Element ◽  
Geometric Modeling ◽  
Geometric Model ◽  
Automatic Identification ◽  
Element Mesh ◽  
Improve Accuracy ◽  
Forward Problems ◽  
Structural Responses ◽  
Improving Accuracy

This paper presents a genetic algorithm based procedure for automatic identification of crack profiles. In the procedure geometric modeling technique is applied to incorporate crack(s) into the structure under evaluation and a geometric model is generated. The geometric model is then used to generate finite element mesh. In solving forward problems, finite element meshes are adapted based on error estimation to improve accuracy in computed structural responses. Numerical results show that error from solving forward problems can largely slow down GA convergence and significantly affect the accuracy of estimated crack parameters. Mesh adaptation can effectively reduce the error, thus speeding up the convergence and improving accuracy.

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