Stretched grid method: Difference between revisions
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The '''Stretched Grid Method (SGM)''' is a [[Numerical_analysis|numerical technique]] for finding approximate solutions of various mathematical and engineering problems that can be related to an elastic grid behavior such as |
The '''Stretched Grid Method (SGM)''' is a [[Numerical_analysis|numerical technique]] for finding approximate solutions of various mathematical and engineering problems that can be related to an elastic grid behavior such as |
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1.[http://FEM/BEM%20mesh%20smoothing FEM/BEM mesh |
1.[http://FEM/BEM%20mesh%20smoothing FEM/BEM mesh ]. |
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2.Minimum surfaces problem solution. |
2.Minimum surfaces problem solution. |
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4.Unfolding problem and cutting pattern generation. |
4.Unfolding problem and cutting pattern generation. |
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5.[http://References References] |
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In recent decades the finite element and boundary element methods (FEM and BEM) have become a mainstay for industrial engineering design and analysis. Increasingly larger and more complex designs are being simulated using the FEM or BEM. However, some problems of FEM/BEM Engineering analysis are still on the cutting edge. The first problem is a reliability of engineering analysis that strongly depends upon the quality of initial data generated at the pre-processing stage. It is known that automatic element mesh generation techniques at this stage have become commonly used tools for the analysis of complex real-world models (see [1]). With FEM/BEM increasing popularity comes the incentive to improve automatic meshing algorithms. However, all of these algorithms can create distorted and even unusable grid elements. Fortunately, several techniques exist which can take an existing mesh and improve its quality. For instance smoothing (also referred to as mesh relaxation) is one of such methods, which repositions nodal locations, so as to minimize element distortion. The Stretched Grid Method (SGM) allows the obtaining of pseudo-regular meshes very easily and quickly in a one-step solution. |
In recent decades the finite element and boundary element methods (FEM and BEM) have become a mainstay for industrial engineering design and analysis. Increasingly larger and more complex designs are being simulated using the FEM or BEM. However, some problems of FEM/BEM Engineering analysis are still on the cutting edge. The first problem is a reliability of engineering analysis that strongly depends upon the quality of initial data generated at the pre-processing stage. It is known that automatic element mesh generation techniques at this stage have become commonly used tools for the analysis of complex real-world models (see [1]). With FEM/BEM increasing popularity comes the incentive to improve automatic meshing algorithms. However, all of these algorithms can create distorted and even unusable grid elements. Fortunately, several techniques exist which can take an existing mesh and improve its quality. For instance smoothing (also referred to as mesh relaxation) is one of such methods, which repositions nodal locations, so as to minimize element distortion. The Stretched Grid Method (SGM) allows the obtaining of pseudo-regular meshes very easily and quickly in a one-step solution. |
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[[File:grid inside.jpg |2D mesh]] |
[[File:grid inside.jpg |2D mesh]] |
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Fig.1 |
Fig.1 |
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[[File:2D mesh.jpg |2D mesh]] |
[[File:2D mesh.jpg |2D mesh]] |
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Fig.2 |
Fig.2 |
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[[File:Dancepol net.jpg]] |
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[[File:Dancepol.jpg]] |
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[[File:Dancepol real.jpg]] |
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===References=== |
===References=== |
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[1] Tabarrok, Y.Xiong. Some Variational Formulations for minimum surface. Acta Mechanica, vol.89/1-4, 1991, pp.33-43. |
[1] Tabarrok, Y.Xiong. Some Variational Formulations for minimum surface. Acta Mechanica, vol.89/1-4, 1991, pp.33-43. |
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[8] [http://tent.k3-cottage.com/ K3-Tent system for tensile fabric structures formfinding and cutting patterning] |
[8] [http://tent.k3-cottage.com/ K3-Tent system for tensile fabric structures formfinding and cutting patterning] |
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[9] [http://www.kubantent.ru/ Kubantent partners] |
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Revision as of 14:38, 2 December 2011
The Stretched Grid Method (SGM) is a numerical technique for finding approximate solutions of various mathematical and engineering problems that can be related to an elastic grid behavior such as
2.Minimum surfaces problem solution.
3.Tensile fabric structures form finding.
4.Unfolding problem and cutting pattern generation.
FEM/BEM mesh refinement
In recent decades the finite element and boundary element methods (FEM and BEM) have become a mainstay for industrial engineering design and analysis. Increasingly larger and more complex designs are being simulated using the FEM or BEM. However, some problems of FEM/BEM Engineering analysis are still on the cutting edge. The first problem is a reliability of engineering analysis that strongly depends upon the quality of initial data generated at the pre-processing stage. It is known that automatic element mesh generation techniques at this stage have become commonly used tools for the analysis of complex real-world models (see [1]). With FEM/BEM increasing popularity comes the incentive to improve automatic meshing algorithms. However, all of these algorithms can create distorted and even unusable grid elements. Fortunately, several techniques exist which can take an existing mesh and improve its quality. For instance smoothing (also referred to as mesh relaxation) is one of such methods, which repositions nodal locations, so as to minimize element distortion. The Stretched Grid Method (SGM) allows the obtaining of pseudo-regular meshes very easily and quickly in a one-step solution.
Let us assume that there is an arbitrary triangle network bounded by plane poly-gonal single-coherent contour and produced by an automeshing procedure (see fig.1) It may be assumed further that the network considered as a physical nodal system is distorted by a number of distortions. It is supposed that the total potential energy of this system is proportional to the length of some n-dimensional vector with all network segments as its components.
Fig.1
Fig.2
References
[1] Tabarrok, Y.Xiong. Some Variational Formulations for minimum surface. Acta Mechanica, vol.89/1-4, 1991, pp.33-43.
[2] B.Tabarrok, Z.Qin. Form Finding and Cutting Pattern Generation for Fabric Tension Structures, -Microcomputers in Civil Engineering J., № 8, 1993, pp.377-384.
[3] Popov E.V., On Some Variational Formulations for Minimum Surface.- Transactions of Canadian Society of Mechanics for Engineering, Univ. of Alberta, vol.20, N 4, 1996, pp. 391-400.
[4] Popov E.V. Geometrical Modeling of Tent Fabric Structures with the Stretched Grid Method. //Proceedings of the 11th International Conference on Computer Graphics&Vision GRAPHICON’2001, UNN, Nizhny Novgorod, 2001. pp.138-143.
[5] Popov, E.V. Cutting pattern generation for tent type structures represented by minimum surfaces. The Transactions of the Canadian Society for Mechanical Engineering, Univ. of Alberta, vol. 22, N 4A, 1999, pp.369-377.
[8] K3-Tent system for tensile fabric structures formfinding and cutting patterning
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