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On the development and some applicat...

BaniHani, Suleiman Mohammad.

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On the development and some application of a genetic algorithm based lookup table approach for efficient numerical integration in the method of finite spheres.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	On the development and some application of a genetic algorithm based lookup table approach for efficient numerical integration in the method of finite spheres./
作者:	BaniHani, Suleiman Mohammad.
面頁冊數:	168 p.
附註:	Adviser: Suvranu De.
Contained By:	Dissertation Abstracts International68-06B.
標題:	Applied Mechanics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3272177
ISBN:	9780549116813

On the development and some application of a genetic algorithm based lookup table approach for efficient numerical integration in the method of finite spheres.
BaniHani, Suleiman Mohammad.

On the development and some application of a genetic algorithm based lookup table approach for efficient numerical integration in the method of finite spheres. - 168 p.

Adviser: Suvranu De.

Thesis (Ph.D.)--Rensselaer Polytechnic Institute, 2007.

There is significant current interest in the development of "meshfree" numerical techniques to overcome long standing drawbacks of traditional finite element methods. However, numerical integration poses a formidable challenge to the efficient implementation and widespread use of these methods since the integrands arising in the Galerkin weak form are nonpolynomial rational functions and the integration domains are complex. The problem is more so when higher-order derivatives are involved. In this thesis we develop a novel numerical integration method based on a Genetic Algorithm-based lookup table approach for the method of finite spheres, a meshfree numerical method for solving boundary value problems.

ISBN: 9780549116813Subjects--Topical Terms:

1018410
Applied Mechanics.

On the development and some application of a genetic algorithm based lookup table approach for efficient numerical integration in the method of finite spheres.
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245 1 0 $a On the development and some application of a genetic algorithm based lookup table approach for efficient numerical integration in the method of finite spheres.
300 $a 168 p.
500 $a Adviser: Suvranu De.
500 $a Source: Dissertation Abstracts International, Volume: 68-06, Section: B, page: 4083.
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520 $a There is significant current interest in the development of "meshfree" numerical techniques to overcome long standing drawbacks of traditional finite element methods. However, numerical integration poses a formidable challenge to the efficient implementation and widespread use of these methods since the integrands arising in the Galerkin weak form are nonpolynomial rational functions and the integration domains are complex. The problem is more so when higher-order derivatives are involved. In this thesis we develop a novel numerical integration method based on a Genetic Algorithm-based lookup table approach for the method of finite spheres, a meshfree numerical method for solving boundary value problems.
520 $a In this technique, the integration points and weights are generated using Genetic Algorithms and stored in a lookup table using normalized coordinates as part of an offline computational step. During online computations, this lookup table is used much like a table of Gaussian integration points and weights in the finite element computations. This technique offers significant reduction of computational time without sacrificing accuracy.
520 $a We have applied the numerical integration technique to successfully solve a variety of problems in computational mechanics. The application to thin and thick plate problems is particularly remarkable since the integrands are highly peaked and alternative integration techniques such as Gauss quadrature and adaptive integration lead to divergence of the solution results unless a very large number of integration points is used.
520 $a Solving a few example problems is not sufficient to demonstrate the stability of the solution procedure. Hence numerical inf-sup tests have been applied to evaluate the stability of displacement-based and mixed discretization schemes for the solution of Reissner-Mindlin plate problems. While, like linear finite elements, pure displacement-based approximation spaces with linear consistency do not pass the inf-sup test and exhibit shear locking, quadratic discretizations, unlike quadratic finite elements, pass the test. Pure displacement-based and mixed approximation spaces that pass the numerical inf-sup test exhibit optimal or near optimal convergence behavior. Our final example concerns the solution of "strain gradient" plasticity models developed to account for the length scale dependence of micron-scale metallic materials. Using the traditional finite element method to solve the resulting boundary value problem leads to a rapid deterioration of the solution results with increase in strain gradient. Using the method of finite spheres and the new numerical integration procedure, we observe excellent convergence rates which may be attributed to the higher-order continuity of the meshfree approximations.
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650 4 $a Applied Mechanics. $3 1018410
650 4 $a Artificial Intelligence. $3 769149
650 4 $a Engineering, Mechanical. $3 783786
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710 2 $a Rensselaer Polytechnic Institute. $3 1019062
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