An improved element removal method for evolutionary structural optimization

The efficiency of the element removal or addition is of significance for evolutionary structural optimization (ESO) process. The key is to find an appropriate rejection criterion (RC) which allows to assess the contribution of each element to the specified behavior（stress, stiffness, displacement, etc.）of the structure, and to subsequently remove elements with least contribution. This paper proposed a varying elements removal ratio (VERR) method which uses a larger ERR (Element Rejection Ratio) value at early iterations where exist a lot of redundant material, and decreases the value of ERR in the optimal process to lessen the number of elements removed at later iterations. Meanwhile, this paper proposed a strategy for element addition based on stress level and the contribution of elements to the structure in order to decide which elements should be added to the model and the sequence of the element addition. With the proposed VERR and the strategy, the optimization procedure of the structure evolves more quickly and smoothly.

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A Finite Element Removal Method for 3D Topology Optimization

Advances in Mechanical Engineering ◽

10.1155/2013/413463 ◽

2013 ◽

Vol 5 ◽

pp. 413463 ◽

Cited By ~ 4

Author(s):

M. Akif Kütük ◽

İbrahim Göv

Keyword(s):

Finite Element ◽

Topology Optimization ◽

Removal Method ◽

Element Removal Method ◽

3D Topology ◽

Element Removal

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Element removal method for singular minimizers in variational problems involving Lavrentiev phenomenon

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1992.0138 ◽

1992 ◽

Vol 439 (1905) ◽

pp. 131-137 ◽

Cited By ~ 6

Keyword(s):

Numerical Methods ◽

Numerical Method ◽

Numerical Experiments ◽

Variational Problems ◽

Lavrentiev Phenomenon ◽

Removal Method ◽

Element Removal Method ◽

Element Removal ◽

Singular Minimizers

A numerical method called element removal method is designed to calculate singular minimizers which cannot be approximated by simple applications of standard numerical methods because of the so-called Lavrentiev phenomenon. The convergence of the method is proved. The results of numerical experiments show that the method is effective.

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ELEMENT REMOVAL METHOD FOR SINGULAR MINIMIZERS IN PROBLEMS OF HYPERELASTICITY

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202595000231 ◽

1995 ◽

Vol 05 (03) ◽

pp. 387-399 ◽

Cited By ~ 6

Author(s):

ZHIPING LI

Keyword(s):

Finite Element ◽

Numerical Method ◽

Lavrentiev Phenomenon ◽

Removal Method ◽

Finite Element Approximations ◽

Element Removal Method ◽

Element Removal ◽

Admissible Functions ◽

Singular Minimizers

A numerical method called element removal method is applied to calculate singular minimizers in problems of hyperelasticity. The method overcomes the difficulty in finite element approximations caused by restrictions, such as det (I+∇u)>0, on admissible functions and can avoid Lavrentiev phenomenon if it does occur in the problem. The convergence of the method is proved.

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A constraint and algorithm for stress-based evolutionary structural optimization of the tie-beam problem

Engineering Computations ◽

10.1108/ec-09-2014-0186 ◽

2015 ◽

Vol 32 (6) ◽

pp. 1753-1778 ◽

Cited By ~ 1

Author(s):

Da-Ke Zhang ◽

Sheng Liang ◽

Yi-Chao Yang ◽

Hai-Tao Zhou

Keyword(s):

Structural Optimization ◽

Load Path ◽

Content Type ◽

Evolutionary Structural Optimization ◽

Stress Threshold ◽

Special Cases ◽

Stress Changes ◽

Virtual Stiffness ◽

Optimum Solution ◽

Element Removal

Purpose – The purpose of this paper is to present a constraint and corresponding algorithm enhancing the evolutionary structural optimization (ESO) method, aiming to circumvent its structure break down problem in some special cases, such as the tie-beam problem. Design/methodology/approach – A virtual soft material introduced to an element will change the stiffness of the element and may consequently change the stress distribution of that element and its neighbors. With this property, the virtual stiffness of the selected element is calculated and the threshold of the stress changes is derived. The stress threshold is used to evaluate the role of an element on the load path and therefore decide the contribution of the element to the structure. Adding this checking operation into the original ESO iterations enables validation of element removal. Findings – The reason for structure break down with the ESO method is that the element removal criterion of ESO only works for certain optimal objectives. It cannot guarantee that the structure does not fail. The proposed operation offers a stronger and stricter constraint condition for ESO’s element removal process, preventing the structure from breaking down in some special cases. Originality/value – The tests on several examples reported in the literature show that the proposed method has the same ability to achieve an optimum solution as the original ESO methods do, while avoiding incorrect deletion of structurally important elements. The benchmark tie-beam problem is solved successfully with this algorithm. The method can be used in other situations as well.

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Bi-Directional Evolutionary Structural Optimization Method with Draw Direction Constraints

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.420.346 ◽

2013 ◽

Vol 420 ◽

pp. 346-351

Author(s):

Tien Tung Chung ◽

Jia Pei Wang ◽

Yan Zuo Chen ◽

Ta Chuan Liu

Keyword(s):

Structural Optimization ◽

Mechanical Design ◽

Optimization Method ◽

Optimized Design ◽

Design Problems ◽

Closed Cavity ◽

Evolutionary Structural Optimization ◽

Draw Direction ◽

Beso Method ◽

Element Removal

This paper proposes a new bi-directional evolutionary structural optimization (BESO) method with draw direction constraints. Draw direction constraints, defined by required manufacturing process, are achieved by modifying element removal/addition criteria such that elements are removed from the top surface of the draw direction to the inner design domain. The optimized design with draw direction constraints is free from hollow or closed cavity geometries which are infeasible for manufacturing. A stiffness design of a motor front cover is carried out to show the ability of the proposed method in practical mechanical design problems.

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