Sage Journals: Discover world-class research

Abstract

In this paper an efficient method is presented to reduce the computational complexity of analysis of structures in the process of size and geometry optimization by genetic algorithms. Applying the present method, results in simultaneously swift analysis and optimal design of structures. In this method, using matrix computations, fast solution of the structures is obtained. The analysis of the structures in the optimal design via GA, includes the solution of the relationship F = KΔ in each generation of the genetic algorithm. Inverting the stiffness matrix in each generation and for each population for finding the displacements and internal forces is very time-consuming and costly. Here, using a closed-form matrix solution, compatible with the features of genetic algorithms, the amount of computations is decreased. The optimal analysis of optimal size is performed using a modified solution for structures with changed members and the optimal analysis of optimal geometry is done via a modified solution for structures with changed supports and nodes. To make the method more efficient, proper orderings are presented using the concept of Fiedler vector and partitioning matrices.

Keywords

optimal analysis size and geometry optimal design genetic algorithm structures

Get full access to this article

View all access options for this article.

References

Abouhamze

and Shakeri

(2007). “Multi-objective stacking sequence optimization of laminated cylindrical panels using a genetic algorithm and neural networks”, Composite Structures, Vol. 81, No. 2, pp. 253–263.

Adams

D.B.

Watson

L.T.

Gürdal

and Anderson-Cook

C.M.

(2004). “Genetic algorithm optimization and blending of composite laminates by locally reducing laminate thickness”. Advances in Engineering Software, Vol. 35, No. 11, pp. 35–43.

Madeira

Aguilar J.F.

Rodrigues

and Pina

(2005). “Multi-objective optimization of structures topology by genetic algorithms”, Advances in Engineering Software, Vol. 36, No. 1, pp. 21–28.

Bouazizi

M.L.

Ghanmi

and Bouhaddi

(2009). “Multi-objective optimization in dynamics of the structures with nonlinear behavior: Contributions of the metamodels”, Finite Elements in Analysis and Design, Vol. 45, No.10, pp. 612–623.

Fiedler

(1973). “Algebraic connectivity of graphs”, Czechoslovak Mathematical Journal, Vol. 23, No. 2, pp. 298–305.

Kaveh

(2006). Optimal Structural Analysis, second edition, John Wiley, Chichester, U.K.

Kaveh

(2013). Optimal Analysis of Structures by Concepts of Symmetry and Regularity, Springer Verlag, GmbH, Wien-NewYork.

Kaveh

Rahami

and Mehanpour

(2012). “Static and modal analyses of structures with different repeated patterns”, Advances in Engineering Software, Vol. 51, September, pp. 1–9.

Kaveh

Shojaei

Golipour

Rahami

(2013). “Seismic design of eccentric braced frames using multi-objective optimization”, Structural Engineering and Mechanics (Techno Press), Vol. 45, No. 2, pp. 211–232.

10.

Shojaei

Kaveh

and Rahami

(2013). “Analysis of structures convertible to repeated structures using graph products”, Computers and Structures, Vol. 125, pp. 153–163.

11.

Lee

D.S.

Morillo

Bugeda

Oller

and Onate

(2012). “Multilayered composite structure design optimisation using distributed/parallel multi-objective evolutionary algorithms”, Composite Structures, Vol. 94, No. 3, pp. 1087–1096.

12.

Kaveh

and Rahami

(2006). “An efficient method for decomposition of regular structures using graph products”, International Journal for Numerical Methods in Engineering, Vol. 61, No. 11, pp. 1797–1808.

13.

Luo

Rong

and Zhang

(2013). “Interval multi-objective optimisation of structures using adaptive Kriging approximations”, Computers and Structures, Vol. 119, April, pp. 68–84.

14.

Sedaghati

(2005). “Benchmark case studies in structural design optimization using the force method”, International Journal of Solids and Structures, Vol. 42, Nos. 21–22, pp. 5848–5871.

15.

Wehrens

Pretsch

and Buydens

L.M.C.

(1999). “The quality of optimisation by genetic algorithms”, Analytica Chimica Acta, Vol. 388, No. 3, pp. 265–271.

Swift Analysis for Size and Geometry Optimization of Structures

Abstract

Keywords

Get full access to this article

References