**6. References**

	- [10] M. Pircher, R. Bridge, The influence of circumferential weld-induced imperfections on the buckling of silos and tanks, *Journal of Constructional Steel Research*, 57(5), p. 569-580, 2001

**Chapter 2** 

© 2012 Maalawi, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

distribution, and reproduction in any medium, provided the original work is properly cited.

1

**Stability, Dynamic and Aeroelastic Optimization** 

Numerous applications of numerical optimization to various structural design problems have been addressed in the literature. A comprehensive survey on this issue was given in [1], presenting a historical review and demonstrating the future needs to assimilate this technology into the practicing design environment. Different approaches were applied successfully by several investigators for treating stress, displacement, buckling and frequency optimization problems. In general, design optimization seeks the best values of a set of *n* design variables represented by the vector, Xnx1, to achieve, within certain *m* constraints, Gmx1(X), its goal of optimality defined by a set of *k* objective functions, Fkx1(X), for specified environmental conditions (see Figure 1). Mathematically, design optimization may be cast in the following standard form: Find the design variables Xnx1

1

Gj(X) 0 , j=1,2,………I (1b)

Gj(X) = 0 , j=I+1,I+2,….m (1c)

0 1

*W*

*W* 

*fi*

*fi*

and reproduction in any medium, provided the original work is properly cited.

*i F(X) (X) W F* 

1

*i*

*k*

*fi i*

(1a)

(1d)

*k*

**of Functionally Graded Composite Structures** 

Karam Maalawi

**1. Introduction** 

that minimize

subject to

http://dx.doi.org/10.5772/45878

Additional information is available at the end of the chapter

