Problems of Structural Optimisation for Post-buckling Behaviour

Introduction

The maximization of the instability load for a prescribed volume of a designed element is a standard problem of optimization under stability constraints. The analysis of nonlinear post-buckling behaviour and the influence of imperfections are, in general, not included in such a standard formulation and therefore important information about the behaviour of a designed element after buckling is not provided. Very often the standard optimal structure represents unstable post-buckling behaviour and is

very sensitive to imperfections. This is a drawback of the design and it indicates that the combination of geometrically nonlinear analysis with the design procedure is necessary, especially from a practical point-of-view. Because of its complexity, this area of research has not been broadly investigated so far. Only recently have papers been published dealing with the optimization of geometrically nonlinear structures exposed to a loss of stabilit (Godoy 1996; Mroz and Piekarski 1996, 1998; Perry and

Grurdal 1996; Pietrzak 1996; Cardoso et al. 1997; Sousa et al. 1999; Sorokin and Terentiev 2001). It has been shown that if geometrical nonlinearity is allowed for and nonlinear instability analysis is performed, more accurate information about the behaviour of the optimized structure can be provided. It is possible to evaluate the quality of the design and, if necessary, to reject solutions that are not applicable. Furthermore, it is possible to implement nonlinear constraints into the formulation of the optimization problem and hence to modify the design. Post-buckling constraints of a special form that depends on the type of instability are added to the mathematical programming problem, which allows the nonlinear equilibrium path of the optimized structure to be altered and a stable post-buckling path to be created. This concept was proposed by Bochenek (1993), and then applied to solving many nonlinear optimization problems (Bochenek 1996, 1997a,b, 1999a,b; Bochenek and Kruzelecki 2001; Bochenek and Bielski 2001).

download link: 

http://sh.st/JWxQu

or

http://cutt.us/24V25