Two‐level approximation concept in structural synthesis

Abstract

A new concept for complex structural optimization problems is presented. Based on investigation of the mechanical nature of the studied problem, a set of basic mechanical characteristics can be introduced as the generalized variables. A high-quality explicit first-level approximate problem FA is formed by first-order Taylor series expansion of the behaviour constraints in terms of the generalized variables. The FA is explicit but highly non-linear with respect to design variables. Therefore, a second-level approximation is introduced to solve the F A by considering a sequence of second-level approximate problems SA in the design variable space. This approach is a Two-Level Approximation Concept. Its application to space frame synthesis shows its good grasp of the mechanical nature of the problem. The computational results for several examples show that the method presented in this paper is very efficient.

DCOC: An optimality criteria method for large systems Part I: theory

“…The approximation methodology was generalized in recent years Salajegheh 1988, 1989;Zhou 1989;Zhou and Xia 1990;Canfield 1990) for a much broader class of structures. These authors have realized that for more complex structural systems, such as frames qr plates or some geometrical optimization problems, the behavioural constraints are more directly influenced by some intermediate quantities rather than the design variables themselves.…”

Approximation concepts for optimum structural design — a review

“…Vanderplaats (1986/1987) and Vanderplaats and Salajegheh (1988) recommended linearizing framework eigenvalues (squared frequencies) in terms of the direct section properties (DSP). Zhou and Xhia (1990a) proposed a two-level approximation to solve framework problems. At the first level, the relevant behaviour variables (e.g.…”

Two-level multipoint constraint approximation concept for structural optimization

“…For each of them, another sequence of approximate problems called the second-level approximate problems is constructed by Taylor expansions, which is solved easily by using dual theory of mathematical programming. The twolevel approximation concept employed here has appeared in the former work of frame synthesis (see Zhou and Xia 1990). The effectiveness of the method presented is demonstrated on a number of numerical examples.…”

“…The intermediate/generalized variables may be the reciprocal truss areas and plate thicknesses, the reciprocal sectional properties of frames, or even the mixing of the direct and reciprocal variables. For example, the reciprocals of the element cross-sectional areas and the moments of inertia were taken as the intermediate variables for frame synthesis problems (see Zhou and Xia 1990) and high quality approximations to static structural responses are generated, especially for displacements. In addition, other approximation techniques based on intermediate responses have also been developed.…”