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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 40
Edited by: B.H.V. Topping
Paper III.4

Multilevel Optimization of Large Scale Structures based on Combining Optimality Criterion and Mathematical Programming Algorithms

S. Maksimovic* and V. Zeljkovic#

*Aeronautical Institute, Belgrade, Yugoslavia
#Lola Institute, Belgrade, Yugoslavia

Full Bibliographic Reference for this paper
S. Maksimovic, V. Zeljkovic, "Multilevel Optimization of Large Scale Structures based on Combining Optimality Criterion and Mathematical Programming Algorithms", in B.H.V. Topping, (Editor), "Advances in Optimization for Structural Engineering", Civil-Comp Press, Edinburgh, UK, pp 65-72, 1996. doi:10.4203/ccp.40.3.4
The aim of the work presented here is the development of efficient method for minimum weight design of the stiffened thin-walled structures. An multilevel approach is used for optimization of structures modeled with bar, beam and layered shell finite elements subjected to stress, displacements, system stability and local buckling constraints. Multilevel optimization permits a large problem to be broken down into a number of smaller ones, at different levels according to the type of problem being solved. Optimization method presented here is based on combining optimality criterion (OC) and mathematical programming (MP) algorithms. The weights of structure, the areas of cross-sections and thickness for the independent finite elements are at system level taken as objective function and system design variables, respectively. They will satisfy the overall deformation and the system stability constraints. Recurrence relations to modify the system design variables and the equations used to estimate the Lagrange multipliers are derived using the optimality criterion approach. Finite element analysis (FEA) are used to compute internal forces at the system level. At the component level the objective is to minimize the weight of each independent element, and the cross-sectional dimensions are the component design variables. The local stress and local buckling in each independent element are component constraints. A sequence of unconstrained minimization technique based on extended interior penalty function formulation and a modified Newton method for caring out the unconstrained minimization are used as the optimized component (local level) synthesis. The use of this MP algorithm is essential to multilevel approach and local level, since it can handle the highly nonlinear component problem, such as local buckling constraints. In order to obtain efficient and reliable solution of the optimization problem, several important techniques are used. These include, design variable linking, constraint deletion, the use reciprocal design variables and explicit approximation of retained constraints based on first order Taylor series expansions with respect to reciprocal variables. Illustrative and practical problems given to show the applicability of the multilevel method to design of structures with a large number of design variables. The multilevel algorithm is applied to minimum-weight design of complex aircraft structures subject to multiple constraints. The proposed method is suitable for designing practical large scale structures with a large number of design variables.

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