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CivilComp Proceedings
ISSN 17593433 CCP: 40
ADVANCES IN OPTIMIZATION FOR STRUCTURAL ENGINEERING 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
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", CivilComp Press, Edinburgh, UK, pp 6572, 1996. doi:10.4203/ccp.40.3.4
Abstract
The aim of the work presented here is the development of
efficient method for minimum weight design of the stiffened
thinwalled 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
crosssections 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
crosssectional 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 minimumweight 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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