In this article the present state of the multicriterion structural optimization is considered from the basis of about seventy publications which all are connected with the Pareto optimality concept. The completed works rather than open questions in the field are particularly emphasized. The basic concepts and the motivation of the multicriterion approach are briefly discussed. The classification of the multicriterion structural design process is proposed and it is used in describing the published applications.

Multicriterion Structural Optimization

Engineering optimization problems, design problems among them, are multicriteria in their essence. When designing machines, mechanisms, and structures, one has to deal with numerous contradictory criteria.

Use of P t -nets for the approximation of the Edgeworth-Pareto set in multicriteria optimization

This paper describes a problem of axisymmetric shell optimization under fracture mechanics and geometric constraints. The problem is formulated as the weight (volume of a shell material) minimization and the meridional contour of the shell is taken as the design variable. The shell is made from quasi-brittle materials and through cracks arising are admitted. It is supposed that the shell is loaded by cyclic forces. A crack propagation process related to the stress intensity factor is described by the Paris fatigue law. The problem of finding the meridian shape (geometric design variable), of the shell having the smallest mass subject to constraint on the cyclic number for fatigue cracks, is investigated using a minimax (guaranteed) approach worked out in the theory of optimization under incomplete information. Optimal designs of the shells are found numerically with the application of genetic algorithms.

Optimal Shape Design of Axisymmetric Shells for Crack Initiation and Propagation Under Cyclic Loading

Optimization of axisymmetric membrane shells

The optimization problems taken into consideration in this paper consist in finding the shape and the thickness distribution of elastic axisymmetric shells in the frame of membrane theory, loaded by fixed statical forces in such a way that the cost functional reaches a maximum, while satisfying some strength mechanics constraints. In this paper the mass effectiveness of the shell is considered as a cost function and as constraint we use the bounds on the maximum normal stress which is typical for shells made from brittle or quasi-brittle materials. The paper gives some possible formulations of optimal structural design problems. Analytical investigations and corresponding solutions are presented.

Optimization of mass effectiveness of axisymmetric pressure vessels

Natural Structural Shapes are derived for axisymmetrically loaded shells of revolution within the membrane theory of shells. The concept of natural structural shapes is based on the simultaneous minimization of the mass and the strain energy of the loaded structure, a multicriteria optimization problem with Edgeworth-Pareto optimality as the basic optimality concept. The problem is formulated as a multicriteria control problem and necessary conditions for arbitrary loading and boundary are derived. Exact and numerical results are obtained for both the case of uniform pressure and that of a ring load with zero surface loads.

Natural structural shapes for shells of revolution in the membrane theory of shells

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Natural structural shapes for shells of revolution in the membrane theory of shells