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Title of Journal: Struct Multidisc Optim

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Abbravation: Structural and Multidisciplinary Optimization

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Springer Berlin Heidelberg

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DOI

10.1007/978-3-319-20789-6_1-1

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ISSN

1615-1488

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On the analytical derivation of the Paretooptimal

Authors: M Gobbi F Levi G Mastinu G Previati
Publish Date: 2014/08/21
Volume: 51, Issue: 3, Pages: 645-657
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Abstract

The Fritz John conditions for Paretooptimality have been set in matrix form and used for introducing a procedure for the analytical derivation of the Paretooptimal set in the design variables domain Subsequently the derivation of the Paretooptimal set in the objective functions domain can be obtained if possible by a proper analytical derivation Both the objective and constraint functions are assumed to be available in analytical form and twice differentiable and convex or pseudoconvex The proposed procedure to find the Paretooptimal set is relatively simple The computation of the determinant of a matrix is required A symbolic manipulator can be exploited If there are two design variables and two objective functions the Paretooptimal set can be easily computed by applying a simple formula derived in the paper If the number of design variables equals the number of objective functions the Paretooptimal set in the design variables domain can be found by computing the product of the constraint functions times the determinant of the Jacobian of the objective functions A number of case studies have been proposed to test the effectiveness of the proposed procedure The optimal structural design of respectively a pair of compressed spheres a cantilever with rectangular cross section have been faced and solved Additionally the test problem proposed by Fonseca and Fleming has been addressed and solved analytically Optimization problems with low dimensionality 2 or 3 design variables and 2 objective functions 2 or more constraints have been easily solved The proposed procedure can be useful in the actual engineering practice at the earliest design stage In this case the designer can be made aware on the proper design variables setting to obtain the desired tradeoff among conflicting objective functions

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  2. Multi-dimensional optimization of functionally graded material composition using polynomial expansion of the volume fraction
  3. On symmetry and non-uniqueness in exact topology optimization
  4. Integrated layout and topology optimization design of multi-frame and multi-component fuselage structure systems
  5. Single-level composite wing optimization based on flexural lamination parameters
  6. Topology optimization of composite structures with data-driven resin filling time manufacturing constraint
  7. A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods
  8. Minimum weight design of solid annular plates under an assigned limit ring load
  9. A sensitivity-based commonality strategy for family products of mild variation, with application to automotive body structures
  10. A new reliability analysis method based on the conjugate gradient direction
  11. Aircraft wing box optimization considering uncertainty in surrogate models
  12. Multidisciplinary dynamic optimization of horizontal axis wind turbine design
  13. Geometrical aspects of optimum truss like structures for three-force problem
  14. Advances in optimization of highrise building structures
  15. Topology optimization of fail-safe structures using a simplified local damage model
  16. Topology optimization of frame structures with flexible joints
  17. A concurrent subspace collaborative optimization architecture to structural synthetical optimization design
  18. Topology optimization of internal partitions in a flow-reversing chamber muffler for noise reduction
  19. Material interpolation schemes for unified topology and multi-material optimization
  20. Variational proof of optimality criteria for Michell structures with pre-existing members
  21. Drop test simulation and surrogate-based optimization of a dishwasher mechanical structure and its packaging module
  22. Resolving issues with member buckling in truss topology optimization using a mixed variable approach
  23. Adaptive infill sampling criterion for multi-fidelity optimization based on Gappy-POD
  24. A comparative study of uncertainty propagation methods for black-box-type problems
  25. Multiobjective optimization for crash safety design of vehicles using stepwise regression model
  26. A double-distribution statistical algorithm for composite laminate optimization
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  29. Hybrid evolutionary algorithm and application to structural optimization
  30. Topology optimization of shell structures using adaptive inner-front (AIF) level set method
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  39. Fracture resistance via topology optimization
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