Abstract
In structural optimization, the implicit nature of the cost function with respect to the optimization parameters, i.e. through the solution of the structural problem calculated with fixed values of these parameters, leads to prohibitive computations whatever the adopted formulation.
Consequently, it yields limitations in both the number of parameters and the size of the structural problem. Moreover, some know-how is required to define a relevant structural problem and a well-behaved cost function.
Here, we profit from the ability of the Proper Generalized Decomposition (PGD) method to handle large-dimensionality problems to transform the optimization parameters into variables of an augmented-structural problem which is solved prior to optimization. As a consequence, the cost function becomes explicit with respect to the parameters.
As the augmented-structural problem is solved a priori, it becomes independent from the a posteriori optimization. Obviously, such approach promises numerous advantages, e.g. the solution of the structural problem can be easily analyzed to provide a guide to define the cost function and advanced optimization schemes become numerically tractable because of the easy evaluation of the cost function and its gradients.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ammar A, Mokdad B, Chinesta F, Keunings R (2006) A new family of solvers for some, classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. J Non-Newton Fluid Mech 139(3):153–176
Ammar A, Mokdad B, Chinesta F, Keunings R (2007) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids—part ii: Transient simulation using space-time separated representations. J Non-Newton Fluid Mech 144(2–3):98–121
Arora JS, Wang Q (2005) Review of formulations for structural and mechanical system optimization. Struct Multidiscip Optim 30(4):251–272
Chinesta F, Ammar A, Joyot P (2008) The nanometric and micrometric scales of the structure and mechanics of materials revisited: an introduction to the challenges of fully deterministic numerical descriptions. Int J Multiscale Comput Eng 6(3):191–213
Chinesta F, Ammar A, Cueto E (2009) Recent advances in the use of the proper generalized decomposition for solving multidimensional models. Arch Comput Methods Eng. doi:10.1007/s11831-010-9049-y
Fuchs M (1982) Explicit optimum design. Int J Solid Struct 18(1):13–22
Fuchs M (1983) Explicit optimum design technique for linear elastic trusses. Eng Optim 6(4):213–218
Rozvany GIN (2009) A critical review of established methods of structural topology optimization. Struct Multidiscip Optim 37(3):217–237
Schmit L, Fox R (1965) An integrated approach to structural synthesis and analysis. AIAA J 3(6):1104
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Leygue, A., Verron, E. A First Step Towards the Use of Proper General Decomposition Method for Structural Optimization. Arch Computat Methods Eng 17, 465–472 (2010). https://doi.org/10.1007/s11831-010-9052-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11831-010-9052-3