Structural analysis and optimization in the framework of reduced-basis method

Afonso, Silvana Maria Bastos; Lyra, Paulo Roberto Maciel; Albuquerque, T. M. M.; Motta, Renato de Siqueira

doi:10.1007/s00158-008-0350-4

Cited by 10 publications

(16 citation statements)

References 17 publications

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“…The reduced order method attempt to approximate high dimension system in a low dimension space. Most of ROMs project the high dimension system into a lower dimension space [11]. A simple example is the discrete system equation:…”

Section: Reduced Order Methodsmentioning

confidence: 99%

Robust Optimization Using Reduced-Order Modeling for Non-Linear Static Truss System

Motta¹,

Afonso²

2014

Proceedings of 10th World Congress on Computational Mechanics

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Abstract. In this work a design optimization tool to obtain robust optimum designs of trusses under nonlinear conditions is described and implemented. The robustness measures considered here are the expected value and standard deviation of the function involved in the optimization problem. To calculate such quantities, we employ two nonintrusive uncertainty propagation analysis techniques that exploit deterministic computer models: Monte Carlo (MC) method and Probabilistic Collocation Method (PCM). When using these robustness measures combined, the search of optimal design appears as a robust multi-objective optimization (RMO) problem. To overcome the time consuming problem inherent in a RMO problem a model reduction technique using the proper orthogonal decomposition (POD) method will be employed to provide fast outputs for nonlinear analysis of trusses. A structural sizing optimization (SSO) algorithm incorporating such procedure in the structural and sensitivity stochastic analyses will be used to obtain efficient optimal trusses design. Optimization studies will be conducted for trusses problems considering different loads level, exploring the material plasticity. Comparisons will be conducted with the SSO approach via traditional FEM and via POD.

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Section: Reduced Order Methodsmentioning

confidence: 99%

Robust Optimization Using Reduced-Order Modeling for Non-Linear Static Truss System

Motta¹,

Afonso²

2014

Proceedings of 10th World Congress on Computational Mechanics

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“…The performance of the modified methods proposed here is also presented. Additionally to the examples presented here, an application on structural MOP with three objective functions, was successfully solved in Motta (2009) using the proposed modification combined with a reduced order modeling approach called Reduced Basis Method (Afonso et al 2009). In the results of the present paper, the parameter n FC is the total number of function evaluations necessary for the Pareto solutions and n E Pp is the number of effective Pareto points (described previously).…”

Section: Numerical Examplesmentioning

confidence: 99%

A modified NBI and NC method for the solution of N-multiobjective optimization problems

Motta

Afonso

Lyra

2012

Struct Multidisc Optim

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Multiobjective optimization (MO) techniques allow a designer to model a specific problem considering a more realistic behavior, which commonly involves the satisfaction of several targets simultaneously. A fundamental concept, which is adopted in the multicriteria optimization task, is that of Pareto optimality. In this paper we test several well-known procedures to deal with multiobjective optimization problems (MOP) and propose a novel modified procedure that when applied to the existing Normal Boundary Intersection (NBI) method and Normal Constraint (NC) method for more than two objectives overcomes some of their deficiencies. For the three and four objective applications analyzed here, the proposed scheme presents the best performance both in terms of quality and efficiency to obtain a set of proper Pareto points, when compared to the analyzed existing approaches.

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“…The use of an affine decomposition and the separability concept to the stiffness matrix and load terms is the requirement to perform inexpensive calculations. Details of the methodology and how the RB governing equations is obtained for a class of 2D problems can be found elsewhere [13,17].…”

Section: Surrogate Model-rbmmentioning

confidence: 99%

“…Tables (1) and (2) summarizes the RBM algorithm for elasticity applications. As can been seen in [13,17], the final RB equations are written in terms of dependent/non dependent parameter (µ µ µ µ − − − − design variables), such that stiffness and load terms that do not depend on µ µ µ µ are computed only once. As a consequence of such subdivision, the computational implementation for reduced-basis output calculations is conducted following an off-line (µ µ µ µ-independent) / on-line (µ µ µ µ-dependent) algorithm as described respectively on Tables (1) and (2).…”

Section: Surrogate Model-rbmmentioning

confidence: 99%

Robust design considering optimization tools and reduced-basis approximations

Afonso¹,

Motta²,

Lyra³

et al. 2010

IOP Conf. Ser.: Mater. Sci. Eng.

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Abstract. This paper performs Robust Design Optimization (RDO) to obtain optimum solutions since some degree of uncertainty in characterizing any real engineering system is inevitable. The robustness measures considered here are the expected value and standard deviation of the function involved in the optimization problem. To calculate such quantities, we employ two nonintrusive uncertainty propagation analysis techniques that exploit deterministic computer models: Monte Carlo (MC) method and Probabilistic Collocation Method (PCM). The uncertainty propagation essentially involves computing the statistical moments of the output. When using these robustness measures combined, the search for optimal design appears as a robust multiobjetive optimization (RMO) problem. Several strategies are implemented to obtain the Pareto front (multiobjective solutions). To overcome the time consuming problem inherent in a RMO problem reduced basis (RB) approximation methodology is added to the optimization system, in the whole optimization process. The integration of all the methodologies described allows the computation of robust design, using a finite element model of 3.900 degrees of freedom, in a practical time (less than a minute).

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Structural analysis and optimization in the framework of reduced-basis method

Cited by 10 publications

References 17 publications

Robust Optimization Using Reduced-Order Modeling for Non-Linear Static Truss System

Robust Optimization Using Reduced-Order Modeling for Non-Linear Static Truss System

A modified NBI and NC method for the solution of N-multiobjective optimization problems

Robust design considering optimization tools and reduced-basis approximations

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