About the accuracy of a novel response surface method for the analysis of finite element modeled uncertain structures

Falsone, G.; Impollonia, N.

doi:10.1016/j.probengmech.2003.11.005

Cited by 30 publications

(24 citation statements)

References 10 publications

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“…The above equation can be cast in a more effective fashion observing that only few eigenvalues collected in the diagonal matrix K i are different than zero [1,6], their number is indeed very small with respect to system dimension. In fact K i is a symmetric sparse matrix and most of its columns are zero vectors so that the non-zero eigenvalues of K À1 b 0 ð ÞK i cannot be greater than the number of columns of K i which have a not-zero entry.…”

Section: The Minimum Distance Approachmentioning

confidence: 99%

“…In fact K i is a symmetric sparse matrix and most of its columns are zero vectors so that the non-zero eigenvalues of K À1 b 0 ð ÞK i cannot be greater than the number of columns of K i which have a not-zero entry. On this regards, more information are given in [1,6].…”

Section: The Minimum Distance Approachmentioning

confidence: 99%

“…The case of statically indeterminate structures is quite more involved and exact explicit solutions have been derived only for simple structures: single beam [3][4][5], structures possessing a single element with variable properties [1,6], structures comprising few elements and few redundancies [7,12].…”

Section: Introductionmentioning

confidence: 99%

“…This method, despite its remarkable efficiency, allows the analysis of systems with moderate variation of the parameters. An improvement of the method is shown in [6].…”

Section: Introductionmentioning

confidence: 99%

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Explicit solution for linear systems with parametric stiffness and application to uncertain structures

Settineri

Impollonia

2015

Meccanica

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The paper proposes a novel approximate explicit solution for the static response of structural systems discretized by finite elements with parametric stiffness. The solution exploits the following properties: (a) if the system comprises one parameter only, i.e. a single finite element has parametric stiffness, then the exact explicit solution can always be obtained; (b) if all element stiffnesses are considered as parameters and the exact solution is available at a given point of the parameter space (i.e. for a given realization of the parameters), then it is also known along the line passing through that point and the origin of the parameter space. The joint use of the two properties allows an accurate explicit relationship for nodal displacements which is suitable for treating different structural problems such as optimization, reanalysis, inverse analysis and reliability. The latter will be investigated in the numerical applications where Monte Carlo samples are produced by the explicit relationship rather than by the re-analysis of the structural problem with an evident reduction of computational burden.

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Section: The Minimum Distance Approachmentioning

confidence: 99%

Section: The Minimum Distance Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…This method, despite its remarkable efficiency, allows the analysis of systems with moderate variation of the parameters. An improvement of the method is shown in [6].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Explicit solution for linear systems with parametric stiffness and application to uncertain structures

Settineri

Impollonia

2015

Meccanica

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“…Uma avaliação sobre a precisão de um novo MSR é feita no trabalho de FALSONE & IMPOLLONIA (2004). Na verdade, esta nova metodologia, também proposta pelos mesmos autores, considera como função de desempenho, uma relação entre os graus de liberdade do elemento finito escolhido na análise e os coeficientes do polinômio aproximador da superfície de resposta.…”

Section: -Confiabilidade Estruturalunclassified

Modelos não lineares do método dos elementos de contorno para análise de problemas de fratura e aplicação de modelos de confiabilidade e otimização em estruturas submetidas à fadiga

Leonel¹

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Matching the principal deformation mode method with the probability transformation method for the analysis of uncertain systems

Falsone

Laudani

2019

Numerical Meth Engineering

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This paper deals with the probabilistic description of the random response of linear uncertain structural system when the uncertainties are modeled as random variables with assigned probability density function (pdf). In particular, a novel approach is presented that allows the direct evaluation of the response pdf starting from the joint pdf characterizing the structural uncertainties. It consists in matching adequately two methods, recently proposed by the authors, which are the Approximated Principal Deformation Modes method and the Probability Transformation Method. The proposed approach, obtained by this coupling, reveals to have good levels of accuracy, even for relatively high uncertainties, and of computational efficiency, as the reported numerical applications show. KEYWORDS probabilistic approaches, probability density function, uncertain systems Int J Numer Methods Eng. 2019;118:395-410.wileyonlinelibrary.com/journal/nme

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About the accuracy of a novel response surface method for the analysis of finite element modeled uncertain structures

Cited by 30 publications

References 10 publications

Explicit solution for linear systems with parametric stiffness and application to uncertain structures

Explicit solution for linear systems with parametric stiffness and application to uncertain structures

Modelos não lineares do método dos elementos de contorno para análise de problemas de fratura e aplicação de modelos de confiabilidade e otimização em estruturas submetidas à fadiga

Matching the principal deformation mode method with the probability transformation method for the analysis of uncertain systems

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