Spectral stochastic finite element analysis for laminated composite plates

Chen, Nian-Zhong; Soares, C. Guedes

doi:10.1016/j.cma.2008.07.003

Cited by 127 publications

(47 citation statements)

References 36 publications

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“…This approach is usually combined in the literature with the polynomial chaos (PC) approximation for the calculation of the response variability of uncertain finite element systems e.g. [1][2][3]19,22,28,29,41,66,67,94,108,113,187,189]. The combination is called the spectral stochastic finite element method (SSFEM).…”

Section: The Spectral Representation Methodsmentioning

confidence: 99%

“…A number of PCG variants with various preconditioning matrices led in most cases to a substantial reduction of the number of iterations (and thus of the computational cost) irrespectively of the coefficient of variation of the input random field which affects the condition number of matrix and thus the convergence behaviour of the iterative algorithms e.g. [66,139,29,95,43,22]. Recently, a generalization of the classical spectral decomposition (truncated K-L expansion) for the solution of the problem interpreted as an ''extended" eigenproblem has been proposed together with ad hoc iterative solution techniques inspired by classical techniques for solving the eigenproblem [122,123].…”

Section: The Spectral Stochastic Finite Element Methods -Ssfemmentioning

confidence: 99%

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The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

865

407

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a b s t r a c tA powerful tool in computational stochastic mechanics is the stochastic finite element method (SFEM). SFEM is an extension of the classical deterministic FE approach to the stochastic framework i.e. to the solution of static and dynamic problems with stochastic mechanical, geometric and/or loading properties. The considerable attention that SFEM received over the last decade can be mainly attributed to the spectacular growth of computing power rendering possible the efficient treatment of large-scale problems. This article aims at providing a state-of-the-art review of past and recent developments in the SFEM area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future.

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Section: The Spectral Representation Methodsmentioning

confidence: 99%

Section: The Spectral Stochastic Finite Element Methods -Ssfemmentioning

confidence: 99%

The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

865

407

View full text Add to dashboard Cite

show abstract

“…The matrix-vector product approach introduced in this reference avoids the assembly of the n(P + 1) × n(P + 1) size system and hence the calculations can be carried out over the deterministic size K (j k) matrices. In other words, the solution of the SFEM system is performed using the equation K (j k) u k = f j , which requires only the storage of the deterministic size K i matrices and the corresponding ξ i ψ j ψ k coefficients according to (13).…”

Section: Galerkin Based Formulationmentioning

confidence: 99%

On the Capabilities of the Polynomial Chaos Expansion Method within SFE Analysis—An Overview

Panayirci

Schuëller

2011

Arch Computat Methods Eng

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This paper addresses the most recent developments concerning the application of the P-C expansion method within the Stochastic Finite Element (SFE) analysis, in particular considering computational solid mechanics. More specifically, the focus has been on the use of the method for the propagation of the stochastic structural responses due to the extensive amount of contributions in this context. Numerical examples presented in the literature are listed in this regard, in order to shed some light on the range of applications, especially in terms of the probabilistic dimensionality of the problem. Furthermore, the recently emerging utilization of the method within the modeling of uncertain input parameters is covered briefly. With this contribution, it is aimed to present an overview on the state-ofart of the P-C literature and the capabilities of the method.

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“…The difficulty is largely computational-additional dimensions introduced into the problem by the random treatment of microstructural material and morphological parameters lead to computational intractability when the material response includes damage and nonlinearity. As Fish and Wu [13] recently demonstrated, model order reduction approaches for the multiscale solvers e.g., [8,24,41], as well as efficient uncertainty quantification algorithms [6,15,39] are critical to the development of computationally tractable stochastic multiscale modeling of composite materials.…”

Section: Introductionmentioning

confidence: 99%

Multiscale modeling of failure in composites under model parameter uncertainty

2015

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This manuscript presents a multiscale stochastic failure modeling approach for fiber reinforced composites. A homogenization based reduced-order multiscale computational model is employed to predict the progressive damage accumulation and failure in the composite. Uncertainty in the composite response is modeled at the scale of the microstructure by considering the constituent material (i.e., matrix and fiber) parameters governing the evolution of damage as random variables. Through the use of the multiscale model, randomness at the constituent scale is propagated to the scale of the composite laminate. The probability distributions of the underlying material parameters are calibrated from unidirectional composite experiments using a Bayesian statistical approach. The calibrated multiscale model is exercised to predict the ultimate tensile strength of quasi-isotropic openhole composite specimens at various loading rates. The effect of random spatial distribution of constituent material properties on the composite response is investigated.

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Spectral stochastic finite element analysis for laminated composite plates

Cited by 127 publications

References 36 publications

The stochastic finite element method: Past, present and future

The stochastic finite element method: Past, present and future

On the Capabilities of the Polynomial Chaos Expansion Method within SFE Analysis—An Overview

Multiscale modeling of failure in composites under model parameter uncertainty

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