Improving the computational efficiency in finite element analysis of shells with uncertain properties

Charmpis, Dimos C.; Papadrakakis, Manolis

doi:10.1016/j.cma.2003.12.075

Cited by 36 publications

(30 citation statements)

References 23 publications

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“…The same convergence criterion is utilized also in the PCG method [2]. However, in PCG the residual vector at each iteration is not directly calculated through an equation of the form of (22), but through a vector update operation, which provides an estimation of the residual.…”

Section: The Fpi-k0 Solution Methodsmentioning

confidence: 99%

“…(1) or (2) is obtained by applying a suitable preconditioner at each iteration to accelerate PCG convergence during the successive FE solutions [1,2]. For this purpose, the FE equations (1) are replaced by the equivalent system:…”

Section: The Pcg-k0 Solution Methodsmentioning

confidence: 99%

“…1 with 100×35 nodes and 6800 elements resulting in 19800 active degrees of freedom is used in all test runs for performing FE calculations. This test example has been examined also in [2,10], where it is described in more detail.…”

Section: Numerical Examplementioning

confidence: 99%

“…[1,2,[4][5][6][7][8][9][10][11][12]). In the present work, an established PCG-based solution method is overviewed and a new FPI-based solution method is introduced.…”

Section: Reanalysis Problems In MC Simulation-based Stochastic Fe Anamentioning

confidence: 99%

“…The nsim Eqs. (1) or (2) solved during MC simulations form a set of reanalysis-type or nearby problems [1][2][3]. The standard direct method based on Cholesky factorization remains even today the most popular solution scheme for FE equations.…”

Section: Reanalysis Problems In MC Simulation-based Stochastic Fe Anamentioning

confidence: 99%

See 4 more Smart Citations

Efficient Iterative Solution Techniques for Finite Element Reanalyses in the Context of Monte Carlo Simulation

Charmpis¹

2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Section: The Fpi-k0 Solution Methodsmentioning

confidence: 99%

Section: The Pcg-k0 Solution Methodsmentioning

confidence: 99%

Section: Numerical Examplementioning

confidence: 99%

“…[1,2,[4][5][6][7][8][9][10][11][12]). In the present work, an established PCG-based solution method is overviewed and a new FPI-based solution method is introduced.…”

Section: Reanalysis Problems In MC Simulation-based Stochastic Fe Anamentioning

confidence: 99%

Section: Reanalysis Problems In MC Simulation-based Stochastic Fe Anamentioning

confidence: 99%

See 3 more Smart Citations

Efficient Iterative Solution Techniques for Finite Element Reanalyses in the Context of Monte Carlo Simulation

Charmpis¹

2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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High‐precision finite element analysis of elastoplastic dynamic responses of super‐high‐rise steel frames

Ohsaki

Miyamura

Kohiyama

et al. 2009

Earthq Engng Struct Dyn

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A new framework is presented for analysis of dynamic collapse behavior of steel frames using large‐scale parallel finite element method based on the domain decomposition method. The analysis software is based on ADVC as a part of the E‐Simulator that takes advantage of recent development of computer science and high‐performance parallel computing in computational mechanics. By making an analysis model with fine meshing, a complicated sequence of local buckling of columns and beams can be simulated. Numerical results are shown for dynamic collapse analysis of single‐story and 5‐story frame models to show that the global and local behaviors are simultaneously simulated by a high‐precision finite element analysis. Eigenvalue analysis is also carried out for a 31‐story frame to demonstrate that dynamic analysis can be carried out for a structure discretized to solid elements with more than 70 million DOFs. Copyright © 2009 John Wiley & Sons, Ltd.

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An adaptive spectral Galerkin stochastic finite element method using variability response functions

Giovanis

Papadopoulos

Stavroulakis

2015

Numerical Meth Engineering

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SUMMARYA methodology is proposed in this paper to construct an adaptive sparse polynomial chaos (PC) expansion of the response of stochastic systems whose input parameters are independent random variables modeled as random fields. The proposed methodology utilizes the concept of variability response function in order to compute an a priori low-cost estimate of the spatial distribution of the second-order error of the response, as a function of the number of terms used in the truncated Karhunen-Loève (KL) expansion. This way the influence of the response variance to the spectral content (correlation structure) of the random input is taken into account through a spatial variation of the truncated KL terms. The criterion for selecting the number of KL terms at different parts of the structure is the uniformity of the spatial distribution of the second-order error. This way a significantly reduced number of PC coefficients, with respect to classical PC expansion, is required in order to reach a uniformly distributed target second-order error. This results in an increase of sparsity of the coefficient matrix of the corresponding linear system of equations leading to an enhancement of the computational efficiency of the spectral stochastic finite element method.

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Improving the computational efficiency in finite element analysis of shells with uncertain properties

Cited by 36 publications

References 23 publications

Efficient Iterative Solution Techniques for Finite Element Reanalyses in the Context of Monte Carlo Simulation

Efficient Iterative Solution Techniques for Finite Element Reanalyses in the Context of Monte Carlo Simulation

High‐precision finite element analysis of elastoplastic dynamic responses of super‐high‐rise steel frames

An adaptive spectral Galerkin stochastic finite element method using variability response functions

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