Hierarchical stochastic finite element method for structural analysis

Yang, Lufeng; Zhou, Yue'e; Zhou, Jingjing; Wang, Meilan

doi:10.1016/s0894-9166(13)60018-x

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…However, the formulation is restricted to cases where such an analytical solution is available. Yang et al [26] proposed a hierarchical formulation for the stochastic FE for static analysis, by using the Krylov subspace method, forming a hierarchical vector basis for the response. In this work, it is proposed to use the hierarchical finite element (HFE) method [1], also known as the p-element formulation, with random fields, in order to reduce computational cost, but keeping the versatility of the FE formulation.…”

Section: Introductionmentioning

confidence: 99%

Structural vibration analysis with random fields using the hierarchical finite element method

Fabro

Ferguson

Mace

2019

J Braz. Soc. Mech. Sci. Eng.

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Element based techniques, like the Finite Element method, are the standard approach in industry for low frequency applications in structural dynamics. However, mesh requirements can significantly increase the computational cost for increasing frequencies. In addition, randomness in system properties starts to play a significant role and its inclusion in the model further increases the computational cost. In this paper, a hierarchical finite element formulation is presented which incorporates spatially random properties. Polynomial and trigonometric hierarchical functions are used in the element formulation. Material and geometrical spatially correlated randomness are represented by the Karhunen-Loève expansion, a series representation for random fields. It allows the element integration to be performed only once for each term of the series which has benefits for a sampling scheme and can be used for non-Gaussian distributions. Free vibration and forced response statistics are calculated using the proposed approach. Compared to the standard h-version, the hierarchical finite element approach produces smaller mass and stiffness matrices, without changing the number of nodes of the element, and tends to be computationally more efficient. These are key factors not only when considering solutions for higher frequencies but also in the calculation of response statistics using a sampling method such as Monte Carlo simulation.

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Section: Introductionmentioning

confidence: 99%

Structural vibration analysis with random fields using the hierarchical finite element method

Fabro

Ferguson

Mace

2019

J Braz. Soc. Mech. Sci. Eng.

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“…Due to different reasons, real engineering structures always have some inevitable uncertainties, such as loads, physical and geometric parameters, boundary conditions, and system failure conditions. 1–5 Many calculation methods have been implemented to solve the uncertainty in solid mechanics, 6–8 structural mechanics, 9,10 fluid mechanics, 11,12 and fluid–structure interaction, 13,14 including stochastic finite element method (FEM), 15–18 fuzzy FEM, 19–21 and interval parameter perturbation method. 22–26 The stochastic FEM requires the statistic characteristics of uncertainty parameters, while the fuzzy FEM is very slow.…”

Section: Introductionmentioning

confidence: 99%

Interval element-free Galerkin method for uncertain mechanical problems

Zhou

Zhao

Ren

2018

Advances in Mechanical Engineering

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An interval element-free Galerkin method was proposed to solve some issues in structural design and analysis of structural parameters that have errors or uncertainties caused by manufacture, installation, measurement, or computation. Based on the interval mathematics and perturbation theory, we deduced interval element-free Galerkin method equilibrium equations using the element-free Galerkin method and solved them using the parameter perturbation of interval number. A bar under uniform load, a bi-material cantilever beam subjected to uniform stress, and collinear double edged cracked plate subjected to uniform tensile stress, including uncertainty parameters, were analyzed. Numerical simulations show that interval element-free Galerkin method is accurate and effective in solving the uncertainty problems.

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“…Proppe implemented multiresolution analysis for stochastic finite element problems with Karhunen-Loeve expansion [14]. Based on Karhunen-Loeve series expansion and hierarchical approach, Yang et al applied the hierarchical stochastic finite element method for structural analysis [15]. Another method is Monte Carlo simulation (MCS) [16]; the name "Monte Carlo" was coined in the 1940s by scientists working in Los Alamos to designate a class of numerical methods based on the use of random numbers.…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Wavelet Finite Element Method for 1D and 2D Structures Analysis

Zhang

Chen

Yang

et al. 2014

Shock and Vibration

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A stochastic finite element method based on B-spline wavelet on the interval (BSWI-SFEM) is presented for static analysis of 1D and 2D structures in this paper. Instead of conventional polynomial interpolation, the scaling functions of BSWI are employed to construct the displacement field. By means of virtual work principle and BSWI, the wavelet finite elements of beam, plate, and plane rigid frame are obtained. Combining the Monte Carlo method and the constructed BSWI elements together, the BSWI-SFEM is formulated. The constructed BSWI-SFEM can deal with the problems of structural response uncertainty caused by the variability of the material properties, static load amplitudes, and so on. Taking the widely used Timoshenko beam, the Mindlin plate, and the plane rigid frame as examples, numerical results have demonstrated that the proposed method can give a higher accuracy and a better constringency than the conventional stochastic finite element methods.

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Hierarchical stochastic finite element method for structural analysis

Cited by 4 publications

References 11 publications

Structural vibration analysis with random fields using the hierarchical finite element method

Structural vibration analysis with random fields using the hierarchical finite element method

Interval element-free Galerkin method for uncertain mechanical problems

A Stochastic Wavelet Finite Element Method for 1D and 2D Structures Analysis

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