Investigation Into The Response Variability of A Higher-Order Beam Resting on A Foundation Using A Stochastic Finite Element Method

Hien, Ta Duy; Thanh, Bui Tien; Long, Nguyen Ngoc; Thuan, Nguyen Van; Hang, Do Thi

doi:10.1007/978-981-15-0802-8_15

Cited by 4 publications

(2 citation statements)

References 17 publications

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“…Structural engineering problems such as in beams, frames, plates, and shells can be solved by experimental methods [1][2][3], analytical methods [4,5], and numerical methods such as finite elements [6][7][8][9][10][11]. The dynamic problem of beams or plates on foundations has been investigated by many researchers [12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

An Analytical Solution for the Dynamics of a Functionally Graded Plate resting on Viscoelastic Foundation

Thuy

Ngoc

Tien

et al. 2023

Eng. Technol. Appl. Sci. Res.

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This paper deals with the dynamic response of Functionally Graded Material (FGM) plates resting on a viscoelastic foundation under dynamic loads. The governing equations are derived by using Hamilton’s principle using the classical plate theory and the higher-order shear deformation plate theory. Using state-space methods to find the closed-form solution of the dynamic response of functionally graded rectangular plates resting on a viscoelastic foundation. Numerical examples are given for displacement and stresses in the plates with various structural parameters and the effects of these parameters are discussed. The result of the numerical example shows a marked decrease in displacement and stresses as the coefficient of viscous damping is increased.

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Section: Introductionmentioning

confidence: 99%

An Analytical Solution for the Dynamics of a Functionally Graded Plate resting on Viscoelastic Foundation

Thuy

Ngoc

Tien

et al. 2023

Eng. Technol. Appl. Sci. Res.

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“…There are several types of Stochastic Finite Element Methods (SFEM), e.g. the probabilistic finite element method [25,26], the Spectral SFEMs (SSFEMs) using Karhunen-Loève expansion series [27], the homogeneous chaos expansion method [28] for the representation of random fields, and the SFEMs that use weighed integration techniques [29,30]. The effect of randomness in elastic modulus on the stochastic free vibration of non-uniform beams is investigated by using an SFEM in [31].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Higher-order Finite Element Model for the Free Vibration of a Continuous Beam resting on Elastic Support with Uncertain Elastic Modulus

Hien

Diem²,

Tan³

et al. 2023

Eng. Technol. Appl. Sci. Res.

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This paper deals with a continuous beam resting on elastic support with elastic modulus derived from a random process. Governing equations of the stochastic higher-order finite element method of the free vibration of the continuous beam were derived from Hamilton's principle. The random process of elastic modulus was discretized by averaging random variables in each element. A solution for the stochastic eigenvalue problem for the free vibration of the continuous beam was obtained by using the perturbation technique, in conjunction with the finite element method. Spectral representation was used to generate a random process and employ the Monte Carlo simulation. A good agreement was obtained between the results of the first-order perturbation technique and the Monte Carlo simulation.

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Probabilistic analysis of a cantilever beam subjected to random loads via probability density functions

et al. 2023

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This paper addresses the probabilistic analysis of the deflection of a cantilever beam by means of a randomization of the classical governing fourth-order differential equation with null boundary conditions. The probabilistic study is based on the calculation of the first probability density function of the solution, which is a stochastic process, as well as the density function of further quantities of interest associated with this engineering problem such as the maximum slope and deflection at the free end of the cantilever beam, that are treated as random variables. In addition, the probability density function of the bending moment and the shear force will also be computed. The study takes extensive advantage of the so called Random Variable Transformation method, also known as Probability Transformation Method, that allows us to fully unify the probabilistic analysis in three relevant cases commonly studied in the deterministic setting. All the theoretical findings are illustrated via detailed numerical examples corresponding to each one of the three scenarios.

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Investigation Into The Response Variability of A Higher-Order Beam Resting on A Foundation Using A Stochastic Finite Element Method

Cited by 4 publications

References 17 publications

An Analytical Solution for the Dynamics of a Functionally Graded Plate resting on Viscoelastic Foundation

An Analytical Solution for the Dynamics of a Functionally Graded Plate resting on Viscoelastic Foundation

Stochastic Higher-order Finite Element Model for the Free Vibration of a Continuous Beam resting on Elastic Support with Uncertain Elastic Modulus

Probabilistic analysis of a cantilever beam subjected to random loads via probability density functions

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