Stochastic analysis of moderately thick plates using the generalized polynomial chaos and element free Galerkin method

Bahmyari, Ehsan; Khedmati, Mohammad Reza; Soares, C. Guedes

doi:10.1016/j.enganabound.2017.03.001

Cited by 14 publications

(5 citation statements)

References 52 publications

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“…(b) Figure 8 shows the energy-level response mean of the 1/3 Oct spectrum within the frequency range [20,200] Hz. e curves in Figure 8 are almost identical, and their results coincide with equation (21), thus implying that the PCE approach is valid and feasible for the broad-band spectrum. Correspondingly, Figure 9 shows the SE of the energy-level response of the 1/3 Oct spectrum.…”

Section: Shock and Vibrationsupporting

confidence: 61%

“…It follows that the proposed PCE approach is reasonable and feasible, by equation ( 21), but its error in equation ( 27) is inevitable, according to equations ( 24) and (25). So, the curve shape distortion (CSD) is defined based on equation (21)…”

Section: Standard Errormentioning

confidence: 99%

“…Sepahvand et al [20] used the truncated PCE of arbitrary random basis to express the uncertain elastic modulus, eigenfrequency, and mode of an orthotropic plate in order to study the stochastic free vibration of the plate. Bahmyari et al [21] combined the meshless Galerkin method with the generalized PCE to analyze the stochastic bending of moderately thick plates with elastic constraint edges. Najlawi et al [22,23] proposed a hybrid multiobjective imperialist competitive algorithm (MOICA) and MCS method for the multiobjective robust design optimization of a mechanism and further developed a hybrid MOICA-PCE algorithm to be exploited for robust optimization [24].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Vibration Analysis of Driving-Point System with Uncertainties Using Polynomial Chaos Expansion

Xiao

Zhou

Gao

et al. 2020

Shock and Vibration

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A vibration transfer analysis method based on polynomial chaos expansion (PCE) is proposed in this study and is used to analyze the stochastic dynamic compliance of uncertain systems with the Gaussian distribution. The random dynamic compliance is established by utilizing mode superposition on the system as the parameters of system uncertainties are regarded as input variables. Considering the asymptotic probability density function of mode shape, the dynamic compliance is decomposed into the mean of mode shape and the subsystem represented as an orthogonal polynomial expansion. Following this, the vibration transmission analysis approach is proposed for the random vibration. Results of a numerical simulation carried out employing the PCE approach show that broad-band spectrum analysis is more effective than narrow-band spectrum analysis because the former jump of the dynamic compliance amplitude is weakened. This proposed approach is valid and feasible, but since broad-band spectrum analysis loses some important information about the random vibration, both the aforementioned processes need to simultaneously be applied to analyze the random vibration transmission of low-medium frequency systems.

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Section: Shock and Vibrationsupporting

confidence: 61%

Section: Standard Errormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vibration Analysis of Driving-Point System with Uncertainties Using Polynomial Chaos Expansion

Xiao

Zhou

Gao

et al. 2020

Shock and Vibration

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“…We mention two papers that also have considered Young's modulus as a random quantity. Bahmyari et al [5] provided a bending analysis of thick plates with elastically restrained edges and resting on Pasternark elastic foundation, where the plate's Young's modulus and stiffness of the boundary conditions and elastic foundation were assumed as random variables. The free vibrations of orthotropic plates with uncertainties in the Young's modulus were investigated by Ernst et al [6] who obtained good correlation between experimental and numerical results.…”

Section: Introductionmentioning

confidence: 99%

Subspace Reduction for Stochastic Planar Elasticity

Hakula

Laaksonen

2021

Applied Mechanics

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Stochastic eigenvalue problems are nonlinear and multiparametric. They require their own solution methods and remain one of the challenge problems in computational mechanics. For the simplest possible reference problems, the key is to have a cluster of at the low end of the spectrum. If the inputs, domain or material, are perturbed, the cluster breaks and tracing of the eigenpairs become difficult due to possible crossing of the modes. In this paper we have shown that the eigenvalue crossing can occur within clusters not only by perturbations of the domain, but also of material parameters. What is new is that in this setting, the crossing can be controlled; that is, the effect of the perturbations can actually be predicted. Moreover, the basis of the subspace is shown to be a well-defined concept and can be used for instance in low-rank approximation of solutions of problems with static loading. In our industrial model problem, the reduction in solution times is significant.

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“…The methods have different names like galerkin, least square, accuracy points according to the mathematical approaches used when the error function is minimized. Bahmyari, Khedmati and Soares (2017) is example for galerkin method; Akcali and Dittrich (1989), Ramírez, Nogueir, Khelladi, Chassaing and Colominas (2014) can be given as example for the least squares method; for accuracy point method Diab and Smaili (2008), Jaiswal and Jawale (2017) can be shown.…”

Section: Introductionmentioning

confidence: 99%

Design of a New Bed Base Mechanism System

Mutlu¹,

Yapanmış²

2017

Uluslararası Muhendislik Arastirma Ve Gelistirme Dergisi

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In daily life, most of the devices, machines and furniture, which we use in our homes and make our life easier, have many different opening and closing systems. Some criteria may be required for the opening/closing shape of systems. For example, in some systems, it may be desirable that opened part uses minimum volume, facilitates daily life, or the system is balanced in each opening position. Those type of opening and closing systems are widely used sofa beds, seats and bed bases in the furniture sector. Many opening/closing systems have various locking mechanisms which are used to ensure opened final position or in some cases it is held in the final position by the force of the human arm. In this study, a kinematic analysis was carried out to design a base mechanism which could be stabilized at every position instead of the final position, and a virtual prototype was made.

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Stochastic analysis of moderately thick plates using the generalized polynomial chaos and element free Galerkin method

Cited by 14 publications

References 52 publications

Vibration Analysis of Driving-Point System with Uncertainties Using Polynomial Chaos Expansion

Vibration Analysis of Driving-Point System with Uncertainties Using Polynomial Chaos Expansion

Subspace Reduction for Stochastic Planar Elasticity

Design of a New Bed Base Mechanism System

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