scholarly journals Reliability Analysis of Damaged Beam Spectral Element with Parameter Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
M. R. Machado ◽  
J. M. C. Dos Santos
Keyword(s):  
Reliability Analysis ◽  
Computational Efficiency ◽  
High Frequency ◽  
Structural Reliability ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Parameter Uncertainties ◽  
Reliability Method ◽  
Uncertainty Parameters ◽  
Element Method

The paper examines the influence of uncertainty parameters on the wave propagation responses at high frequencies for a damaged beam structure in the structural reliability context. The reliability analyses were performed using the perturbation method, First-Order Reliability Method (FORM), and response surface method (RSM) which were compared with Monte Carlo simulation (MCS) under the spectral element method environment. The simulated results were performed to investigate the effects of material property and geometric uncertainties on the response at high frequency modes, such as the computational efficiency of reliability methods. For the first time, the spectral element method is used in the context of reliability analysis at medium and high frequency bands applied to damage detection. It has shown the effects of parameters uncertainty on the dynamic beam response due on an impulsive load and the robustness of each method. Numerical examples in a bending vibrating beam with random parameters are performed to verify the computational efficiency of the present study.

Impact Response Analysis of a Coaxial Double-Pipe Structure by Using Spectral Element Method

2011 ◽  
Author(s):  
Akemi Nishida ◽  
Kazuhiko Iigaki
Keyword(s):  
High Frequency ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Impact Response ◽  
Response Analysis ◽  
Damping Properties ◽  
High Frequency Region ◽  
Parametric Studies ◽  
Double Pipe ◽  
Element Method

A coaxial double-pipe structure is to be used in the primary and auxiliary coolant system of a high-temperature gas-cooled reactor. In order to study the vibration characteristics of the coaxial double-pipe structure, hammering experiments were performed using specimens of the structure. Because the structural responses obtained in the experiments contained high-frequency components, impact response analysis was performed by using the spectral element method, which has high accuracy in the high-frequency region. A comparison between analysis results and experiment results showed good agreement between them. We also performed parametric studies on the damping properties of the specimens. The damping properties determined from the experiment results indicated that the inner and outer pipes had different damping properties.

scholarly journals Multi-Fidelity Modeling-Based Structural Reliability Analysis with the Boundary Element Method

2017 ◽  
Vol 08 (03n04) ◽  
pp. 1740001 ◽  
Author(s):  
Llewellyn Morse ◽  
Zahra Sharif Khodaei ◽  
M. H. Aliabadi
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Computational Cost ◽  
Response Surfaces ◽  
Second Order ◽  
Reliability Method ◽  
Fidelity Model ◽  
Element Method

In this work, a method for the application of multi-fidelity modeling to the reliability analysis of 2D elastostatic structures using the boundary element method (BEM) is proposed. Reliability analyses were carried out on a rectangular plate with a center circular hole subjected to uniaxial tension using Monte Carlo simulations (MCS), the first-order reliability method (FORM), and the second-order reliability method (SORM). Two BEM models were investigated, a low-fidelity model (LFM) of 20 elements and a high-fidelity model (HFM) of 100 elements. The response of these models at several design points was used to create multi-fidelity models (MFMs) utilizing second-order polynomial response surfaces and their reliability, alongside that of the LFM and the HFM, was evaluated. Results show that the MFMs that directly called the LFM were significantly superior in terms of accuracy to the LFM, achieving very similar levels of accuracy to the HFM, while also being of similar computational cost to the LFM. These direct MFMs were found to provide good substitutes for the HFM for MCS, FORM, and SORM.

WAVE PROPAGATION MODELING IN HIGHLY HETEROGENEOUS MEDIA BY A POLY-GRID CHEBYSHEV SPECTRAL ELEMENT METHOD

2012 ◽  
Vol 20 (02) ◽  
pp. 1240004 ◽  
Author(s):  
GÉZA SERIANI ◽  
CHANG SU
Keyword(s):  
Wave Propagation ◽  
Computational Efficiency ◽  
Spectral Element Method ◽  
Heterogeneous Media ◽  
Spectral Element ◽  
Small Scale ◽  
Computational Domain ◽  
Problem Size ◽  
Wide Range ◽  
Element Method

A wide range of applications requires the modeling of wave propagation phenomena in media with variable physical properties in the domain of interest, while highly accurate algorithms are needed to avoid unphysical effects. Spectral element methods (SEM), based on either a Chebyshev or a Legendre polynomial basis, have excellent properties of accuracy and flexibility in describing complex models, outperforming other techniques. In the standard SEM approach the computational domain is discretized by using very coarse meshes and constant-property elements, but in some cases the accuracy and the computational efficiency may be seriously reduced. For instance, a finely heterogeneous medium requires grid resolution down to the finest scales, leading to an extremely large problem dimension. In such problems the wavelength scale of interest is much larger but cannot be exploited in order to reduce the problem size. A poly-grid Chebyshev spectral element method (PG-CSEM) can overcome this limitation. In order to accurately deal with continuous variation in the properties, or even with small scale fluctuations, temporary auxiliary grids are introduced which avoid the need of using any finer global grid, and at the macroscopic level the wave field propagation is solved maintaining the SEM accuracy and computational efficiency.

scholarly journals Spectral Element Method Modeling of Eddy Current Losses in High-Frequency Transformers

2019 ◽  
Vol 24 (1) ◽  
pp. 28 ◽  
Author(s):  
Koen Bastiaens ◽  
Mitrofan Curti ◽  
Dave Krop ◽  
Sultan Jumayev ◽  
Elena Lomonova
Keyword(s):  
Eddy Current ◽  
High Frequency ◽  
Spectral Element Method ◽  
Spectral Element ◽  
High Ratio ◽  
Two Dimensional ◽  
Eddy Current Losses ◽  
High Frequency Transformer ◽  
Benchmark System ◽  
Element Method

This paper concerns the modeling of eddy current losses in conductive materials in the vicinity of a high-frequency transformer; more specifically, in two-dimensional problems where a high ratio between the object dimensions and the skin-depth exists. The analysis is performed using the Spectral Element Method (SEM), where high order Legendre–Gauss–Lobatto polynomials are applied to increase the accuracy of the results with respect to the Finite Element Method (FEM). A convergence analysis is performed on a two-dimensional benchmark system, for both the SEM and FEM. The benchmark system consists of a high-frequency transformer confined by a conductive cylinder and is free of complex geometrical shapes. Two different objectives are investigated. First, the discretizations at which the relative error with respect to a reference solution is minimized are compared. Second, the discretizations at which the trade-off between computational effort and accuracy is optimized are compared. The results indicated that by applying the SEM to the two-dimensional benchmark system, a higher accuracy per degree of freedom and significantly lower computation time are obtained with respect to the FEM. Therefore, the SEM is proven to be particularly useful for this type of problem.

scholarly journals Time-Dependent Reliability Analysis of Reinforced Concrete Beams Subjected to Uniform and Pitting Corrosion and Brittle Fracture

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1820
Author(s):  
Mohamed El Amine Ben Seghier ◽  
Behrooz Keshtegar ◽  
Hussam Mahmoud
Keyword(s):  
Reinforced Concrete ◽  
Brittle Fracture ◽  
Reliability Analysis ◽  
Pitting Corrosion ◽  
Structural Reliability ◽  
Time Dependent ◽  
State Function ◽  
Rc Beams ◽  
Highly Nonlinear ◽  
Reliability Method

Reinforced concrete (RC) beams are basic elements used in the construction of various structures and infrastructural systems. When exposed to harsh environmental conditions, the integrity of RC beams could be compromised as a result of various deterioration mechanisms. One of the most common deterioration mechanisms is the formation of different types of corrosion in the steel reinforcements of the beams, which could impact the overall reliability of the beam. Existing classical reliability analysis methods have shown unstable results when used for the assessment of highly nonlinear problems, such as corroded RC beams. To that end, the main purpose of this paper is to explore the use of a structural reliability method for the multi-state assessment of corroded RC beams. To do so, an improved reliability method, namely the three-term conjugate map (TCM) based on the first order reliability method (FORM), is used. The application of the TCM method to identify the multi-state failure of RC beams is validated against various well-known structural reliability-based FORM formulations. The limit state function (LSF) for corroded RC beams is formulated in accordance with two corrosion types, namely uniform and pitting corrosion, and with consideration of brittle fracture due to the pit-to-crack transition probability. The time-dependent reliability analyses conducted in this study are also used to assess the influence of various parameters on the resulting failure probability of the corroded beams. The results show that the nominal bar diameter, corrosion initiation rate, and the external loads have an important influence on the safety of these structures. In addition, the proposed method is shown to outperform other reliability-based FORM formulations in predicting the level of reliability in RC beams.

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