Stress recovery and error estimation for shell structures

Yazdani, A.; Riggs, H. R.; Tessler, Alexander

doi:10.1002/(sici)1097-0207(20000420)47:11<1825::aid-nme820>3.0.co;2-6

Cited by 14 publications

(5 citation statements)

References 32 publications

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“…This methodology effectively enhances monitoring capabilities with a limited number of strain sensors and is not necessarily confined to planar problems. The SEA has demonstrated successful application to three-dimensional structures like curved shells [ 45 ] and stiffened panels [ 46 ]. Therefore, the integration of sensor placement optimization with strain pre-extrapolation in the implementation of the inverse finite element method can be extended to industrial systems, offering a practical and efficient choice for structural health monitoring (SHM) applications.…”

Section: Discussionmentioning

confidence: 99%

Shape Sensing in Plate Structures through Inverse Finite Element Method Enhanced by Multi-Objective Genetic Optimization of Sensor Placement and Strain Pre-Extrapolation

Del Priore,

Lampani

2024

Sensors

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The real-time reconstruction of the displacement field of a structure from a network of in situ strain sensors is commonly referred to as “shape sensing”. The inverse finite element method (iFEM) stands out as a highly effective and promising approach to perform this task. In the current investigation, this technique is employed to monitor different plate structures experiencing flexural and torsional deformation fields. In order to reduce the number of installed sensors and obtain more accurate results, the iFEM is applied in synergy with smoothing element analysis (SEA), which allows the pre-extrapolation of the strain field over the entire structure from a limited number of measurement points. For the SEA extrapolation to be effective for a multitude of load cases, it is necessary to position the strain sensors appropriately. In this study, an innovative sensor placement strategy that relies on a multi-objective genetic algorithm (NSGA-II) is proposed. This approach aims to minimize the root mean square error of the pre-extrapolated strain field across a set of mode shapes for the examined plate structures. The optimized strain reconstruction is subsequently utilized as input for the iFEM technique. Comparisons are drawn between the displacement field reconstructions obtained using the proposed methodology and the conventional iFEM. In order to validate such methodology, two different numerical case studies, one involving a rectangular cantilevered plate and the other encompassing a square plate clamped at the edges, are investigated. For the considered case studies, the results obtained by the proposed approach reveal a significant improvement in the monitoring capabilities over the basic iFEM algorithm with the same number of sensors.

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Section: Discussionmentioning

confidence: 99%

Shape Sensing in Plate Structures through Inverse Finite Element Method Enhanced by Multi-Objective Genetic Optimization of Sensor Placement and Strain Pre-Extrapolation

Del Priore,

Lampani

2024

Sensors

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“…Based on experimental semivariogram, three different theoretical semivariogram modules as shown in Table 1 have been tested. In this study, the Gauss model with Δℎ = 25% of ℎ has been adopted to find the weight factor for the OK process explained in (2).…”

Section: Numerical Analysismentioning

confidence: 99%

“…The error assessment tools used in finite element analysis are well known and usually classified into two strategies: recovery-based error estimators and residual-type estimators [1,2]. Stress recovery procedures can be classified as local (i.e., element level), patch-based, and global.…”

Section: Introductionmentioning

confidence: 99%

p‐Adaptive Refinement Based on Stress Recovery Technique Considering Ordinary Kriging Interpolation in L‐Shaped Domain

Woo

Ahn

2017

Mathematical Problems in Engineering

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The primary objectives of this study are twofold. Firstly, the original SPR method of stress recovery has been modified by incorporating the kriging interpolation technique to fit a polynomial to the derivatives recovered at the Gauss points. For this purpose, the -version of finite element analysis is performed to produce the stresses at the fixed 10 × 10 Gauss points where the integrals of Legendre polynomials are used as a basis function. In contrast to the conventional least square method for stress recovery, the weight factor is determined by experimental and theoretical variograms for interpolation of stress data, unlike the conventional interpolation methods that use an equal weight factor. Secondly, an adaptive procedure for hierarchical -refinement in conjunction with a posteriori error based on the modified SPR (superconvergent patch recovery) method is proposed. Thirdly, a new error estimator based on the limit value approach is proposed by predicting the exact strain energy to verify the kriging-based SPR method. The validity of the proposed approach has been tested by analyzing two-dimensional plates with a rectangular cutout in the presence of stress singularity.

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“…* Corresponding author. During post-processing of analysis data, the recovery of solutions of higher accuracy can be local (or elemental), patch-based (or over a cluster of elements), and global [1]. To extract a smooth derivative field, averaging either projected or consistent nodal derivatives is an example of a patch-based scheme.…”

Section: Introductionmentioning

confidence: 99%

Stress intensity factor by p-adaptive refinement based on ordinary Kriging interpolation

Woo

Basu

et al. 2009

Finite Elements in Analysis and Design

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Stress recovery and error estimation for shell structures

Cited by 14 publications

References 32 publications

Shape Sensing in Plate Structures through Inverse Finite Element Method Enhanced by Multi-Objective Genetic Optimization of Sensor Placement and Strain Pre-Extrapolation

Shape Sensing in Plate Structures through Inverse Finite Element Method Enhanced by Multi-Objective Genetic Optimization of Sensor Placement and Strain Pre-Extrapolation

p‐Adaptive Refinement Based on Stress Recovery Technique Considering Ordinary Kriging Interpolation in L‐Shaped Domain

Stress intensity factor by p-adaptive refinement based on ordinary Kriging interpolation

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