Errors, Recovery Processes, and Error Estimates

Zienkiewicz, O.C.; Taylor, Robert L.; Zhu, J.Z.

doi:10.1016/b978-1-85617-633-0.00015-0

Cited by 7 publications

(3 citation statements)

References 93 publications

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“…It is seen from Figure 6c that with the increasing of the total elements in the FEM model, the FEM results shift to the lower frequency side and move closer to the MRRM result. This fact is in accordance with the convergence process of the FEM analysis [68]. The discrete FEM model generally overvalues the stiffness of the real structure for the following reason.…”

Section: Validation Of Theoretical Methods By Experimental Measurementmentioning

confidence: 65%

“…Figure 6a compares the result by the MRRM theoretical analysis with the damping ratios being 0.01, the result by the FBG experiment, and the result by the FEM with the isotropic structural loss factors being 0.01 [65] and with 6227 elements. The FEM result corresponding to the most refined mesh (i.e., extremely finer mesh) is selected in Figure 6a for comparison, because it should be the most accurate FEM result among the four cases of element sizes according to the convergence criterion of FEM analysis [68]. Figure 6a indicates that the transmission spectra obtained by MRRM theory, by FBG experiment, and by FEM simulation are agreed in general within the considered frequency range.…”

Section: Validation Of Theoretical Methods By Experimental Measurementmentioning

confidence: 85%

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Analysis of Bending Waves in Phononic Crystal Beams with Defects

Guo

Chuang

2018

Crystals

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Existing investigations on imperfect phononic crystal beams mainly concern periodic multi-span beams carrying either one or two channel waves with random or deterministic disorder in span-length. This paper studies the two channel bending waves in phononic crystal beams consisting of many phases of materials with defects introduced as one structural segment having different cross-sectional dimensions or material parameters. The method of reverberation-ray matrix (MRRM) based on the Timoshenko beam theory, which can conduct high-frequency analysis, is extended for the theoretical analysis of dispersion and transmission of bending waves. The supercell technique and the Floquet-Bloch theorem are adopted for modeling the dispersion characteristics, and the whole finite structural model is used to calculate the transmission spectra. Experimental measurements and numerical calculations are provided to validate the displacement transmission obtained by the proposed MRRM, with the effect of damping on transmission spectra being concerned. The high-frequency calculation applicability of the proposed MRRM is also confirmed by comparing the present results with the corresponding ones either using the transfer matrix method (TMM) or MRRM based on Euler-Bernoulli beam theory. The influences of defect size, defect form, and unit-cell number on the transmission spectra and the band structures are discussed. The drawn conclusions may be useful for designing or evaluating the defected phononic crystal beams in bending wave control. In addition, our conclusions are especially potential for identifying the defect location through bending wave signals.

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Section: Validation Of Theoretical Methods By Experimental Measurementmentioning

confidence: 65%

Section: Validation Of Theoretical Methods By Experimental Measurementmentioning

confidence: 85%

Analysis of Bending Waves in Phononic Crystal Beams with Defects

Guo

Chuang

2018

Crystals

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show abstract

“…Similar projections, though often performed element-by-element, are used in a posteriori error estimation methods, to quantify the distance between the finite element solution and an actual equilibrium solution, i.e., the discretization error [27,28]. However, the objective here is opposite, i.e., we want to discard the discretization error and quantify the intrinsic equilibrium gap of the considered finite element field.…”

Section: Body Stresses Regularizationmentioning

confidence: 99%