• Structural Engineering and Mechanics
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• v.48 no.4
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• pp.501-518
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• 2013

Apart from thinning of cortical layers, the local bone curvature, varying along bone periphery, modulates ultrasound waves as well, which is however often underestimated or overlooked in clinical quantitative ultrasound (QUS). A dedicated three-dimensional finite element modelling technique for cortical bones was established, for quantitatively exploring and calibrating the effect of local curvature of cortical bone on ultrasound. Using a correlation-based mode extraction technique, high-velocity group (HVG) and low-velocity group (LVG) wave modes in a human radius were examined. Experimental verification using acrylic cylinders and in vitro testing using a porcine femur were accomplished. Results coherently unravelled the cortical curvature exerts evident influence on bone-guided ultrasound when RoC/${\lambda}$ <1 for HVG mode and RoC/${\lambda}$ <2 for LVG mode (RoC/${\lambda}$: the ratio of local bone curvature radius to wavelength); the sensitivity of LVG mode to bone curvature is higher than HVG mode. It has also been demonstrated the local group velocity of an HVG or LVG mode at a particular skeletal site is equivalent to the velocity when propagating in a uniform cylinder having an outer radius identical to the radius of curvature at that site. This study provides a rule of thumb to compensate for the effect of bone curvature in QUS.

• Structural Engineering and Mechanics
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• v.52 no.2
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• pp.307-322
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• 2014

A two-step procedure to detect and quantify damages in structures from changes in curvature mode shapes is presented here. In the first step the maximum difference in curvature mode shapes of the undamaged and damaged structure are used for visual identification of the damaged internal-substructure. In the next step, the identified substructures are searched using unified particle swarm optimization technique for exact identification of damage location and amount. Efficiency of the developed procedure is demonstrated using beam like structures. This methodology may be extended for identifying damages in general frame structures.

• Advances in Computational Design
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• v.7 no.1
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• pp.81-98
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• 2022

This study presents the application of two indices for the locating of cracks in Reinforced Concrete (RC) structures, as well as the development of their modified forms to overcome limitations. The first index is based on mode shape curvature and the second index is based on the fourth derivative of the mode shape. In order to confirm the indices' effectiveness, both eigenvalues coupled with nonlinear static analyses were carried out and the eigenvectors for two different damage locations and intensities of load were obtained from the finite element model of RC beams. The values of the damage-locating indices derived using both indices were then compared. Generally, the mode shape curvature-based index suffered from insensitivity when attempting to detect the damage location; this also applied to the mode shape fourth derivative-based index at lower modes. However, at higher modes, the mode shape fourth derivative-based index gave an acceptable indication of the damage location. Both the indices showed inconsistencies and anomalies at the supports. This study proposed modification to both indices to overcome identified flaws. The results proved that modified forms exhibited better sensitivity for identifying the damage location. In addition, anomalies at the supports were eliminated.

• Structural Engineering and Mechanics
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• v.53 no.4
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• pp.725-744
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• 2015

In this paper, a new damage indicator based on mode shape data is introduced to identify damage in beam structures. In order to construct the indicator proposed, the mode shape, mode shape slope and mode shape curvature of a beam before and after damage are utilized. Mode shape data of the beam are first obtained here using a finite element modeling and then the slope and curvature of mode shape are evaluated via the central finite difference method. In order to assess the robustness of the proposed indicator, two test examples including a simply supported beam and a two-span beam are considered. Numerical results demonstrate that using the proposed indicator, the location of single and multiple damage cases having different characteristics can be accurately determined. Moreover, the indicator shows a better performance when compared with a well-known indicator found in the literature.

• Smart Structures and Systems
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• v.3 no.1
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• pp.23-49
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• 2007

Wavelet transforms are the emerging signal-processing tools for damage identification and time-frequency localization. A small perturbation in a static or dynamic displacement profile could be captured using multi-resolution technique of wavelet analysis. The paper presents the wavelet analysis of damaged linear structural elements using DB4 or BIOR6.8 family of wavelets. Starting with a localized reduction of EI at the mid-span of a simply supported beam, damage modeling is done for a typical steel and reinforced concrete beam element. Rotation and curvature mode shapes are found to be the improved indicators of damage and when these are coupled with wavelet analysis, a clear picture of damage singularity emerges. In the steel beam, the damage is modeled as a rotational spring and for an RC section, moment curvature relationship is used to compute the effective EI. Wavelet analysis is performed for these damage models for displacement, rotation and curvature mode shapes as well as static deformation profiles. It is shown that all the damage indicators like displacement, slope and curvature are magnified under higher modes. A localization scheme with arbitrary location of curvature nodes within a pseudo span is developed for steady state dynamic loads, such that curvature response and damages are maximized and the scheme is numerically tested and proved.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.1434-1439
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• 2004

CFRP composite materials have wide application in structure materials of airplane, ships, and aero space vehicles because of their high strength and stiffness. This paper is to study the effects of curvature and orientation angle on the penetration characteristics of CFRP laminate shell. They are staked with 8 Ply specimens [0$_2$/90$_2$]$_{s}$, [0/90$_2$/0]$_{s}$ and the stacked of outer plates degree with 12 Ply specimens [0$_3$/90$_3$]$_{s}$, [0$_2$/90$_2$/0]$_{s}$ and [90$_3$/0$_3$], [90$_2$/0$_2$/90]S. They are manufactured to varied curvature radius (R=100,150,200mm and $\infty$). They are cured by heating to the appropriate harding temperature(13$0^{\circ}C$) by mean of a heater at the vaccum bag of the autoclave. Test specimens were prepared with dimensions 100mm$\times$140mm. When the specimen is subjected to transverse impact by a steel ball, the velocity of the steel ball was measured both before and after impact by determining the time for it to pass two ballistic-screen sensor located a known distance apart. In general, kinetic energy after impact-kinetic energy before impact rised in all specimens. This study observed a fracture mode inside the specimen after a penetration test using a digital camera and it examined a fracture mode and a penetration mode to stack of outer orientation angle and curvature.rvature.

• Structural Engineering and Mechanics
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• v.54 no.4
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• pp.711-723
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• 2015

This study investigates the identification of added mass and its location in the glass fiber reinforced polymer (GFRP) beam structures. The main emphasis of this paper is to ascertain the importance of inclusion of rotational degrees of freedom (dofs) in the introduction of added mass or damage identification. Two identification indices that include the rotational dofs have been introduced in this paper: the modal force index (MFI) and the modal rotational curvature index (MRCI). The MFI amplifies damage signature using undamaged numerical stiffness matrix which is related to changes in the altered mode shapes from the original mode shapes. The MRCI is obtained by using a higher derivative of rotational mode shapes. Experimental and numerical results are compared with the existing methods leading to a conclusion that the contributions of the rotational modes play a key role in the identification of added mass. The authors believe that the similar results are likely in the case of damage identification also.

• Journal of KSNVE
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• v.10 no.2
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• pp.353-360
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• 2000

Numerical methods are developed for calculating the natural frequencies and mode shapes of the tapered cantilever arches with variable curvature. The differential equations governing the free vibrations of such arches are derived and solved numerically, in which the effect of rotatory inertia is included. The parabolic shape is chosen as the arch with variable curvature while both the prime and quadratic arched members are considered as the tapered arch with variable curvature while both the prime and quadratic arched members are considered as the tapered arch. Comparisons the natural jfrequencies between this study and finite element method SAP 90 seve to validate the numerical method developed herein. The lowest four natural frequencies are reported as a function of four non-dimensional system parameters. The effects of both the rotatory inertia and cross-sectional shape are reported. Also, the typical mode shapes of stress resultants as well as the displacements are reported.

• International Journal of Concrete Structures and Materials
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• v.10 no.3
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• pp.393-406
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• 2016

Axially loaded reinforced concrete columns are hardly exist in practice due to the development of some bending moments. These moments could be produced by gravity loads or the lateral loads. First, the current paper presents a detailed analysis on the overall structural behavior of 15 eccentrically loaded columns as well as one concentrically loaded control one. Columns bent in either single curvature or double curvature modes are tested experimentally up to failure under the effect of different end eccentricities combinations. Three end eccentricities ratio were studied, namely, 0.1b, 0.3b and 0.5b, where b is the column width. Second, an expression correlated the decay in the normalized axial capacity of the column and the acting end eccentricities was developed based on the experimental results and then verified against the available formula. Third, based on the equivalent column concept, the equivalent pin-ended columns were obtained for columns bent in either single or double curvature modes. And then, the effect of end eccentricity ratio was correlated to the equivalent column length. Finally, a simplified design procedure was proposed for eccentrically loaded braced column by transferring it to an equivalent axially loaded pin-ended slender column. The results of the proposed design procedure showed comparable results against the results of the ACI 318-14 code.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2008.10a
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• pp.42-45
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• 2008

Recently, aluminum is widely used to reduce the vehicle weight. Aluminum curved extruded products are used for the design of automotive frame parts. This study focuses on the determination of process condition fur automotive bumper beam with various curvatures. In this study, a curvature prediction model has been proposed considering the geometric relationship and the characteristic of the curvature extrusion equipment. Using the proposed model and FE analysis, the appropriated process condition was determined to produce the bumper beam. Finally, curvature extrusion experiment was carried out to verify the effectiveness of the proposed curvature prediction model and the process condition.