• Structural Engineering and Mechanics
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• 제5권6호
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• pp.715-728
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• 1997

The aim of this paper is to investigate the secondary buckling behaviour and mode-coupling of spherical caps under uniformly external pressure. The analysis makes use of a rotational finite shell element on the basis of strain-displacement relations according to Koiter's shell theory (Small Finite Deflections). The post-buckling behaviours after a bifurcation point are analyzed precisely by considering multi-mode coupling between several higher order harmonic wave numbers: and on the way of post-buckling path the positive definiteness of incremental stiffness matrix of uncoupled modes is examined step by step. The secondary buckling point that has zero eigen-value of incremental stiffness matrix and the corresponding secondary mode are obtained, moreover, the secondary post-buckling path is traced.

• Structural Engineering and Mechanics
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• 제51권5호
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• pp.773-792
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• 2014

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

• Proceedings of the KSME Conference
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• 대한기계학회 2001년도 춘계학술대회논문집A
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• pp.969-974
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• 2001

Circular cylindrical tubes are widely used in structures such as vehicles and aircraft structures, where light weight and high compressive/bending/torsional load carrying capacity are required. When axially compressed, relatively thick circular cylindrical tubes deform in a so-called ring mode. Each ring develops and completely collapses one by one until the entire length of the tube collapses. During the collapse process the tube absorbs a large amount of energy. Like honey-comb structures, circular cylindrical tubes are light weighted, are capable of high axial compressive load, and absorb a large amount of energy before being completely collapsed. In this report, the subject of axial plastic buckling of circular cylindrical tubes was reviewed first. Then, the axial collapse process of the tubes in a so-called ring mode was studied both experimentally and numerically. In the experiment, steel tubes were axially compressed slowly until they were completely collapsed. Fixed boundary condition was provided. Numerical study involves axisymmetric, elastic-plastic, large deflection, self-contact mechanisms. The measured and calculated results were presented and compared with each other. The purpose of the study was to evaluate the load carrying capacity and the energy absorbing capacity of the tube.

• Smart Structures and Systems
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• 제5권3호
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• pp.291-316
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• 2009

Damage detection using structural classical deflection flexibility has received considerable attention due to the unique features of the flexibility in the last two decades. However, for relatively complex structures, most methods based on classical deflection flexibility fail to locate damage sites to the exact members. In this study, for structures whose members are dominated by axial forces, such as truss structures, a more feasible flexibility for damage detection is proposed, which is called the Axial Strain (AS) flexibility. It is synthesized from measured modal frequencies and axial strain mode shapes which are expressed in terms of translational mode shapes. A damage indicator based on AS flexibility is proposed. In addition, how to integrate the AS flexibility into the Damage Location Vector (DLV) approach (Bernal and Gunes 2004) to improve its performance of damage localization is presented. The methods based on AS flexbility localize multiple damages to the exact members and they are suitable for the cases where the baseline data of the intact structure is not available. The proposed methods are demonstrated by numerical simulations of a 14-bay planar truss and a five-story steel frame and experiments on a five-story steel frame.

• Structural Engineering and Mechanics
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• 제84권1호
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• pp.49-61
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• 2022

This paper presents an experimental investigation into the effectiveness of using carbon fibre reinforced polymer (CFRP) and steel plates to repair damaged reinforced concrete (RC) beams with circular web openings at shear zones. It highlights the effectiveness of externally bonded CFRP and steel plates in repairing damaged RC beams by analysing the repaired beams'load capacity, deflection, strain, and failure mode. For the experiment, a total of five beams were used, with one solid beam as a control beam and the other four beams having an opening near the shear zone. Two beams with openings were repaired using inclined and vertical configuration CFRP plates, and the other two were repaired using inclined and vertical configuration steel plates. The results confirm the effectiveness of CFRP and steel plates for repairing damaged RC beams with circular openings. The CFRP and steel plates significantly increase ultimate capacity and reduce deflection under the openings. The inclined configuration of both CFRP and steel plates was more effective than the vertical configuration. Using an inclined configuration not only increases the ultimate capacity of the beams but also changes the mode of failure from shear to flexural.

• Current Optics and Photonics
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• 제4권2호
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• pp.95-102
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• 2020

The impact of graphene and poly(methyl methacrylate) (PMMA) substrates on the response of a fiber Bragg grating (FBG) due to mechanical deflection was investigated. For this purpose, four FBGs with grating lengths of 5, 15, 25, and 35.9 mm were utilized. Higher sensitivity was found for FBGs of larger grating length and for those bonded to graphene substrate. It was concluded that FBGs of smaller grating length (5 and 15 mm) were more sensitive in compression mode, while those of larger grating length (25 and 35.9 mm) were seen to be highly sensitive in tension mode.

• Steel and Composite Structures
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• 제3권5호
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• pp.321-331
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• 2003

The paper presents the results of an experimental investigation conducted on welded tubular joints, that are employed in offshore platforms, to study the behaviour and strength of these joints under axial brace compression loading. The geometrical configuration of the joints tested were T and Y. The nominal diameter of the chord and brace members of the joint were 324 and 219 mm respectively. The chord thickness was 12 mm and the brace 8 mm. The tested joints are approximately quarter size when compared to the largest joints in the platforms built in a shallow water depth of 80 m in the Bombay High field. Some of the joints were actually fabricated by a leading offshore agency which firm is directly involved in the fabrication of prototype structures. Strength of the internally ring-stiffened joints was found to be almost twice that of the unstiffened joints of the same configuration and dimensions. Bending of the chord as a whole was observed to be the predominant mode of deformation of the internally ring-stiffened joints in contrast to ovaling and punching shear of the unstiffened joints. It was observed in this investigation that unstiffened joint was stiffer in ovaling mode than in bending and that midspan deflection of unstiffened joint was insignificant when compared to that of the internally ring stiffened joint. The measured midspan deflection of the unstiffened joint in this investigation and its relation with the applied axial load compares very well with that predicted for the brace axial displacement by energy method published in the literature. A comparison of the measured deflection and ovaling of the unstiffened joint was made with that published by the author elsewhere in which numerical prediction of both quantities have been made using ANSYS software package. The agreement was found to be quite good.

• Magazine of the Korean Society of Agricultural Engineers
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• 제38권3호
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• pp.50-57
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• 1996

A numerical method is presented to obtain the natural frequencies and mode shapes of the arbitrary tapered beams with static deflection due to arbitrary distributed dead loads. The differential equation governing free vibration of such beams is derived and solved numerically. The double integration method using the trapezoidal rule is used to solve the static behaviour of beams loaded arbitrary distributed dead load. Also, the Improved Euler method and the determinant search method are used to integrate the differential equation subjected to the boundary conditions and to determine the natural frequencies of the beams, respectively. In the numerical examples, the various geometries of the beams are considered : (1) linearly tapered beams as the arbitrary variable cross-section, (2) the triangular, sinusoidal and uniform loads as the arbitrary distributed dead loads and (3) the hinged-hinged, clamped-clamped and hinged-clamped ends as the end constraints. All numerical results are shown as the non-dimensional forms of the system parameters. The lowest three natural frequencies versus load parameter, slenderness ratio and section ratio are reported in figures. And for the comparison purpose, the typical mode shapes with and without the effects of static deflection are presented in the figure. According to the numerical results obtained in this analysis, the following conclusions may be drawn : (1) the natural frequencies increase when the effects of static deflections are included, (2) the effects are larger at the lower modes than the higher ones and (3) it should be betteF to include the effect of static deflection for calculating the frequencies when the beams are supported by both hinged ends or one hinged end.

• Journal of the Korea Concrete Institute
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• 제12권2호
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• pp.63-69
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• 2000

This study investigates a new method of using a concrete disk to calculate stress intensity factor (SIF) for mixed mode cases. The results indicate that the disk method is more accurate than three point bending test (TPB) in obtaining correct SIF values for mixed mode fracture propagation. Stress intensity factors $K_{I}$ and $K_{II}$ are calculated using a center notched disk subjected to splitting load. The notch angle is calculated by finite element (FEM). Fracture toughness $K_\textsc{k}$ of the concrete is obtained from the load intensities at the initiation of crack propagation. According to the finite element analysis(FEA) and disk test, the results show that mode I and mixed mode cracks propagate toward the directions of crack face and loading point, respectively. The results from FEA with maximum stress theory compare well with the experimental date. Unlike TPB method where an accurate fracture toughness value is difficult to obtain due to the irregular shape of load deflection curve and delayed final crack propagation (following slow stable cracking). fracture toughness value is easily measured in the disk test from the crack initial load. Therefore, it is safe to conclude that disk method is more advantageous than TPB method in analyzing combined mode fracture problems.

• Journal of Mechanical Science and Technology
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• 제20권9호
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• pp.1371-1381
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• 2006

This paper deals with the active vibration control of a simply-supported beam traversed by a moving mass using fuzzy control. Governing equations for dynamic responses of a beam under a moving mass are derived by Galerkin's mode summation method, and the effect of forces (gravity force, Coliolis force, inertia force caused by the slope of the beam, transverse inertia force of the beam) due to the moving mass on the dynamic response of a beam is discussed. For the active control of dynamic deflection and vibration of a beam under the moving mass, the controller based on fuzzy logic is used and the experiments are conducted by VCM (voice coil motor) actuator to suppress the vibration of a beam. Through the numerical and experimental studies, the following conclusions were obtained. With increasing mass ratio y at a fixed velocity of the moving mass under the critical velocity, the position of moving mass at the maximum dynamic deflection moves to the right end of the beam. With increasing velocity of the moving mass at a fixed mass ratio ${\gamma}$, the position of moving mass at the maximum dynamic deflection moves to the right end of the beam too. The numerical predictions of dynamic deflection of the beam have a good agreement with the experimental results. With the fuzzy control, more than 50% reductions of dynamic deflection and residual vibration of the tested beam under the moving mass are obtained.