• Journal of the Korea institute for structural maintenance and inspection
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• v.10 no.6
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• pp.154-163
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• 2006

This paper presents a nonlinear analysis method for the reinforced concrete beams strengthened by the external bonding of high strength, lightweight fiber sheets on the tension face of the beams. The method is based on the results of experimental studies. The experimental study involved tensile tests of 120 specimens to evaluate the tensile properties of fiber sheets(carbon, glass, and aramid fiber) and bending tests of 75 beams strengthened with various types of fiber sheets to evaluate the flexural capacities. Based on these experimental results, reasonable rupture strains of the fiber sheets were estimated. The nonlinear flexural analysis considered nonlinear flexural stresses as compressive and tensile stresses of concrete, load-deflection curves, and rupture strains of fiber sheets. The nonlinear flexural analysis accurately predicts the load-deflection response and the flexural behavior of the retrofitted beams.

• International Journal of Aeronautical and Space Sciences
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• v.7 no.2
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• pp.110-120
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• 2006

There have been developed many structural and fluid rotorcraft analysis models in rotorcraft community, and also lots of investigations have been conducted to combine these two models. These investigations turn out to be good at predicting the airloads precisely, but they have not taken the blade nonlinear deflection into account. For this reason, the present paper adopts a sophisticated structural model which can describe three-dimensional nonlinear deflection of the blade. And it is combined with two types of aerodynamic model. First one is generalized Greenberg type of finite-time aerodynamic model, which is originally established for a fixed wing, but later modified to be suitable for coupled flap-lag-torsional aeroelastic analysis of the rotor blade. Second aerodynamic model is based on the unsteady source-doublet panel method coupled with a free wake model. The advantages of the present method are capabilities to consider thickness of the blade and more precise wake effects. Transient responses of the airloads and structural deflections in time domain are mainly analyzed in this paper.

• Journal of Korean Association for Spatial Structures
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• v.9 no.2
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• pp.91-97
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• 2009

This study presents geometric nonlinear and material analysis of under-tension structure using Total Lagrangian and Updated Lagrangian method. In the regard, the under-tension system enables the load of upper part to carry to the end of beam by pre-tensional force in cable. The under-tension system on lower part of the structure is applied in order to reduce the deflection and size of member. This study is performed with conforming of the effect by pretension value in the cable and applying loading. Dead and Live loads are supposed to apply nodal on the top member. The member force and deflection of the structure are with MIDAS and ADINA.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11a
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• pp.297-303
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• 2001

This research presents an analytical model to characterize the ball bearing vibration due to the waviness in a rigid rotor supported by multi-row ball bearings considering centrifugal force and gyroscopic moment of ball. The effects of centrifugal force and gyroscopic moment are introduced to the kinematic constraints and force equilibrium equations. The waviness of ball and races is modeled by the superposition of sinusoidal function and it is introduced to position vectors of race curvature center to use the Hertzian contact theory in order to calculate the elastic deflection and nonlinear contact force resulting from the waviness while the rotor has translational and angular motion. They can be determined by solving the nonlinear equations of motion with five degrees of freedom by using the Runge-Kutta-Fehlberg algorithm. The accuracy of this research is validated by comparing with the results of the prior researches. It characterizes the vibration frequencies resulting from the various kinds of waviness in rolling elements, the harmonic frequencies resulting from the nonlinear load-deflection characteristics of ball bearing resulting from the waviness interaction.

• Steel and Composite Structures
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• v.44 no.3
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• pp.371-388
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• 2022

The present study tackles the problem of forced vibration of imperfect axially functionally graded shell structure with truncated conical geometry. The linear and nonlinear large-deflection of the structure are considered in the mathematical formulation using von-Kármán models. Modified coupled stress method and principle of minimum virtual work are employed in the modeling to obtain the final governing equations. In addition, formulations of classical elasticity theory are also presented. Different functions, including the linear, convex, and exponential cross-section shapes, are considered in the grading material modeling along the thickness direction. The grading properties of the material are a direct result of the porosity change in the thickness direction. Vibration responses of the structure are calculated using the semi-analytical method of a couple of homotopy perturbation methods (HPM) and the generalized differential quadrature method (GDQM). Contradicting effects of small-scale, porosity, and volume fraction parameters on the nonlinear amplitude, frequency ratio, dynamic deflection, resonance frequency, and natural frequency are observed for shell structure under various boundary conditions.

• Structural Engineering and Mechanics
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• v.24 no.6
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• pp.647-664
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• 2006

In this study, an improved finite element formulation with a scheme of solution for the large deflection analysis of inextensible prismatic and nonprismatic slender beams is developed. For this purpose, a three-noded Lagrangian beam-element with two dependent degrees of freedom per node (i.e., the vertical displacement, y, and the actual slope, $dy/ds=sin{\theta}$, where s is the curved coordinate along the deflected beam) is used to derive the element stiffness matrix. The element stiffness matrix in the global xy-coordinate system is achieved by means of coordinate transformation of a highly nonlinear ($6{\times}6$) element matrix in the local sy-coordinate. Because of bending with large curvature, highly nonlinear expressions are developed within the global stiffness matrix. To achieve the solution after specifying the proper loading and boundary conditions, an iterative quasi-linearization technique with successive corrections are employed considering these nonlinear expressions to remain constant during all iterations of the solution. In order to verify the validity and the accuracy of this study, the vertical and the horizontal displacements of prismatic and nonprismatic beams subjected to various cases of loading and boundary conditions are evaluated and compared with analytic solutions and numerical results by available references and the results by ADINA, and excellent agreements were achieved. The main advantage of the present technique is that the solution is directly obtained, i.e., non-incremental approach, using few iterations (3 to 6 iterations) and without the need to split the stiffness matrix into elastic and geometric matrices.

• Structural Engineering and Mechanics
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• v.68 no.2
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• pp.247-259
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• 2018

In this study (Part I), an advanced empirical formulation was proposed to predict the ultimate strength of initially deflected steel plate subjected to longitudinal compression. An advanced empirical formulation was proposed by adopting Initial Deflection Index (IDI) concept for plate element which is a function of plate slenderness ratio (${\beta}$) and coefficient of initial deflection. In case of initial deflection, buckling mode shape, which is mostly assumed type in the ships and offshore industry, was adopted. For the numerical simulation by ANSYS nonlinear finite element method (NLFEM), with a total of seven hundred 700 plate scenarios, including the combination of one hundred (100) cases of plate slenderness ratios with seven (7) representative initial deflection coefficients, were selected based on obtained probability density distributions of plate element from collected commercial ships. The obtained empirical formulation showed good agreement ($R^2=0.99$) with numerical simulation results. The obtained outcome with proposed procedure will be very useful in predicting the ultimate strength performance of plate element subjected to longitudinal compression.

• Steel and Composite Structures
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• v.26 no.5
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• pp.595-606
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• 2018

A calculation method was presented to calculate the deflection of GFRP-concrete-steel beams with full or partial shear connections. First, the sectional analysis method was improved by considering concrete nonlinearity and shear connection stiffness variation along the beam direction. Then the equivalent slip strain was used to take into consideration of variable cross-sections. Experiments and nonlinear finite element analysis were performed to validate the calculation method. The experimental results showed the deflection of composite beams could be accurately predicted by using the theoretical model or the finite element simulation. Furthermore, more finite element models were established to verify the accuracy of the theoretical model, which included different GFRP plates and different numbers of shear connectors. The theoretical results agreed well with the numerical results. In addition, parametric studies using theoretical method were also performed to find out the effect of parameters on the deflection. Based on the parametric studies, a simplified calculation formula of GFRP-concrete-steel composite beam was exhibited. In general, the calculation method could provide a more accurate theoretical result without complex finite element simulation, and serve for the further study of continuous GFRP-concrete-steel composite beams.

• Structural Engineering and Mechanics
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• v.35 no.4
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• pp.387-407
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• 2010

In this paper, using perturbation and Galerkin method, the response of a resonant viscoelastic microbeam to an electric actuation is obtained. The microbeam is under axial load and electrical load. It is assumed that midplane is stretched, when the beam is deflected. The equation of motion is derived using the Newton's second law. The viscoelastic model is taken to be the Kelvin-Voigt model. In the first section, the static deflection is obtained using the Galerkin method. Exact linear symmetric mode shape of a straight beam and its deflection function under constant transverse load are used as admissible functions. So, an analytical expression that describes the static deflection at all points is obtained. Comparing the result with previous research show that using deflection function as admissible function decreases the computation errors and previous calculations volume. In the second section, the response of a microbeam resonator system under primary and secondary resonance excitation has been obtained by analytical multiple scale perturbation method combined with the Galerkin method. It is shown, that a small amount of viscoelastic damping has an important effect and causes to decrease the maximum amplitude of response, and to shift the resonance frequency. Also, it shown, that an increase of the DC voltage, ratio of the air gap to the microbeam thickness, tensile axial load, would increase the effect of viscoelastic damping, and an increase of the compressive axial load would decrease the effect of viscoelastic damping.

• Structural Engineering and Mechanics
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• v.84 no.3
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• pp.361-373
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• 2022

This paper examines the flexural performance of concrete beams reinforced with glass fibre-reinforced polymer (GFRP) bars under fatigue loading. Experiments were carried out on concrete beams of size 1500×200×100 mm reinforced with 10 mm and 13 mm diameter GFRP bars under fatigue loading. Experimental investigations revealed that fatigue loading affects both strength and serviceability properties of GFRP reinforced concrete. Experimental results indicated that (i) the concrete beams experienced increase in deflection with increase in number of cycles and failed suddenly due to snapping of rebars and (ii) the fatigue life of concrete beams drastically decreased with increase in stress level. Analytical model presented a procedure for predicting the deflection of concrete beams reinforced with GFRP bars under cyclic loading. Deflection of concrete beams was computed by considering the aspects such as stiffness degradation, force equilibrium equations and effective moment of inertia. Nonlinear finite element (FE) analysis was performed on concrete beams reinforced with GFRP bars. Appropriate constitutive relationships for concrete and GFRP bars were considered in the numerical modelling. Concrete non linearity has been accounted through concrete damage plasticity model available in ABAQUS. Deflection versus number of cycles obtained experimentally for various beams was compared with the analytical and numerical predictions. It was observed that the predicted values are comparable (less than 20% difference) with the corresponding experimental observations.