• Structural Engineering and Mechanics
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• v.49 no.3
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• pp.373-393
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• 2014

A finite element model for predicting the entire nonlinear behavior of reinforced high-strength concrete continuous beams is described. The model is based on the moment-curvature relations pre-generated through section analysis, and is formulated utilizing the Timoshenko beam theory. The validity of the model is verified with experimental results of a series of continuous high-strength concrete beam specimens. Some important aspects of behavior of the beams having different tensile reinforcement ratios are evaluated. In addition, a parametric study is carried out on continuous high-strength concrete beams with practical dimensions to examine the effect of tensile reinforcement on the degree of moment redistribution. The analysis shows that the tensile reinforcement in continuous high-strength concrete beams affects significantly the member behavior, namely, the flexural cracking stiffness, flexural ductility, neutral axis depth and redistribution of moments. It is also found that the relation between the tensile reinforcement ratios at critical negative and positive moment regions has great influence on the moment redistribution, while the importance of this factor is neglected in various codes.

• Structural Engineering and Mechanics
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• v.75 no.5
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• pp.633-642
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• 2020

Artificial neural networks (ANNs) are known as intelligent methods for modeling the behavior of physical phenomena because of it is a soft computing technique and takes data samples rather than entire data sets to arrive at solutions, which saves both time and money. ANN is successfully used in the civil engineering applications which are suitable examining the complicated relations between variables. Functionally graded materials (FGMs) are advanced composites that successfully used in various engineering design. The FGMs are nonhomogeneous materials and made of two different type of materials. In the present study, the bending analysis of functionally graded material (FGM) beams presents on theoretical based on combination of mixed-finite element method, Gâteaux differential and Timoshenko beam theory. The main idea in this study is to build a model using ANN with four parameters that are: Young's modulus ratio (E_t/E_b), a shear correction factor (k_s), power-law exponent (n) and length to thickness ratio (L/h). The output data is the maximum displacement (w). In the experiments: 252 different data are used. The proposed ANN model is evaluated by the correlation of the coefficient (R), MAE and MSE statistical methods. The ANN model is very good and the maximum displacement can be predicted in ANN without attempting any experiments.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.3 s.96
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• pp.251-258
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• 2005

The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings (HDB) in an HDD is analyzed by FEM. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Reynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigen value problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.572-578
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• 2003

The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings in a HDD is analyzed by FEM. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Raynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigenvalue problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

• Journal of the Society of Naval Architects of Korea
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• v.53 no.4
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• pp.307-314
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• 2016

Energy flow analysis(EFA) is a representative method that can predict the statistical energetics of structures at high frequencies. Generally, as the frequency increases, the shear distortion and rotatory inertia effects in the out-of-plane motion of beams or plates become important. Therefore, to predict the out-of-plane energetics of coupled structures in the high frequency range, the energy flow analyses of Timoshenko beam and Mindlin plate are required. Unlike the energy flow model of Kirchhoff plate, the energy flow model of Mindlin plate is composed of three kinds of energy governing equations(out-of-plane shear wave, bending dominant flexural wave, and shear dominant flexural wave). This paper performed the energy flow finite element analysis(EFFEA) of coplanar coupled Mindlin plates. For EFFEA of coplanar coupled Mindlin plates, the energy flow finite element formulation of out-of-plane energetics in the Mindlin plate was performed. The general EFFEA program was implemented by MATLAB® language. For the verification of EFFEA of Mindlin plate, the various numerical applications were done successfully.

• Steel and Composite Structures
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• v.31 no.6
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• pp.591-600
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• 2019

Based on the energy-variational principle, a coupling vibration analysis model of high-speed railway simply supported beam bridge-track structure system (HSRBTS) was established by considering the effect of shear deformation. The vibration differential equation and natural boundary conditions of HSRBTS were derived by considering the interlayer slip effect. Then, an analytic calculation method for the natural vibration frequency of this system was obtained. By taking two simply supported beam bridges of high-speed railway of 24 m and 32 m in span as examples, ANSYS and MIDAS finite-element numerical calculation methods were compared with the analytic method established in this paper. The calculation results show that two of them agree well with each other, validating the analytic method reported in this paper. The analytic method established in this study was used to evaluate the natural vibration characteristics of HSRBTS under different interlayer stiffness and length of rails at different subgrade sections. The results show that the vertical interlayer compressive stiffness had a great influence on the high-order natural vibration frequency of HSRBTS, and the effect of longitudinal interlayer slip stiffness on the natural vibration frequency of HSRBTS could be ignored. Under different vertical interlayer stiffness conditions, the subgrade section of HSRBTS has a critical rail length, and the critical length of rail at subgrade section decreases with the increase in vertical interlayer compressive stiffness.

• Steel and Composite Structures
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• v.52 no.1
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• pp.77-87
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• 2024

Analytical methods for assessment of the out-of-plane buckling of unbraced top chords of truss bridges may look obsolete while comparing them to finite element analysis. However they are, usually, superior when rapid assessment is necessary. Analytical methods consider the top chord as a bar on elastic supports provided by bracing (Holt, Timoshenko). Correct assessment of the support elasticity (stiffness) is crucial. In the case of truss bridge spans of traditional structural layout (cross-beams at the truss chord nodes only), the elasticity may be set based on the analysis of the, so called, U-frame stiffness. Here the analyses consider the U-frame itself (a pair of verticals and a cross-beam) or the U-frame with adjacent diagonals or the pair of diagonals (in the absence of verticals) and the members of the bottom chord in the adjacent panels. For all the cases, the stability analysis of the chord as a bar in compression is necessary. Unfortunately, the method cannot be applied to contemporary truss bridges without verticals, that usually have independent cross-beam decks (the cross-beams attached to truss chords at their nodes and between them). This is the motivation for the analysis resulting in the method of setting the stiffness of the equivalent U-frame for the aforementioned truss bridges. Truss girders of both, gussetless and gusseted, joints are taken into account.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.859-865
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• 2007

This paper presents a method to analyze the unbalance response of a high speed polygon mirror scanner motor supported by sintered bearing and flexible supporting structures by using the finite element method and the mode superposition method. The appropriate finite element equations for polygon mirror are described by rotating annular sector element using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. The rotating components except for the polygon mirror are modeled by Timoshenko beam element including the gyroscopic effect. The flexible supporting structures are modeled by using a 4-node tetrahedron element and 4-node shell element with rotational degrees of freedom. Finite element equations of each component of the polygon mirror scanner motor and the flexible supporting structures are consistently derived by satisfying the geometric compatibility in the internal boundary between each component. The rigid link constraints are also imposed at the interface area between sleeve and sintered bearing to describe the physical motion at this interface. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem by using the restarted Arnoldi iteration method. Unbalance responses in time and frequency domain are performed by superposing the eigenvalues and eigenvectors from the free vibration analysis. The validity of the proposed method is verified by comparing the simulated unbalance response with the experimental results. This research also shows that the flexibility of supporting structures plays an important role in determining the unbalance response of the polygon mirror scanner motor.

• Steel and Composite Structures
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• v.35 no.1
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• pp.61-76
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• 2020

In this paper, the dynamic behaviour of an inclined functionally graded material (FGM) beam with different boundary conditions under a moving mass is investigated based on the first-order shear deformation theory (FSDT). The material properties vary continuously along the beam thickness based on the power-law distribution. The system of motion equations is derived by using Hamilton's principle. The finite element method (FEM) is adopted to develop a general solution procedure. The moving mass is considered on the top surface of the beam instead of supposing it on the mid-plane. In order to consider the Coriolis, centrifugal accelerations and the friction force, the contact force method is used. Moreover, the effects of boundary conditions, the moving mass velocity and various material distributions are studied. For verification of the present results, a comparative fundamental frequency analysis of an FGM beam is conducted and the dynamic transverse displacements of the homogeneous and FGM beams traversed by a moving mass are compared with those in the existing literature. There is a good accord in all compared cases. In this study for the first time in dynamic analysis of the inclined FGM beams, the Coriolis and centrifugal accelerations of the moving mass are taken into account, and it is observed that these accelerations can be ignored for the low-speeds of the moving mass. The new provided results for dynamics of the inclined FGM beams traversed by a moving mass can be significant for the scientific and engineering community in the area of FGM structures.

• Advances in nano research
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• v.7 no.6
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• pp.443-457
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• 2019

In this investigation, dynamic and bending behaviors of isolated protein microtubules are analyzed. Microtubules (MTs) can be considered as bio-composite structures that are elements of the cytoskeleton in eukaryotic cells and posses considerable roles in cellular activities. They have higher mechanical characteristics such as superior flexibility and stiffness. In the modeling purpose of microtubules according to a hollow beam element, a novel single variable sinusoidal beam model is proposed with the conjunction of modified strain gradient theory. The advantage of this model is found in its new displacement field involving only one unknown as the Euler-Bernoulli beam theory, which is even less than the Timoshenko beam theory. The equations of motion are constructed by considering Hamilton's principle. The obtained results are validated by comparing them with those given based on higher shear deformation beam theory containing a higher number of variables. A parametric investigation is established to examine the impacts of shear deformation, length scale coefficient, aspect ratio and shear modulus ratio on dynamic and bending behaviors of microtubules. It is remarked that when length scale coefficients are almost identical of the outer diameter of MTs, microstructure-dependent behavior becomes more important.