• Journal of Korean Association for Spatial Structures
• /
• v.6 no.4 s.22
• /
• pp.81-92
• /
• 2006

This paper presents exact solutions for the free vibrations and buckling of rectangular plates having two opposite, simply supported edges subjected to linearly varying normal stresses causing pure in-plane moments, the other two edges being free. Assuming displacement functions which are sinusoidal in the direction of loading (x), the simply supported edge conditions are satisfied exactly. With this the differential equation of motion for the plate is reduced to an ordinary one having variable coefficients (in y). This equation is solved exactly by assuming power series in y and obtaining its proper coefficients (the method of Frobenius). Applying the free edge boundary conditions at y=0, b yields a fourth order characteristic determinant for the critical buckling moments and vibration frequencies. Convergence of the series is studied carefully. Numerical results are obtained for the critical buckling moments and some of their associated mode shapes. Comparisons are made with known results from less accurate one-dimensional beam theory. Free vibration frequency and mode shape results are also presented. Because the buckling and frequency parameters depend upon Poisson's ratio ( V ), results are shown for $0{\leq}v{\leq}0.5$, valid for isotropic materials.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.27 no.2
• /
• pp.63-70
• /
• 2014

Design sensitivity analysis and topology design optimization for a piezoelectric crystal resonator are developed. The piezoelectric crystal resonator is deformed mechanically when subjected to electric charge on the electrodes, or vice versa. The Mindlin plate theory with higher-order interpolations along thickness direction is employed for analyzing the thickness-shear vibrations of the crystal resonator. Thin electrode plates are masked on the top and bottom layers of the crystal plate in order to enforce to vibrate it or detect electric signals. Although the electrode is very thin, its weight and shape could change the performance of the resonators. Thus, the design variables are the bulk material densities corresponding to the mass of masking electrode plates. An optimization problem is formulated to find the optimal topology of electrodes, maximizing the thickness-shear contribution of strain energy at the desired motion and restricting the allowable volume and area of masking plates. The necessary design gradients for the thickness-shear frequency(eigenvalue) and the corresponding mode shape(eigenvector) are computed very efficiently and accurately using the analytical design sensitivity analysis method using the eigenvector expansion concept. Through some demonstrative numerical examples, the design sensitivity analysis method is verified to be very efficient and accurate by comparing with the finite difference method. It is also observed that the optimal electrode design yields an improved mode shape and thickness-shear energy.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.29 no.1A
• /
• pp.31-43
• /
• 2009

In this study, the numerical method is presented, which can consider the various train types and can solve the equations of motion for a vehicle-bridge interaction analysis by non-iteration procedure through formulating the coupled equations of motion. The coupled equations of motion for the vehicle-bridge interaction are solved by the Newmark ${\beta}$ of a direct integration method, and by composing the effective stiffness matrix and the effective force vector according to a analysis step, those can be solved with the same manner of the solving procedure of equilibrium equations in static analysis. Also, the effective stiffness matrix is reconstructed by the Skyline method for increasing the analysis effectiveness. The Cholesky's matrix decomposition scheme is applied to the analysis procedure for minimizing the numerical errors that can be generated in directly calculating the inverse matrix. The equations of motion for the conventional trains are derived, and the numerical models of the conventional trains are idealized by a set of linear springs and dashpots with 16 degrees of freedom. The bridge models are simplified by the 3 dimensional space frame element which is based on the Euler-Bernoulli theory. The rail irregularities of vertical and lateral directions are generated by the PSD functions of the Federal Railroad Administration (FRA). The results of the vehicle-bridge interaction analysis are verified by the experimental results for the railway plate girder bridges of a span length with 12 m, 18 m, and the experimental and analytical data are applied to the low pass filtering scheme, and the basis frequency of the filtering is a 2 times of the 1st fundamental frequency of a bridge bending.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.5 no.1
• /
• pp.43-53
• /
• 1985

This study proposes a reliability based design criteria for the steel bridge (H-beam, plate-girder and composite-beam), which is most common type of steel bridge, and also proposes the theoretical bases of nominal safety factors as well as load and rasistance factors based on the reliability theory. Major 2nd moment reliability analysis and design theories including both Cornell's MFOSM (Mean First Order 2nd Moment) Methods and Lind-Hasofer's AFOSM(Advanced First Order 2nd Moment) Methods are summarized and compared, and it has been found that Lind-Hasofer's approximate and an approximate Log-normal type reliability formula are well suited for the proposed reliability study. A target reliability index (${\beta}_0=3.5$) is selected as an optimal value considering our practice based on the calibration with the safety pravisions of the current steel bridge design code. Galambo's theory is used for the derivation of the algorithm for the evaluation of uncertainties associated with resistences by LRFD Format and SGST Format, whereas the magnitude of the uncertainties associated with load effects are chosen primarily by considering our level of practice. It may be concluded that the proposed LRFD reliability based design provisions for the steel highway bridge give more rational design than the current standard code for steel highway bridge.

• Composites Research
• /
• v.13 no.5
• /
• pp.50-59
• /
• 2000

In this paper, two methods to suppress flutter of the composite panel are examined. First, in the active control method, a controller based on the linear optimal control theory is designed and control input voltage is applied on the actuators and a PZT is used as actuator. Second, a new technique, passive suppression scheme, is suggested for suppression of the nonlinear panel flutter. In the passive suppression scheme, a shunt circuit which consists of inductor-resistor is used to increase damping of the system and as a result the flutter can be attenuated. A passive damping technology, which is believed to be more robust suppression system in practical operation, requires very little or no electrical power and additional apparatuses such as sensor system and controller are not needed. To achieve the great actuating force/damping effect, the optimal shape and location of the actuators are determined by using genetic algorithms. The governing equations are derived by using extended Hamilton's principle. They are based on the nonlinear von Karman strain-displacement relationship for the panel structure and quasi-steady first-order piston theory for the supersonic airflow. The discretized finite element equations are obtained by using 4-node conforming plate element. A modal reduction is performed to the finite element equations in order to suppress the panel flutter effectively and nonlinear-coupled modal equations are obtained. Numerical suppression results, which are based on the reduced nonlinear modal equations, are presented in time domain by using Newmark nonlinear time integration method.

• Journal of Korean Society of Steel Construction
• /
• v.9 no.4 s.33
• /
• pp.543-555
• /
• 1997

Generally, in a steel-concrete composite gilder, the shear connector which was constructed between concrete deck and steel girder should have enough stiffness to behave as one body, because the conformity between plate and concrete deck is influences by the stiffness and spacing of the shear connectors. If the stiffness of shear connectors are insufficient, slip would happen at the contact surface. Partial interaction is the case that takes account of slips. In this paper, an easy method is presented to evaluate the stiffness or spacing of the shear connector according to the degree of imperfection without difficult calculations for a composite gilder with partial interaction. Also, the horizontal shearing force applied to the shear connector and the longitudinal axial force, which is occurs at contact surface between concrete deck and steel girder, have been presented in a simple influence line that is various to the parameters of sectional properties, degree of imperfection and applied load points. Furthermore, through the case study, it determined the relationships between the degree of imperfection and the follows 1) spring constants 2) axial force and horizontal shearing force 3) stress and neutral axis by using the partial differential equation based on Newmark's Partial Interaction Theory.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.32 no.1
• /
• pp.37-44
• /
• 2019

A bond-based peridynamic model has been reported dynamic fracture characteristic of brittle materials through a simple constitutive model. In the model, each bond is assumed to be a simple spring operating independently. As a result, this simple bond interaction modeling restricts the material behavior having a fixed Poisson's ratio of 1/4 and not being capable of expressing shear deformation. We consider a state-based peridynamics as a generalized peridynamic model. Constitutive models in the state-based peridynamics are corresponding to those in continuum theory. In state-based peridynamics, thus, the response of a material particle depends collectively on deformation of all bonds connected to other particles. So, a state-based peridynamic theory can represent the volume and shear changes of the material. In this paper, the perfect plasticity is considered to express plastic deformation of material by the state-based peridynamic constitutive model with perfect plastic flow rule. The elastic-plastic behavior of the material is verified through the stress-strain curves of the flat plate example. Furthermore, we simulate the high-speed impact on 3D granite model with a nonlocal contact modeling. It is observed that the damage patterns obtained by peridynamics are similar to experimental observations.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.38 no.6
• /
• pp.697-705
• /
• 2020

This paper deals with an analysis of crustal movement for the sourthern part of Korean peninsula using GNSS (Global Navigation Satellite System) data. An earthquake of more than 5.0 occurred in the southeastern region of the Korean Peninsula, and it is necessary to evaluate the risk of earthquakes in various ways.In order to reveal long-term tectonic movement patten in Pohang and Gyeongju provinces, we derived crustal movement parameters related with elastic theory. We used GAMIT/GLOBK for analyzing seven-year interval GNSS data of CORS (Continuously Operating Reference Stations). The azimuth of velocity vectors trended generally about 110° with an mean magnitude of 31mm/yr.The main characteristics of the strain change for seven-year in Korea obtaind from our study. Direction of the principal axis of the maximum compression is ENE-WSW as a whole, through there are some exceptions. The mean rate of the maximum shear strain change is (0.11±0.07)μ/yr, that is approximately one third that of Chubu district, Central Japan. Taking into account our results, the mean rate of maximum shear in southern part of Korean peninsula is considered as reasonable. The mean azimuth of principal strain is about (85.4°±26.8°). There are some exceptions of azimuth because the average azimuth differ from the left and right side in Yangsan fault which are about (73.2°±21.5°) and (105.2°±17.0°) respectively, It is noteworthy that the high seismicity areas in the southern part of Korea peninsula almost coincides with the area of large strain rate. As a conclusion, it could be stated that the our study represents the characteristics of crustal deformation in the southern part of peninsula, and contributes to the researches on earthquake disaster management.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.28 no.5A
• /
• pp.649-656
• /
• 2008

The enhancement of the service life of damaged or cracked structures is a major issue for researchers and engineers. The hierarchic void element based on the integrals of Legendre polynomials is used to characterize the fracture behaviour of unpatched crack as well as repaired crack with bonded composite patches by computing the stress intensity factors and stress contours at the crack tip. Since the equivalent single layer approach is adopted in this study, the proposed element is necessary to represent a discontinuous crack part as a continuum body with zero stiffness. Thus the aspect ratio of this element to represent the crack should be extremely slender. The sensitivity of numerical solution with respect to energy release rate, displacement and stress has been tested to show the robustness of zero stiffness element as the aspect ratio is increased up to 2000. The stiffness derivative method and displacement extrapolation method have been applied to calculate the stress intensity factors of Mode I problem. It is noted that the proposed hierarchical void element can be one of alternatives to analyze the patched crack problems.

• Structural Engineering and Mechanics
• /
• v.63 no.6
• /
• pp.713-723
• /
• 2017

As a new type of ballastless track, longitudinal continuous slab track (CST) has been widely used in China. It can partly isolate the interaction between the ballastless track and the bridge and thus the rail expansion device would be unnecessary. Compared with the traditional track, CST is composed of multi layers of continuous structures and various connecting components. In order to investigate the performance of CST on a long-span bridge, the spatial finite element model considering each layer of the CST structure, connecting components, bridge, and subgrade is established and verified according to the theory of beam-rail interaction. The nonlinear resistance of materials between multilayer track structures is measured by experiments, while the temperature gradients of the bridge and CST are based on the long-term measured data. This study compares the force distribution rules of ballasted track and CST as respectively applied to a long span bridge. The effects of different damage conditions on CST structures are also discussed. The results show that the additional rail stress is small and the CST structure has a high safety factor under the measured temperature load. The rail expansion device can be cancelled when CST is adopted on the long span bridge. Beam end rotation caused by temperature gradient and vertical load will have a significant effect on the rail stress of CST. The additional flexure stress should be considered with the additional expansion stress simultaneously when the rail stress of CST requires to be checked. Both the maximum sliding friction coefficient of sliding layer and cracking condition of concrete plate should be considered to decide the arrangement of connecting components and the ultimate expansion span of the bridge when adopting CST.