• Coupled systems mechanics
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• v.7 no.2
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• pp.141-162
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• 2018

This work presents a novel model for analysis of the loading rate influence onto structure response. The model is based on the principles of nonlinear system dynamics, i.e., consists of a system of nonlinear differential equations. In contrast to classical linearized models, this one comprises mass and loading as integral parts of the model. Application of the Kelvin and the Maxwell material models relates the novel formulation to the existing material formulations. All the analysis is performed on a proprietary computer program based on Wolfram Mathematica. This work can be considered as an extended proof of concept for the application of the nonlinear solid model in material response to dynamic loading.

• Coupled systems mechanics
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• v.2 no.1
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• pp.111-126
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• 2013

The structural design requirements of an offshore platform subjected to wave induced forces and moments in the jacket can play a major role in the design of the offshore structures. For an economic and reliable design; good estimation of wave loadings are essential. A nonlinear response analysis of a fixed offshore platform under structural and wave loading is presented, the structure is discretized using the finite element method, wave plus current kinematics (velocity and acceleration fields) are generated using 5th order Stokes wave theory, the wave force acting on the member is calculated using Morison's equation. Hydrodynamic loading on horizontal and vertical tubular members and the dynamic response of fixed offshore structure together with the distribution of displacement, axial force and bending moment along the leg are investigated for regular and extreme conditions, where the structure should keep production capability in conditions of the 1-yr return period wave and must be able to survive the 100-yr return period storm conditions. The result of the study shows that the nonlinear response investigation is quite crucial for safe design and operation of offshore platform.

• Journal of the Earthquake Engineering Society of Korea
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• v.7 no.1
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• pp.57-63
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• 2003

A comparative study was performed for a suspension bridge to grasp the possible differences in seismic responses evaluated by several analytical methods. The items mainly investigated are the linear vs. nonlinear response, the response spectrum method vs. the linear dynamic analysis method, and the damping ratio and it's implementation into analysis procedures. According to the numerical example, it is found that the seismic responses are considerably affected by the damping-related parameters even though slight differences are shown depending on the response quantities and the exciting directions. On the other hand, it is also confirmed that the seismic responses are less affected by the analysis method-related parameters such as the response spectrum method vs. the linear dynamic analysis method, and the linear and nonlinear analysis method. The response spectrum method is expected to give conservative results for the examined bridge, provided that the design response spectrum in the Korean Highway Design Specification is modified according to the proper damping ratio.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.4
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• pp.501-509
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• 2010

A floating crane is a crane-mounted ship and is used to assemble or to transport heavy blocks in shipyards. In this paper, the static and dynamic response of a floating crane and a heavy block that are connected using elastic booms and wire ropes are described. The static and dynamic equations of surge, pitch, and heave for the system are derived on the basis of flexible multibody system dynamics. The equations of motion are fully coupled and highly nonlinear since they involve nonlinear mass matrices, elastic stiffness matrices, quadratic velocity vectors, and generalized external forces. A floating frame of reference and nodal coordinates are employed to model the boom as a flexible body. The nonlinear hydrostatic force, linear hydrodynamic force, wire-rope force, and mooring force are considered as the external forces. For numerical analysis, the Hilber-Hughes-Taylor method for implicit integration is used. The dynamic responses of the cargo are analyzed with respect to the results obtained by static and numerical analyses.

• Interaction and multiscale mechanics
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• v.3 no.4
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• pp.309-320
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• 2010

With taking the geometric nonlinearity of bridge structure into account, a framework is presented for predicting the dynamic responses of a long-span suspension bridge subjected to running train and turbulent wind. The nonlinear dynamic equations of the coupled train-bridge-wind system are established, and solved with the Newmark numerical integration and direct interactive method. The corresponding linear and nonlinear processes for solving the system equation are described, and the corresponding computer codes are written. The proposed framework is then applied to a schemed long-span suspension bridge with the main span of 1120 m. The whole histories of the train passing through the bridge under turbulent wind are simulated, and the dynamic responses of the bridge are obtained. The results demonstrate that the geometric nonlinearity does not influence the variation tendency of the bridge displacement histories, but the maximum responses will be changed obviously; the lateral displacement of bridge are more sensitive to the wind than the vertical ones; compared with wind velocity, train speed affects the vertical maximum responses a little more clearly.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.9
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• pp.879-888
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• 2012

This study aims to apply multistage homotopy perturbation method(MHPM) to space truss composed of discrete members to obtain a semi-analytical solution. For the purpose of this research, a nonlinear governing equation of the structures is formulated in consideration of geometrical nonlinearity, and homotopy equation is derived. The result of carrying out dynamic analysis on a simple model is compared to a numerical method of 4th order Runge-Kutta method(RK4), and the dynamic response by MHPM concurs with the numerical result. Besides, the displacement response and attractor in the phase space is able to delineate dynamic snapping properties under step excitations and the responses of damped system are reflected well the reduction effect of the displacement.

• Journal of Korean Society of Steel Construction
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• v.8 no.4 s.29
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• pp.77-84
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• 1996

The structural members under seismic loading actually show inelastic behavior, so the inelastic responses should be calculated for the seismic design of structures or estimating the structural damage level. Although direct time history analysis may calculate the exact dynamic nonlinear responses for given ground motions, this approach involves a high computational cost and long period. Therefore, it should be developed the approach to estimate nonlinear responses for the practical purpose. The artificial earthquake accelerograms were generated to obtain the smoothed responses spectra, and the samples of generated accelerogram for each seismic event was used to examine average nonlinear response spectra. The stabilized response spectra for each earthquake event was used to evaluate the effects of various yield strength ratios, damping values and nonlinear hysteretic models. The approach, which can simply predict the nonlinear seismic responses of structures, was shown in this study.

• Structural Engineering and Mechanics
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• v.53 no.2
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• pp.355-372
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• 2015

This paper identifies the effects of infill wall existence and arrangement in the seismic response of steel frame structures. The methodology followed was based on the utilisation of overall seismic response indicators that distil the complexity of structural response in a single value hence enabling their straightforward comparative and statistical post process. The overall structure damage index after Park/Ang ($OSDI_{PA}$) and the maximum inter-story drift ratio (MISDR) have been selected as widely utilized structural seismic response parameters in contemporary state of art. In this respect a set of 225 Greek antiseismic code (EAK) spectrum compatible artificial accelerograms have been created and a series of non-linear dynamic analyses have been executed. Data were obtained through nonlinear dynamic analyses carried on an indicative steel frame structure with 5 different infill wall topologies. Results indicated the significant overall contribution of infill walls with a reduction that ranged 35-47% of the maximum and 74-81% of the average recorded $OSDI_{PA}$ values followed by an overall reduction of 64-67% and 58-61% for the respective maximum and average recorded MISDR values demonstrating the relative benefits of infill walls presence overall as well as localised with similar reductions observed in 1st level damage indicators.

• Steel and Composite Structures
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• v.46 no.5
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• pp.637-647
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• 2023

Nonlinear free vibration and stability responses of a carbon nanotube reinforced composite beam under temperature rising are investigated in this paper. The material of the beam is considered as a polymeric matrix by reinforced the single-walled carbon nanotubes according to different distributions with temperature-dependent physical properties. With using the Hamilton's principle, the governing nonlinear partial differential equation is derived based on the Euler-Bernoulli beam theory. In the nonlinear kinematic assumption, the Von Kármán nonlinearity is used. The Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The critical buckling temperatures, the nonlinear natural frequencies and the nonlinear free response of the system is obtained. The effect of different patterns of reinforcement on the critical buckling temperature, nonlinear natural frequency, nonlinear free response and phase plane trajectory of the carbon nanotube reinforced composite beam investigated with temperature-dependent physical property.

• Composites Research
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• v.25 no.6
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• pp.217-223
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• 2012

This study investigates a geometrical nonlinear dynamic behaviors of laminated skew plates made of advanced composite materials (ACM). Based on the first-order shear deformation plate theory (FSDT), the Newmark method and Newton-Raphson iteration are used for the nonlinear dynamic solution. The effects of cutout sizes, skew angles and lay up sequences on the nonlinear dynamic response for various parameters are studied using a nonlinear dynamic finite element program developed for this study. The several numerical results were in good agreement with those reported by other investigators for square composite plates with or without central cutouts, and the new results reported in this paper show the significant interactions between the cutout, skew angles and layup sequence in the laminate. Key observation points are discussed and a brief design guideline of skew laminates is given.