• Structural Engineering and Mechanics
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• v.45 no.4
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• pp.521-542
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• 2013

In this study a truss model is used for the geometrically nonlinear static and dynamic analysis of a thin shallow arch subject to snap-through. Thanks to the very simple geometry of a truss, the equilibrium conditions can be easily written and the global stiffness matrix can be easily updated with respect to the deformed structure, within each step of the analysis. A very coarse discretization is applied; so, in a very simple way, the high frequency modes are suppressed from the beginning and there is no need to develop a complicated reduced-order technique. Two short computer programs have been developed for the geometrically nonlinear static analysis by displacement control of a plane truss model of a structure as well as for its dynamic analysis by the step-by-step time integration algorithm of trapezoidal rule, combined with a predictor-corrector technique. These two short, fully documented computer programs are applied on the geometrically nonlinear static and dynamic analysis of a specific thin shallow arch subject to snap-through.

• Steel and Composite Structures
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• v.32 no.3
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• pp.293-304
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• 2019

In the present paper, the element free Galerkin (EFG) method is developed for geometrically nonlinear analysis of deep beams considering small scale effect. To interpret the behavior of structure at the nano scale, the higher-order gradient elasticity nonlocal theory is taken into account. The radial point interpolation method with high order of continuity is used to construct the shape functions. The nonlinear equation of motion is derived using the principle of the minimization of total potential energy based on total Lagrangian approach. The Newmark method with the small time steps is used to solve the time dependent equations. At each time step, the iterative Newton-Raphson technique is applied to minimize the residential forces caused by the nonlinearity of the equations. The effects of nonlocal parameter and aspect ratio on stiffness and dynamic parameters are discussed by numerical examples. This paper furnishes a ground to develop the EFG method for large deformation analysis of structures considering small scale effects.

• Steel and Composite Structures
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• v.35 no.1
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• pp.77-92
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• 2020

The present paper outlined a procedure for geometrically nonlinear dynamic analysis of functionally graded graphene platelets-reinforced (GPLR-FG) nanocomposite cylinder subjected to mechanical shock loading. The governing equation of motion for large deformation problems is derived using meshless local Petrov-Galerkin (MLPG) method based on total lagrangian approach. In the MLPG method, the radial point interpolation technique is employed to construct the shape functions. A micromechanical model based on the Halpin-Tsai model and rule of mixture is used for formulation the nonlinear functionally graded distribution of GPLs in polymer matrix of composites. Energy dissipation in analyses of the structure responding to dynamic loads is considered using the Rayleigh damping. The Newmark-Newton/Raphson method which is an incremental-iterative approach is implemented to solve the nonlinear dynamic equations. The results of the proposed method for homogenous material are compared with the finite element ones. A very good agreement is achieved between the MLPG and FEM with very fine meshing. In addition, the results have demonstrated that the MLPG method is more effective method compared with the FEM for very large deformation problems due to avoiding mesh distortion issues. Finally, the effect of GPLs distribution on strength, stiffness and dynamic characteristics of the cylinder are discussed in details. The obtained results show that the distribution of GPLs changed the mechanical properties, so a classification of different types and volume fraction exponent is established. Indeed by comparing the obtained results, the best compromise of nanocomposite cylinder is determined in terms of mechanical and dynamic properties for different load patterns. All these applications have shown that the present MLPG method is very effective for geometrically nonlinear analyses of GPLR-FG nanocomposite cylinder because of vanishing mesh distortion issue in large deformation problems. In addition, since in proposed method the distributed nodes are used for discretization the problem domain (rather than the meshing), modeling the functionally graded media yields to more accurate results.

• Advances in Computational Design
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• v.2 no.1
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• pp.71-87
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• 2017

This study focuses on the efficiency and applicability of dynamic relaxation methods in form-finding of membrane structures. Membrane structures have large deformations that require complex nonlinear analysis. The first step of analysis of these structures is the form-finding process including a geometrically nonlinear analysis. Several numerical methods for form-finding have been introduced such as the dynamic relaxation, force density method, particle spring systems and the updated reference strategy. In the present study, dynamic relaxation method (DRM) is investigated. The dynamic relaxation method is an iterative process that is used for the static equilibrium analysis of geometrically nonlinear problems. Five different examples are used in this paper. To achieve the grading of the different dynamic relaxation methods in form-finding of membrane structures, a performance index is introduced. The results indicate that viscous damping methods show better performance than kinetic damping in finding the shapes of membrane structures.

• Journal of the Korean Society of Safety
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• v.14 no.4
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• pp.148-157
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• 1999

Dynamic structural behavior in long span bridges, especially cable structures, is very sophisticated due to their flexibility and structural members are sequentially erected in each construction step. In this study, the consistent mass matrix for dynamic analysis is formulated and computational program considering construction sequences is developed where structural members can be builded or removed by command language and automatically reanalyzed in the moment when structural system is changed. The dynamic analysis, i.e. eigenvalue and time series analysis and the geometrically nonlinear analysis considering construction sequence are conducted to the Namhae Bridge. The analytical results are satisfactory compared with measuring values and the developed computational program can successfully be applied to design and safety check.

• Wind and Structures
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• v.8 no.1
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• pp.35-48
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• 2005

Wind loading is very important in structural design of large-span single-layer reticulated shell structures. In this paper, a geometrically nonlinear wind-induced vibration analysis strategy for large-span single-layer reticulated shell structures based on the nonlinear finite element method is introduced. According to this strategy, a computation program has been developed. With the information of the wind pressure distribution measured simultaneously in the wind tunnel, nonlinear dynamic analysis, including dynamic instability analysis, for the wind-induced vibration of a single-layer reticulated shell is conducted as an example to investigate the efficiency of the strategy. Finally, suggestions are given for dynamic wind-resistant analysis of single-layer reticulated shells.

• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.163-177
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• 2012

This paper presents a LMI(linear matrix inequality)-based fuzzy approach of modeling and active vibration control of geometrically nonlinear flexible plates with piezoelectric materials as actuators and sensors. The large-amplitude vibration characteristics and dynamic partial differential equation of a piezoelectric flexible rectangular thin plate structure are obtained by using generalized Fourier series and numerical integral. Takagi-Sugeno (T-S) fuzzy model is employed to approximate the nonlinear structural system, which combines the fuzzy inference rule with the local linear state space model. A robust fuzzy dynamic output feedback control law based on the T-S fuzzy model is designed by the parallel distributed compensation (PDC) technique, and stability analysis and disturbance rejection problems are guaranteed by LMI method. The simulation result shows that the fuzzy dynamic output feedback controller based on a two-rule T-S fuzzy model performs well, and the vibration of plate structure with geometrical nonlinearity is suppressed, which is less complex in computation and can be practically implemented.

• Smart Structures and Systems
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• v.20 no.6
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• pp.729-737
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• 2017

Piezoelectric composite laminates are a powerful material system that offers vast options to improve structural behavior. Successful design of piezoelectric adaptive structures and testing of control laws call for highly accurate, reliable and numerically efficient numerical tools. This paper puts focus onto linear and geometrically nonlinear static and dynamic analysis of smart structures made of such a material system. For this purpose, highly efficient linear 3-node and 4-node finite shell elements are proposed. Both elements employ the Mindlin-Reissner kinematics. The shear locking effect is treated by the discrete shear gap (DSG) technique with the 3-node element and by the assumed natural strain (ANS) approach with the 4-node element. Geometrically nonlinear effects are considered using the co-rotational approach. Static and dynamic examples involving actuator and sensor function of piezoelectric layers are considered.

• Steel and Composite Structures
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• v.18 no.1
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• pp.51-69
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• 2015

In recent years, the use of fiber reinforced polymer composites has increased because of their unique features. They have been used widely in the aircraft and space industries, medical and sporting goods and automotive industries. Thanks to their beneficial and various advantages over traditional materials such as high strength, high rigidity, low weight, corrosion resistance, low maintenance cost, aesthetic appearance and easy demountable or moveable construction. In this paper, it is aimed to determine and compare the geometrically nonlinear static and dynamic analysis results of footbridges using steel and glass fiber reinforced polymer composite (GFRP) materials. For this purpose, Halgavor suspension footbridge is selected as numerical examples. The analyses are performed using three identical footbridges, first constructed from steel, second built only with GFRP material and third made of steel- GFRP material, under static and dynamic loadings using finite element method. In the finite element modeling and analyses, SAP2000 program is used. Geometric nonlinearities are taken into consideration in the analysis using P-Delta criterion. The numerical results have indicated that the responses of the three bridges are different and that the response values obtained for the GFRP composite bridge are quite less compared to the steel bridge. It is understood that GFRP material is more useful than the steel for the footbridges.

• 한국공간정보시스템학회:학술대회논문집
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• 2004.05a
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• pp.113-122
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• 2004

Cable domes deform very largely because of the characteristics of flexible hybrid system and pre-tension, and include geometrical non-linearity in those structural behavior. Especially wind load is more dominant than seismic load, because cable domes are flexible structures whose bending stiffness is very small and self-weight is very light. Therefore, in this paper, the Modified Stiffly Stable Method is applied to analyze the nonlinear dynamic behavior of cable domes and compared these results with ones of the $Newmark-{\beta}$ Method which is generally used. The Seoul Olympic Gymnastic Arena is taken as an numerical example and three kinds of models with giving each different intensity of pre-tension are selected. And dynamic nonlinear behavior of cable domes are analyzed by artificial spectrum of wind velocity wave which is similar to actual wind loads.