• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.04a
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• pp.9-18
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• 1996

The primary objective of this paper is to grasp many characteristics of buckling behavior of latticed spherical domes under various conditions. The Arc-Length Method proposed by E.Riks is used for the computation and evaluation of geometrically nonlinear fundamental equilibrium paths and bifurcation points. And the direction of the path after the bifurcation point is decided by means of Hosono's concept. Three different nonlinear stiffness matrices of the Slope-Deflection Method are derived for the system with rigid nodes and results of the numerical analysis are examined in regard in geometrical parameters such as slenderness ratio, half-open angle, boundary conditions, and various loading types. But in case of analytical model 2 (rigid node), the post-buckling path could not be surveyed because of Newton-Raphson iteration process being diversed on the critical point since many eigenvalues become zero simultaneously.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.85-91
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• 2000

The smallest value of the load when the equilibrium condition becomes to be unstable is defined as the buckling load. The primary objective of this paper is to analyse stability boundaries for star dome under combined loads and is to investigate the iteration diagram under the independent loading parameter In numerical procedure of the geometrically nonlinear problems, Arc Length Method and Newton-Raphson iteration method is used to find accurate critical point(bifurcation point and limit point). In this paper independent loading vector is combined as proportional value and star dome was used as numerical analysis model to find stability boundary among load parameters and many other models as multi-star dome and arches were studied. Through this study we can find the type of buckling mode and the value of buckling load.

• Steel and Composite Structures
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• v.13 no.2
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• pp.157-169
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• 2012

Shell structures are very interesting from the design point of view and these are well recognized in the scientific literature. In this paper the analysis of the buckling loads and stability paths of a sandwich conical shell with unsymmetrical faces under combined load based on the assumptions of moderately large deflections (geometrically nonlinear theory) is considered and elastic-plastic properties of the material of the faces are taken into considerations. External load is assumed to be two-parametrical one and it is assumed that the shell deforms into the plastic range before buckling. Constitutive relations in the analysis are those of the Nadai-Hencky deformation theory of plasticity and Prandtl-Reuss plastic flow theory with the H-M-H (Huber-Mises-Hencky) yield condition. The governing stability equations are obtained by strain energy approach and Ritz method is used to solve the equations with the help of analytical-numerical methods using computer.

• Steel and Composite Structures
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• v.46 no.4
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• pp.513-523
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• 2023

Buckling and post-buckling behaviors of geometrically perfect double-curvature shells made from smart composites have been investigated. The shell has been supposed to be exposed to transverse mechanical loading and magneto-electro-elastic (MEE) coupling. The composite shell has been made of two constituents which are piezoelectric and magnetic ingredients. Thus, the elastic properties might be variable based upon the percentages of the constituents. Incorporating small scale impacts in regard to nonlocal theory leads to the establishment of the governing equations for the double-curvature nanoshell. Such nanoshell stability will be shown to be affected by composite ingredients. More focus has been paid to the effects of small scale factor, electric voltage and magnetic intensity on stability curves of the nanoshell.

• Steel and Composite Structures
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• v.15 no.4
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• pp.439-449
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• 2013

In this study simply supported nonlinear Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads is investigated. A new kind of analytical technique for a non-linear problem called He's Energy Balance Method (EBM) is used to obtain the analytical solution for non-linear vibration behavior of the problem. Analytical expressions for geometrically non-linear vibration of Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads are provided. The effect of vibration amplitude on the non-linear frequency and buckling load is discussed. The variation of different parameter to the nonlinear frequency is considered completely in this study. The nonlinear vibration equation is analyzed numerically using Runge-Kutta $4^{th}$ technique. Comparison of Energy Balance Method (EBM) with Runge-Kutta $4^{th}$ leads to highly accurate solutions.

• Journal of Korean Association for Spatial Structures
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• v.1 no.1 s.1
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• pp.117-124
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• 2001

In Single-layer latticed domes with rectangular network which is composed of ring of circumferential direction and rafter of longitudinal direction, that is, rib domes, if we use the cross-membered junction's method for the advantage in fabrication and construction, the eccentricity is occurred in the nodal point of crossing members. This paper is aimed at investigating the buckling characteristics for the effect of eccentricity according to rise-span ratios and distance of eccentricity. Analysis method is based on FEM dealing with the geometrically nonlinear deflection problems. The conclusion were given as follows: 1. The maximum decreasing ratio of buckling strength due to the junction's eccentricity is about 60% in models of this paper. 2. In the increasing ratio of buckling strength for rise-span ratio, that of Type 3 models is larger than that of type 2 models. On the other hand, that of Type 2 mode is larger than that of Type 3 for eccentricity-distance. 3. In the viewpoint of the value of buckling strength, that of Type 2 models is larger than that of type 3 models. The effect of the junction's rigidity on buckling strength is not great for overall models. Therefore if we use the cross-membered junction's method for the advantage in fabrication and construction, the method of Type 2 will have the great advantage of that of Type 3.

• Journal of Korean Association for Spatial Structures
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• v.3 no.2 s.8
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• pp.69-75
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• 2003

In case of rectangular lattice dome which shearing rigidity is very small, it has a concern to drop Buckling strength considerably by external force. So, by means of system to increase buckling-strength, there is a method of construction that lattice of dome is one with roof material. In a case like this, shearing rigidity of roof material increases buckling-strength of the whole of structure and can be designed economically from the viewpoint of practice. In case of analysis is achieved considering roof material that adheres to lattice of dame, there is method that considers the rigidity that use effective width frame as method to evaluate rigidity of roof material. therefore, this study is aimed at deciding effective width of roof material united with rectangular lattice dome to evaluate rigidity of roof material by effective width of frame and investigating how much does rigidity of roof material united with lattice of dome increase buckling-strength of the whole of structure according to rise-ratio. Conditions of loading are vertical-type-uniform loading. Analysis method is based on FEM dealing with the geometrically nonlinear deflection problems.

• Computers and Concrete
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• v.25 no.4
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• pp.283-291
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• 2020

The present paper researches post-buckling behaviors of geometrically imperfect concrete beam resting on elastic foundation reinforced with graphene oxide powders (GOPs) based on finite element method (FEM). Distribution of GOPs are considered as uniform and linearly graded through the thickness. Geometric imperfection is considered as first buckling mode shape of the beam, the GOP reinforced beam is rested in initial position. The material properties of GOP reinforced composite have been calculated via employment of Halpin-Tsai micromechanical scheme. The provided refined beam element verifies the shear deformation impacts needless of any shear correction coefficient. The post-buckling load-deflections relations have been calculated via solving the governing equations having cubic non-linearity implementing FEM. Obtained findings indicate the importance of GOP distributions, GOP weight fraction, matrix material, geometric imperfection, shear deformation and foundation parameters on nonlinear buckling behavior of GOP reinforced beam.

• Computational Structural Engineering
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• v.10 no.4
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• pp.205-216
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• 1997

In order to trace the lateral post-buckling behaviors of thin-wafled space frames, a geometrically nonlinear finite element formulation is presented by applying incremental equilibrium equations based on the updated Lagrangian formulation and introducing Vlasov's assumption. The improved displacement field for symmetric thin-walled cross sections is introduced based on inclusion of second order terms of finite rotations, and the potential energy corresponding to the semitangential rotations and moments is consistently derived. For finite element analysis, tangent stiffness matrices of the thinwalled space frame element with 7 degrees of freedom including the restrained warping for each node are derived by using the Hermition polynomials as shape functions. A co-rotational formulation in order to evaluate the unbalanced loads is presented by separating the rigid body rotations and pure deformations from incremental displacements and evaluating the updated direction cosines of the frame element due to rigid body rotations and incremental member forces from pure deformations. Finite element solutions for the spatial buckling and post-buckling analysis of thin-walled space frames are presented and compared with available solutions and other researcher's results.

• Journal of Korean Society of Steel Construction
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• v.29 no.2
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• pp.123-134
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• 2017

Ultimate axial strength of longitudinally stiffened cylindrical steel shells for wind turbine tower was investigated by applying the geometrically and materially nonlinear finite element method. The effects of radius to thickness ratio of shell, shape and amplitude of initial imperfections, area ratio between effective shell and stiffener, and stiffener spacing on the ultimate axial strength of cylindrical shells were analyzed. The ultimate axial strengths of stiffened cylindrical shells by FEA were compared with design buckling strengths specified in DNV-RP-C202. The shell buckling modes obtained from a linear elastic bifurcation FE analysis as well as the weld depression during fabrication specified in Eurocode 3 were introduced in the nonlinear FE analysis as initial geometric imperfections. The radius to thickness ratio of cylindrical shell models was selected to be in the range of 50 to 200. The longitudinal stiffeners were designed according to DNV-RP-C202 to prevent the lateral torsional buckling and local buckling of stiffeners.