• Structural Engineering and Mechanics
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• v.5 no.6
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• pp.715-728
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• 1997

The aim of this paper is to investigate the secondary buckling behaviour and mode-coupling of spherical caps under uniformly external pressure. The analysis makes use of a rotational finite shell element on the basis of strain-displacement relations according to Koiter's shell theory (Small Finite Deflections). The post-buckling behaviours after a bifurcation point are analyzed precisely by considering multi-mode coupling between several higher order harmonic wave numbers: and on the way of post-buckling path the positive definiteness of incremental stiffness matrix of uncoupled modes is examined step by step. The secondary buckling point that has zero eigen-value of incremental stiffness matrix and the corresponding secondary mode are obtained, moreover, the secondary post-buckling path is traced.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.10a
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• pp.195-201
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• 1996

This paper is mainly forcused on the application of modal analysis In analyze the geometrically non-linear buckling behaviors of large span spatial structures, and the evaluation of each eigen mode affected post-buckling behaviors and buckling loads. Modal analysis is applied . to derivation of the system matrices transforming actual displacement space into generalized coordinates space represented by coefficients multiplied in the linear combination of eigen modes which are independent and orthogonal each other. By using modal analysis method, it will be expected to save the calculating time by computer extremely. For example, we can obtain the satisfactorily good results by using about 7% of total eigen modes only in case of single layer latticed dome. And we can decrease the possibility of divergence on the bifurcation point in the calculation of post-buckling path. Arc-length method and Newton-Raphson iteration method are used to calculate the nonlinear equilibrium path.

• Structural Engineering and Mechanics
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• v.78 no.1
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• pp.15-22
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• 2021

An investigation of the nonlinear thermal buckling behavior of a nano-sized beam constructed from intelligent materials called piezo-magnetic materials has been presented in this article. The nano-sized beam geometry has been considered based on two assumptions: an ideal straight beam and an imperfect beam. For incorporating nano-size impacts, the nano-sized beam formulation has been presented according to nonlocal elasticity. After establishing the governing equations based on classic beam theory and nonlocal elasticity, the nonlinear buckling path has been obtained via Galerkin's method together with an analytical trend. The dependency of buckling path to piezo-magnetic material composition, electro-magnetic fields and geometry imperfectness has been studied in detail.

• Journal of the Architectural Institute of Korea Structure & Construction
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• v.35 no.8
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• pp.139-148
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• 2019

The lightweight structures such as domes are particularly vulnerable when it has been subjected to high temperature induced by the fire. It is therefore crucial to predict the possible instability path of structures exposed to the fire in structural design process. In this study, the instabilities of single-layer domes is investigated by using finite element technologies with the consideration of high temperature. The material properties of members under high temperature are considered by using the reduction factors which is provided in Eurocodes 3. Some damage patterns are assumed with use of a structural unit which is symmetric in radial direction. For numerical evaluations, the geometrically nonlinear truss element is implemented and the arch-length control method is employed to trace the post-buckling behaviour of domes. From numerical results, it is found to be that a significant change of post-buckling behaviour is detected in dome structures when structural members are exposed to the fire.

• Advances in materials Research
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• v.8 no.3
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• pp.219-235
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• 2019

This research is devoted to analyzing mechanical-thermal post-buckling behavior of a micro-size beam reinforced with graphene platelets (GPLs) based on geometric imperfection effects. Graphene platelets have three types of dispersion within the structure including uniform-type, linear-type and nonlinear-type. The micro-size beam is considered to be perfect (ideal) or imperfect. Buckling mode shape of the micro-size beam has been assumed as geometric imperfection. Modified couple stress theory has been used for describing scale-dependent character of the beam having micro dimension. Via an analytical procedure, post-buckling path of the micro-size beam has been derived. It will be demonstrated that nonlinear buckling characteristics of the micro-size beam are dependent on geometric imperfection amplitude, thermal loading, graphene distribution and couple stress effects.

• Journal of Korean Society of Steel Construction
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• v.21 no.6
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• pp.563-574
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• 2009

This paper briefly describes the fundamental strategies--path-tracing, pin-pointing, and path-switching--in the computational elastic bifurcation theory of geometrically non-linear single-load-parameter conservative elastic spatial structures. The stability points in the non-linear elasticity may be classified into limit points and bifurcation points. For the limit points, the path tracing scheme that successively computes the regular equilibrium points on the equilibrium path, and the pinpointing scheme that precisely locates the singular equilibrium points were sufficient for the computational stability analysis. For the bifurcation points, however, a specific procedure for path-switching was also necessary to detect the branching paths to be traced in the post-buckling region. After the introduction, a general theory of elastic stability based on the energy concept was given. Then path tracing, an indirect method of detecting multiple bifurcation points, and path switching strategies were described. Next, some numerical examples of bifurcation analysis were carried out for a trussed stardome, and a pin-supported plane circular arch was described. Finally, concluding remarks were given.

• Structural Engineering and Mechanics
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• v.38 no.6
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• pp.767-802
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• 2011

Developers of new finite elements or nonlinear solution techniques rely on discriminative benchmark tests drawn from the literature to assess the advantages and drawbacks of new formulations. Buckling benchmark tests provide a rigorous evaluation of finite elements applied to thin structures, and a complete and detailed set of reference results would therefore prove very useful in carrying out such evaluations. Results are usually presented in the form of load-deflection curves that developers must reconstruct by extracting the points, a procedure which is often tedious and inaccurate. Moreover the curves are usually given without accompanying information such as the calculation time or number of iterations it took for the model to converge, even though this type of data is equally important in practice. This paper presents ten different limit-point buckling benchmark tests, and provides for each one the reference load-deflection curve, all the points necessary to recreate the curve in tabulated form, analysis data such as calculation time, number of iterations and increments, and all of the inputs used to obtain these results.

• Computational Structural Engineering
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• v.9 no.3
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• pp.209-216
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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 to 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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• 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.

• Structural Engineering and Mechanics
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• v.22 no.3
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• pp.311-330
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• 2006

Standard compression tests of steel fiber reinforced concrete (SFRC) cylinders are conducted to formulate compressive stress versus compressive strain relationship of SFRC. Axial pullout tests of SFRC specimens are also conducted to explore its tensile stress strain relationship. Cover concrete spalling and reinforcement buckling models developed originally for normal reinforced concrete are modified to extend their application to SFRC. Thus obtained monotonic material models of concrete and reinforcing bars in SFRC members are combined with unloading/reloading loops used in the cyclic models of concrete and reinforcing bars in normal reinforced concrete. The resulting path-dependent cyclic material models are then incorporated in a finite-element based fiber analysis program. The applicability of these models at member level is verified by simulating cyclic lateral loading tests of SFRC columns under constant axial compression. The analysis using the proposed SFRC models yield results that are much closer to the experimental results than the analytical results obtained using the normal reinforced concrete models are.