• Advances in Computational Design
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• v.4 no.4
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• pp.397-413
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• 2019

In this paper, static nonlinear analysis of gable frame is performed using OpenSees software. Both geometric and material nonlinearities are considered in analyses. To consider large displacements, co-rotational coordinate transformation is used in software. The effects of symmetric and asymmetric support conditions including clamped and simple supports are studied. On the other hand, the material nonlinearity is reflected on analyses using Giuffre-Menegotto-Pinto steel material. Note that strain hardening characteristics are also considered in this model. Moreover, I-shaped cross-section is assumed for all members. The results are provided for different geometry properties of gable frame including shallow and deep inclined roof. It should be added that buckling and post-buckling behaviors of gable frame are investigated using related equilibrium paths. A comparison study is also implemented on the responses of buckling loads obtained for different support and geometry conditions. To trace snap-through paths completely, a displacement control method entitled arc-length is utilized. Findings show the capability of proposed model in nonlinear analysis of gable frames.

• Structural Engineering and Mechanics
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• v.56 no.1
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• pp.85-106
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• 2015

Postbuckling of thick plates made of functionally graded material (FGM) subjected to in-plane compressive, thermal and thermomechanical loads is investigated in this work. It is assumed that the plate is in contact with a Pasternak-type elastic foundation during deformation. Thermomechanical non-homogeneous properties are considered to be temperature independent, and graded smoothly by the distribution of power law across the thickness in the thickness in terms of the volume fractions of constituents. By employing the higher order shear deformation plate theory together the non-linear von-Karman strain-displacement relations, the equilibrium and compatibility equations of imperfect FGM plates are derived. The Galerkin technique is used to determine the buckling loads and postbuckling equilibrium paths for simply supported plates. Numerical examples are presented to show the influences of power law index, foundation stiffness and imperfection on the buckling and postbuckling loading capacity of the plates.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.10a
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• pp.47-54
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• 1993

This paper is concerned with the geometrically nonlinear behavior of elastic systems under conservative loading conditions. In particular, the topic are snap through problems and the arc-length method to pass limit points of space trusses is used. And numerical examples are presented to trace nonlinear equilibrium paths.

• Journal of the Korean institute of surface engineering
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• v.23 no.1
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• pp.27-33
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• 1990

Thermodynamic analysis on silicon consumpton during the chemical vapor deposition of tungten was carried out by calculation equilibrium concerations of all possible product species utilizing a computer progrom according to VCS.(Villars-Cruise-Smith) algorithm. The calculation could show various reaction paths which dominate the tungsten deposition under different process conditions. According to the calculation, the consumption of silicon can also be reduced at a lower total pressure SiH4 without H2 as the reacting gas is most effective for suppression of the excessive consumption of silicon during the deposition process.

• Structural Engineering and Mechanics
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• v.58 no.3
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• pp.515-532
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• 2016

The elastoplastic response of functionally graded material (FGM) beams resting on a nonlinear elastic foundation to an eccentric axial load is investigated by using the finite element method. The FGM is assumed to be formed from ceramic and metal phases with their volume fraction vary in the thickness direction by a power-law function. A bilinear elastoplastic behavior is assumed for the metallic phase, and the effective elastoplastic properties of the FGM are evaluated by Tamura-Tomota-Ozawa (TTO) model. Based on the classical beam theory, a nonlinear finite beam element taking the shift in the neutral axis position into account is formulated and employed in the investigation. An incremental-iterative procedure in combination with the arc-length control method is employed in computing the equilibrium paths of the beams. The validation of the formulated element is confirmed by comparing the equilibrium paths obtained by using the present element and the one available in the literature. The numerical results show that the elastoplastic post-buckling of the FGM beams is unstable, and the post-buckling strength is higher for the beams associated with a higher ceramic content. Different from homogeneous beams, yielding in the FGM beam occurs in the layer near the ceramic layer before in the layer near metal surface. A parametric study is carried out to highlight the effect of the material distribution, foundation support and eccentric ratio on the elastoplastic response of the beams.

• Advances in Computational Design
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• v.1 no.1
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• pp.61-77
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• 2016

Seismic performance of structures depends on the force flow mechanism inside the structure. Discontinuity regions, like beam-column joints, are often affected during earthquake event due to the complex and discontinuous load paths. The evaluation of shear strength and identification of failure mode of the joint region are helpful to (i) define the strength hierarchy of the beam-column sub-assemblage, (ii) quantify the influence of different parameters on the behaviour of beam-column joint and, (iii) develop suitable and adequate strengthening scheme for the joints, if required, to obtain the desired strength hierarchy. In view of this, it is very important to estimate the joint shear strength and identify the failure modes of the joint region as it is the most critical part in any beam-column sub-assemblage. One of the most effective models is softened strut and tie model which was developed by incorporating force equilibrium, strain compatibility and constitutive laws of cracked reinforced concrete. In this study, softened strut and tie model, which incorporates force equilibrium equations, compatibility conditions and material constitutive relation of the cracked concrete, are used to simulate the shear strength behaviour and to identify failure mechanisms of the beam-column joints. The observations of the present study will be helpful to arrive at the design strategy of the joints to ensure the desired failure mechanism and strength hierarchy to achieve sustainability of structural systems under seismic loading.

• Structural Engineering and Mechanics
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• v.18 no.6
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• pp.807-829
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• 2004

The Element-Based Lagrangian Formulation of a 9-node resultant-stress shell element is presented for the isotropic and anisotropic composite material. The effect of the coupling term between the bending strain and displacement has been investigated in the warping problem. The strains, stresses and constitutive equations based on the natural co-ordinate have been used throughout the Element-Based Lagrangian Formulation of the present shell element which offers an advantage of easy implementation compared with the traditional Lagrangian Formulation. The element is free of both membrane and shear locking behavior by using the assumed natural strain method such that the element performs very well in thin shell problems. In composite plates and shells, the transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Several numerical analyses are presented and discussed in order to investigate the capabilities of the present shell element. The results showed very good agreement compared with well-established formulations in the literature.

• Steel and Composite Structures
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• v.30 no.6
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• pp.517-534
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• 2019

In this paper, the effects of inevitable out-of-plane defects on the postbuckling behavior of single-layered graphene sheets (SLGSs) under in-plane loadings are investigated based on nonlocal first order shear deformation theory (FSDT) and von-Karman nonlinear model. A generic imperfection function, which takes the form of the products of hyperbolic and trigonometric functions, is employed to model out-of-plane defects as initial geometrical imperfections of SLGSs. Nonlinear equilibrium equations are derived from the principle of virtual work and variational formulation. The postbuckling equilibrium paths of imperfect graphene sheets (GSs) are presented by solving the governing equations via isogeometric analysis (IGA) and Newton-Raphson iterative method. Finally, the sensitivity of the postbuckling behavior of GS to shape, amplitude, extension on the surface, and location of initial imperfection is studied. Results showed that the small scale and initial imperfection effects on the postbuckling behavior of defective SLGS are important and cannot be ignored.

• Structural Engineering and Mechanics
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• v.85 no.5
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• pp.665-677
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• 2023

In the present study, the limit point buckling and postbuckling behaviors of sinusoidal, shallow arches with pinned supports subjected to localized sinusoidal loading, based on the Euler-Bernoulli beam theory, are numerically analyzed. There are some studies on the buckling of sinusoidal shallow arches under the effect of sinusoidal loading. However, in these studies, the sinusoidal loading acts along the horizontal projection of the entire shallow arch. No study has been found in the relevant literature pertaining to the stability of the shallow arches subjected to various lengths of sinusoidal loading. Therefore, the purpose of this paper is to contribute to the literature by examining the effect of the length of the localized sinusoidal loading and the initial rise of the shallow arch on the limit point buckling and postbuckling behaviors. Equilibrium paths corresponding to certain values of the length of the localized sinusoidal loading and various values of the initial rise parameter are presented. It has been observed that the length of the sinusoidal loading and the initial rise parameter affects the transition from no buckling to limit point instability remarkably. The deformed configurations of the sinusoidal shallow arch under localized loading regarding buckling and postbuckling states are illustrated, as well. The effects of the length of the localized sinusoidal loading on the internal forces of the shallow arch are investigated during various stages of the loading.

• 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.