• Structural Engineering and Mechanics
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• v.67 no.4
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• pp.337-346
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• 2018

The purpose of this study is to investigate thermal post-buckling analysis of a laminated composite beam subjected under uniform temperature rising with temperature dependent physical properties. The beam is pinned at both ends and immovable ends. Under temperature rising, thermal buckling and post-buckling phenomena occurs with immovable ends of the beam. In the nonlinear kinematic model of the post-buckling problem, total Lagrangian approach is used in conjunction with the Timoshenko beam theory. Also, material properties of the laminated composite beam are temperature dependent: that is the coefficients of the governing equations are not constant. In the solution of the nonlinear problem, incremental displacement-based finite element method is used with Newton-Raphson iteration method. The effects of the fibber orientation angles, the stacking sequence of laminates and temperature rising on the post-buckling deflections, configurations and critical buckling temperatures of the composite laminated beam are illustrated and discussed in the numerical results. Also, the differences between temperature dependent and independent physical properties are investigated for post-buckling responses of laminated composite beams.

• Advances in nano research
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• v.8 no.3
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• pp.255-264
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• 2020

Buckling and post-buckling cases are often occurred in aorta artery because it affected by higher pressure. Also, its stability has a vital importance to humans and animals. The loss of stability in arteries may lead to arterial tortuosity and kinking. In this paper, post-buckling analysis of aorta artery is investigated under axial compression loads on the basis of Euler-Bernoulli beam theory by using finite element method. It is known that post-buckling problems are geometrically nonlinear problems. In the geometrically nonlinear model, the Von Karman nonlinear kinematic relationship is employed. Two types of support conditions for the aorta artery are considered. The considered non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The aorta artery is modeled as a cylindrical tube with different average diameters. In the numerical results, the effects of the geometry parameters of aorta artery on the post-buckling case are investigated in detail. Nonlinear deflections and critical buckling loads are obtained and discussed on the post-buckling case.

• Geomechanics and Engineering
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• v.31 no.3
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• pp.329-337
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• 2022

In this paper, the thermal post-buckling characteristics of functionally graded (FG) pipes with initial geometric imperfection are studied. Considering the influence of initial geometric defects, temperature and geometric nonlinearity, Euler-Lagrange principle is used to derive the nonlinear governing equations of the FG pipes. Considering three different boundary conditions, the two-step perturbation method is used to solve the nonlinear governing equations, and the expressions of thermal post-buckling responses are also obtained. Finally, the correctness of this paper is verified by numerical analyses, and the effects of initial geometric defects, functional graded index, elastic foundation, porosity, thickness of pipe and boundary conditions on thermal post-buckling response are analyzed. It is found that, bifurcation buckling exists for the pipes without initial geometric imperfection. In contrast, there is no bifurcation buckling phenomenon for the pipes with initial geometric imperfection. Meanwhile, the elastic stiffness can significantly improve thermal post-buckling load and thermal post-buckling strength. The larger the porosity, the greater the thermal buckling load and the thermal buckling strength.

• Structural Engineering and Mechanics
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• v.44 no.1
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• pp.109-125
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• 2012

Post-buckling behavior of Timoshenko beams subjected to uniform temperature rising with temperature dependent physical properties are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. The beam is clamped at both ends. In the case of beams with immovable ends, temperature rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. Also, the material properties (Young's modulus, coefficient of thermal expansion, yield stress) are temperature dependent: That is the coefficients of the governing equations are not constant in this study. This situation suggests the physical nonlinearity of the problem. Hence, the considered problem is both geometrically and physically nonlinear. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The beams considered in numerical examples are made of Austenitic Stainless Steel (316). The convergence studies are made. In this study, the difference between temperature dependent and independent physical properties are investigated in detail in post-buckling case. The relationships between deflections, thermal post-buckling configuration, critical buckling temperature, maximum stresses of the beams and temperature rising are illustrated in detail in post-buckling case.

• Steel and Composite Structures
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• v.46 no.5
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• pp.649-658
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• 2023

Although some scholars have studied the thermal post-buckling of graphene platelets strengthened metal foams (GPLRMFs) plates, they have not considered the influence of initial geometrical imperfection. Inspired by this fact, the present paper studies the thermal post-buckling characteristics of GPLRMFs plates with initial geometrical imperfection. Three kinds of graphene platelets (GPLs) distribution patterns including three patterns have been considered. The governing equations are derived according to the first-order plate theory and solved with the help of the Galerkin method. According to the comparison with published paper, the accuracy and correctness of the present research are verified. In the end, the effects of material properties and initial geometrical imperfection on the thermal post-buckling response of the GPLRMFs plates are examined. It can be found that the presence of initial geometrical imperfection reduces the thermal post-buckling strength. In addition, the present study indicates that GPL-A pattern is best way to improve thermal post-buckling strength for GPLRMFs plates, and the presence of foams can improve the thermal post-buckling strength of GPLRMFs plates, the Foam- II and Foam- I patterns have the lowest and highest thermal post-buckling strength. Our research can provide guidance for the thermal stability analysis of GPLRMFs plates.

• Structural Engineering and Mechanics
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• v.40 no.3
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• pp.347-371
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• 2011

This paper focuses on post-buckling analysis of Timoshenko beams with various boundary conditions subjected to a non-uniform thermal loading by using the total Lagrangian Timoshenko beam element approximation. Six types of support conditions for the beams are considered. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. As far as the authors know, there is no study on the post-buckling analysis of Timoshenko beams under uniform and non-uniform thermal loading considering full geometric non-linearity investigated by using finite element method. The convergence studies are made and the obtained results are compared with the published results. In the study, the relationships between deflections, end rotational angles, end constraint forces, thermal buckling configuration, stress distributions through the thickness of the beams and temperature rising are illustrated in detail in post-buckling case.

• Structural Engineering and Mechanics
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• v.41 no.6
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• pp.775-789
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• 2012

This paper focuses on post-buckling analysis of functionally graded Timoshenko beam subjected to thermal loading by using the total Lagrangian Timoshenko beam element approximation. Material properties of the beam change in the thickness direction according to a power-law function. The beam is clamped at both ends. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. As far as the authors know, there is no study on the post-buckling analysis of functionally graded Timoshenko beams under thermal loading considering full geometric non-linearity investigated by using finite element method. The convergence studies are made and the obtained results are compared with the published results. In the study, with the effects of material gradient property and thermal load, the relationships between deflections, end constraint forces, thermal buckling configuration and stress distributions through the thickness of the beams are illustrated in detail in post-buckling case.

• Structural Engineering and Mechanics
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• v.2 no.1
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• pp.113-123
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• 1994

A method for computing the elastic buckling prestressing force of a post-tensioned composite steel-concrete tee-beam is presented. The method is based on a virtual work formulation, and incorporates the restraint provided by the concrete slab to the buckling displacements of the steel beam. The distortional buckling solutions are shown to be given by a quadratic equation. The application of the analysis to calculation buckling strengths is given, based on codified rules for beam-columns. Conclusions are then drawn on the importance of distortional buckling when a post-tensioned composite beam is stressed during jacking.

• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.955-971
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• 2014

Large post-buckling behavior of Timoshenko beams subjected to non-follower axial compression loads are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. Two types of support conditions for the beams are considered. In the case of beams subjected to compression loads, load rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of lower-Carbon Steel. In the study, the relationships between deflections, rotational angles, critical buckling loads, post-buckling configuration, Cauchy stress of the beams and load rising are illustrated in detail in post-buckling case.

• Steel and Composite Structures
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• v.22 no.2
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• pp.411-427
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• 2016

In this study, by using finite element non-linear static analysis and comparing it with experimental models, the buckling and post-buckling behavior of bracing gusset plates has been investigated. The effects of such parameters as dimension and thickness of the gusset plate and the influence of position of the bracing member on the behavior of gusset plate have been examined. The results of the analyses clearly suggest that capacity, buckling and post-buckling behaviors of gusset plates depend on the position of the bracing splice plate with respect to the free bending line as well as on the size and thickness of the gusset plate. Also, with respect to numerical analysis results, some practical graphs for the calculation of buckling capacity of gusset plate connections are presented. For steel structures, the proposed method is apparently more accurate than available code procedures.