• 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.

• 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.43 no.3
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• pp.341-351
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• 2022

This paper presents an inelastic buckling behavior analysis of rectangular hollow steel tubes with geometrical imperfections under elevated temperatures. The main variables are the temperature loads, slenderness ratios, and exposure conditions at high temperatures. The material and structural properties of steels at different temperatures are based on Eurocode (EN 1993-1-2, 2005). In the elastic buckling analysis, the buckling strength decreases linearly with the exposure conditions, whereas the inelastic buckling analysis shows that the buckling strength decreases in clusters based on the exposure conditions of strong and weak axes. The buckling shape of the rectangular steel column in the elastic buckling mode, which depicts geometrical imperfection, shows a shift in the position at which bending buckling occurs when the lower section of the member is exposed to high temperatures. Furthermore, lateral torsional buckling occurs owing to cross-section deformation when the strong axial plane of the model is exposed to high temperatures. The elastic buckling analysis indicates a conservative value when the model is exposed to a relatively low temperature, whereas the inelastic buckling analysis indicates a conservative value at a certain temperature or higher. The comparative results between the inelastic buckling analysis and Eurocode 3 show that a range exists in which the buckling strength in the design equation result is overestimated at elevated temperatures, and the shapes of the buckling curves are different.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.6
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• pp.347-353
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• 2021

In this study, we presented a novel size optimization framework to control the linear buckling temperature and several buckling modes of plates, by optimizing thickness values of composite structures for practical engineering applications. Predicting the buckling temperature and mode shape of structures is a vital research topic in engineering to achieve structural stability. However, optimizing designs of engineering structures through engineering intuition is challenging. To address this limitation, we proposed a method that combines finite element simulation and size optimization. Based on the idea that the structural buckling temperature and mode shape of a plate are affected by the thickness of the structure, the thickness values of the nodes of the target structure were set as the design variables in this optimization method; and the buckling temperature values, and buckling mode shapes were set as the objective functions. This size optimization method enabled the determination of optimal thickness distributions, to induce the desired buckling temperature values and mode shapes. The validity of the proposed method was verified in terms of their buckling temperature values and buckling mode shapes, using several numerical examples of rectangular composite structures.

• Steel and Composite Structures
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• v.15 no.5
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• pp.481-505
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• 2013

This paper focuses on thermal post-buckling analysis of functionally graded beams with temperature dependent physical properties 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. In the case of beams with immovable ends, temperature rise causes compressible forces and 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. In this study, the differences between temperature dependent and independent physical properties are investigated for functionally graded beams in detail in post-buckling case. With the effects of material gradient property and thermal load, the relationships between deflections, critical buckling temperature and maximum stresses of the beams are illustrated in detail in post-buckling case.

• Structural Engineering and Mechanics
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• v.57 no.3
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• pp.543-567
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• 2016

This study attempts to address the buckling and free vibration characteristics of an isotropic cylindrical panel subjected to non-uniform temperature rise using numerical approach. Finite element analysis has been used in the present study. The approach involves three parts, in the first part non-uniform temperature field is obtained using heat transfer analysis, in the second part, the stress field is computed under the thermal load using static condition and, the last part, the buckling and pre-stressed modal analysis are carried out to compute critical buckling temperature as well as natural frequencies and associated mode shapes. In the present study, the effect of non-uniform temperature field, heat sink temperatures and in-plane boundary constraints are considered. The relation between buckling temperature under uniform and non-uniform temperature fields has been established. Results revealed that decrease (Case (ii)) type temperature variation field influences the fundamental buckling mode shape significantly. Further, it is observed that natural frequencies under free vibration state, decreases as temperature increases. However, the reduction is significantly higher for the lowest natural frequency. It is also found that, with an increase in temperature, nodal and anti-nodal positions of free vibration mode shapes is shifting towards the location where the intensity of the heat source is high and structural stiffness is low.

• Steel and Composite Structures
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• v.22 no.6
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• pp.1359-1389
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• 2016

Buckling and free vibration behavior of a laminated cylindrical panel exposed to non-uniform thermal load is addressed in the present study. The approach comprises of three portions, in the first portion, heat transfer analysis is carried out to compute the non-uniform temperature fields, whereas second portion consists of static analysis wherein stress fields due to thermal load is obtained, and the last portion consists of buckling and prestressed modal analyzes to capture the critical buckling temperature as well as first five natural frequencies and associated mode shapes. Finite element is used to perform the numerical investigation. The detailed parametric study is carried out to analyze the effect of nature of temperature variation across the panel, laminate sequence and structural boundary constraints on the buckling and free vibration behavior. The relation between the buckling temperature of the panel under uniform temperature field and non-uniform temperature field is established using magnification factor. Among four cases considered in this study for position of heat sources, highest magnification factor is observed at the forefront curved edge of the panel where heat source is placed. It is also observed that thermal buckling strength and buckling mode shapes are highly sensitive to nature of temperature field and the effect is significant for the above-mentioned temperature field. Furthermore, it is also observed that the panel with antisymmetric laminate has better buckling strength. Free vibration frequencies and the associated mode shapes are significantly influenced by the non-uniform temperature variations.

• Steel and Composite Structures
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• v.9 no.2
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• pp.89-101
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• 2009

This paper presents a simplified model to study post-buckling behaviours of the axially restrained steel column at elevated temperatures in fire. The contribution of axial deformation to the curvature of column section is included in theoretical equations. The possible unloading at the convex side of the column when buckling occurs is considered in the stress-strain relationship of steel at elevated temperatures. Parameters that affect structural behaviours of the axial restrained column in fire are studied. The axial restraint cause an increase in the axial force before the column buckles; the buckling temperature of restrained columns will be lower than non-restrained steel columns. However, the axial force of a restrained column decreases after the column buckles with the elevation of temperatures, so make use of the post-buckling behaviour can increase the critical temperature of restrained columns. Columns with temperature gradient across the section will produce lower axial force at elevated temperatures.

• Steel and Composite Structures
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• v.8 no.2
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• pp.159-178
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• 2008

An analytical procedure is presented for the determination of the buckling load and the buckling temperature of a straight, slender, geometrically perfect, axially loaded, translationally and rotationally restrained steel column exposed to fire. The exact kinematical equations of the column are considered, but the shear strain is neglected. The linearized stability theory is employed in the buckling analysis. Behaviour of steel at the elevated temperature is assumed in accordance with the European standard EC 3. Theoretical findings are applied in the parametric analysis of restrained columns. It is found that the buckling length factor decreases with temperature and depends both on the material model and stiffnesses of rotational and translational restraints. This is in disagreement with the buckling length for intermediate storeys of braced frames proposed by EC 3, where it is assumed to be temperature independent. The present analysis indicates that this is a reasonable approximation only for rather stiff rotational springs.

• Steel and Composite Structures
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• v.23 no.6
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• pp.623-631
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• 2017

Present paper deals with the temperature-dependent buckling analysis of sandwich nanocomposite plates resting on elastic medium subjected to magnetic field. The lamina layers are reinforced with carbon nanotubes (CNTs) as uniform and functionally graded (FG). The elastic medium is considered as orthotropic Pasternak foundation with considering the effects of thermal loading on the spring and shear constants of medium. Mixture rule is utilized for obtaining the effective material properties of each layer. Adopting the Reddy shear deformation plate theory, the governing equations are derived based on energy method and Hamilton's principle. The buckling load of the structure is calculated with the Navier's method for the simply supported sandwich nanocomposite plates. Parametric study is conducted on the combined effects of the volume percent and distribution types of the CNTs, temperature change, elastic medium, magnetic field and geometrical parameters of the plates on the buckling load of the sandwich structure. The results show that FGX distribution of the CNTs leads to higher stiffness and consequently higher buckling load. In addition, considering the magnetic field increases the buckling load of the sandwich nanocomposite plate.