• Advances in nano research
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• 제10권5호
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• pp.423-435
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• 2021

This paper examines the thermal post-buckling behaviors of graphene-reinforced metal matrix composite (GRMMC) laminated cylindrical panels which possess in-plane negative Poisson's ratio (NPR) and rest on an elastic foundation. A panel consists of GRMMC layers of piece-wise varying graphene volume fractions to obtain functionally graded (FG) patterns. Based on the MD simulation results, the GRMMCs exhibit in-plane NPR as well as temperature-dependent material properties. The governing equations for the thermal post-buckling of panels are based on the Reddy's third order shear deformation shell theory. The von Karman nonlinear strain-displacement relationship and the elastic foundation are also included. The nonlinear partial differential equations for GRMMC laminated cylindrical panels are solved by means of a singular perturbation technique in associate with a two-step perturbation approach and in the solution process the boundary layer effect is considered. The results of numerical investigations reveal that the thermal post-buckling strength for (0/90)_5T GRMMC laminated cylindrical panels can be enhanced with an FG-X pattern. The thermal post-buckling load-deflection curve of 6-layer (0/90/0)_S and (0/90)_3T panels of FG-X pattern are higher than those of 10-layer (0/90/0/90/0)_S and (0/90)_5T panels of FG-X pattern.

• Structural Engineering and Mechanics
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• 제90권5호
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• pp.517-530
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• 2024

This paper presents a new four-unknown equivalent single layer (ESL) refined plate theory for the buckling analysis of functionally graded (FG) rectangular plates with all simply supported edges and subjected to in-plane mechanical loading conditions. The present model accounts for a parabolic variation of transverse shear stress over the thickness, and accommodates correctly the zero shear stress conditions on the top and bottom surfaces of the plate. The material properties are supposed to vary smoothly in the thickness direction through the rules of mixture named power-law gradation. The governing equilibrium equations are formulated based on the total potential energy principle and solved for simply supported boundary conditions by implementing the Navier's method. A numerical result on elastic buckling using the current theory was computed and compared with those published in the literature to examine the accuracy of the proposed analytical solution. The effects of changing power-law exponent, aspect ratio, thickness ratio and modulus ratio on the critical buckling load of FG plates under different in-plane loading conditions are investigated in detail. Moreover, it was found that the geometric parameters and power-law exponent play significant influences on the buckling behavior of the FG plates.

• Structural Engineering and Mechanics
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• 제34권2호
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• pp.175-188
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• 2010

This paper deals with the buckling and postbuckling responses, and the progressive failure of square laminates of symmetric lay-up with a central rectangular cutout under in-plane shear load. A detailed investigation is made to show the effects of cutout size and cutout aspect ratio on the buckling and postbuckling responses, failure loads and failure characteristics of $(+45/-45/0/90)_{2s}$, $(+45/-45)_{4s}$ and $(0/90)_{4s}$ laminates. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. In addition, the effects of boundary conditions on buckling loads, failure loads, failure modes, and maximum transverse deflection for a $(+45/-45/0/90)_{2s}$ laminate with and without a square cutout have been presented. It is concluded that because of early onset of delamination at the net section of cutouts before first-ply failure, total strength of the laminate with very small cutouts can not be utilized.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2001년도 추계학술발표대회 논문집
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• pp.17-20
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• 2001

This paper presents the results of an elastic buckling analysis of elastically restrained orthotropic plate with a longitudinal stiffener under in-plane linearly distributed load. It is assumed that the loaded edges of web plate are simply supported and other two edges are elastically restrained against rotation. The stiffener is modeled as a beam element and its torsional rigidity is neglected. For the buckling analysis Lagrangian multiplier method is employed. The effects of restraint and longitudinal stiffener are presented in a graphical form.

• Steel and Composite Structures
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• 제30권5호
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• pp.471-481
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• 2019

Beam-columns are structural members subjected to a combination of axial and bending forces. Lateral-torsional buckling is one of the main failure modes. Beam-columns that are bent about its strong axis may buckle out of the plane by deflecting laterally and twisting as the values of the applied loads reach a limiting state. Lateral-torsional buckling failure occurs suddenly in beam-column elements with a much greater in-plane bending stiffness than torsional or lateral bending stiffness. This study intends to establish a unique convenient closed-form equation that it can be used for calculating critical elastic lateral-torsional buckling load of beam-column in the presence of a known axial load. The presented equation includes first order bending distribution, the position of the loads acting transversely on the beam-column and mono-symmetry property of the section. Effects of axial loads, slenderness and load positions on lateral torsional buckling behavior of beam-columns are investigated. The proposed solutions are compared to finite element simulations where thin-walled shell elements including warping are used. Good agreement between the analytical and the numerical solutions is demonstrated. It is found out that the lateral-torsional buckling load of beam-columns with mono-symmetric sections can be determined by the presented equation and can be safely used in design procedures.

• 한국생산제조학회지
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• 제7권5호
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• pp.106-112
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• 1998

Experience and experiments show that in many cases the buckling limit is reached at a much smaller load level than is predicted by linear buckling analysis. In this paper, it is considered linear and nonlinear of plane vehicle structure and estimates design sensitivity of the cross sectional area that is composed plane vehicle structure and performs optimal design. It compares linear vehicle structure with nonlinear vehicle structure for optima design result that is selected constraint condition of buckling load.

• Advances in nano research
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• 제7권3호
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• pp.181-190
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• 2019

The thermal buckling temperature values of the graded carbon nanotube reinforced composite shell structure is explored using higher-order mid-plane kinematics and multiscale constituent modeling under two different thermal fields. The critical values of buckling temperature including the effect of in-plane thermal loading are computed numerically by minimizing the final energy expression through a linear isoparametric finite element technique. The governing equation of the multiscale nanocomposite is derived via the variational principle including the geometrical distortion through Green-Lagrange strain. Additionally, the model includes different grading patterns of nanotube through the panel thickness to improve the structural strength. The reliability and accuracy of the developed finite element model are varified by comparison and convergence studies. Finally, the applicability of present developed model was highlight by enlighten several numerical examples for various type shell geometries and design parameters.

• Steel and Composite Structures
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• 제45권5호
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• pp.729-747
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• 2022

The critical buckling loads and buckling modes of bi-directional functionally graded porous unified higher order shear plate with elastic foundation are investigated. A mathematical model based on neutral axis rather than midplane is developed in comprehensive way for the first time in this article. The material constituents form ceramic and metal are graded through thickness and axial direction by the power function distribution. The voids and cavities inside the material are proposed by three different porosity models through the thickness of plate. The constitutive parameters and force resultants are evaluated relative to the neutral axis. Unified higher order shear plate theories are used to satisfy the zero-shear strain/stress at the top and bottom surfaces. The governing equilibrium equations of bi-directional functionally graded porous unified plate (BDFGPUP) are derived by Hamilton's principle. The equilibrium equations in the form of coupled variable coefficients partial differential equations is solved by using numerical differential integral quadrature method (DIQM). The validation of the present model is presented and compared with previous works for bucking. Deviation in buckling loads for both mid-plane and neutral plane are developed and discussed. The numerical results prove that the shear functions, distribution indices, boundary conditions, elastic foundation and porosity type have significant influence on buckling stability of BDFGPUP. The current mathematical model may be used in design and analysis of BDFGPU used in nuclear, mechanical, aerospace, and naval application.

• Steel and Composite Structures
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• 제11권5호
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• pp.359-374
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• 2011

In this paper, the influence of fibre orientation and aspect ratio on stability analysis of simply supported skew plates subjected to in plane loading is studied by using a four noded hybrid plate finite element. The formulation of the element is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. Some numerical problems are solved and the effects of skew angle, aspect ratio, fibre orientation and loading type on the critical buckling loads are highlighted.

• Steel and Composite Structures
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• 제43권3호
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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.