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In this paper elastoplastic buckling of thin rectangular plates are analyzed with deformation theory (DT) and incremental theory (IT) and the results are investigated under different loads and boundary conditions. Load is applied in plane and in uniform tension and compression form. The used material is AL7075T6 and the plate geometry is . The Generalize Differential Quadrature method is employed as numerical method to analyze the problem. The influences of loading ratio, plate thickness and various boundary conditions on buckling factor were investigated in the analysis using both incremental and deformation theories. In thin plates the results obtained from both plasticity theories are close to each other, however, with increasing the thickness of plates a considerable difference between the buckling loads obtained from two theories of plasticity is observed. The results are compared with those of others published reports. Moreover, for some different situations new results are presented. Some new consequences are achieved regarding the range of validation of two theories.

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In this paper, the thermal buckling behavior of circular plates with variable thicknesses made of bimorph functionally graded materials, under uniform thermal loading circumstances, considering the first-order shear deformation plate theory and also assumptions of von Karman has been studied. The material characteristics are symmetric to the middle surface of the plate and, based on the power law, vary along with thickness; where the middle surface is intended pure metal, and the sides are pure ceramic. In order to determine the distribution of pre-buckling force in the radial direction, the membrane equation is solved using the shooting method. And the stability equations are solved numerically, with the help of pseudo-spectral method by choosing Chebyshev functions as basic functions. The numerical results in clamped and simply supported boundary conditions and the linear and parabolic thickness variations are presented. And the influence of various parameters like volume fraction index, the thickness profile and side ratio on the buckling behavior of these plates has been evaluated.

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In this paper, simulation and analysis of thin steel cylindrical shells of various lengths and diameters and thickness with triangular cutouts have been studied. In this research buckling and post-buckling analyses were carried out using the finite element method by ABAQUS software. Moreover, the effect of cutout position and the length-to-diameter (L/D) and diameter-to-thickness (D/t) ratios on the buckling and post-buckling behavior of cylindrical shells have been investigated. In this work the cylindrical shells used for this study were made of mild steel and their mechanical properties were determined using servo hydraulic machine. Then buckling tests were performed using a servo hydraulic machine. In order to numerical analyze the buckling subject to axial load similar to what was done in the experiments; a displacement was applied to the center of the upper of the specimens. The results of experimental tests were compared to the results of the finite element method. A very good correlation was observed between numerical simulation and experimental result.

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Abstract - In this article , thermal buckling analysis of functionally graded annular sector plate is studied. The mechanical and thermal properties of the functionally graded sector plate are assumed to be graded in the thickness direction . The equilibrium and stability equations are derived based on the first order shear deformation plate theory (FSDT) in conjunction with nonlinear von-karman assumptions. Differential quadrature method is used to discretize the equilibrium and stability equations. In this method a non-uniform mesh point distribution (Chebyshev-Gauss-Lobatto) is used for provide accuracy of solutions and convergence rate . By using this method, there is no restriction on implementation of boundary conditions and various boundary conditions can be implemented along any edges . Finally, The results compared with other researches and the effects of plate thickness, sector angle, annularity, power law index and various boundary conditions on the critical buckling temperature are discussed in details .

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Sandwich panels have high strength to weight ratio because of their special structure. The variables which are defined for designing sandwich panels should be determined with applying necessary strength and lowest weight. In this paper, the imperialist competitive algorithm (ICA) has been used for minimizing the weight of a sandwich panel with prismatic core based on yielding and buckling criteria. ICA is inspired of imperialist competitions and it is based on two special criteria as recruitment policy and stable imperialist competition. Arrays numbers, core and surface thickness and panel height are assumed as design variables for decreasing panel weight. The results were shown that core and surface thickness and the total height of panel has been increased by increasing loading for given number of arrays. Also the core and surface thickness has been decreased and the total height have been increased by increasing array number for a determined loading and so panel weight has been decreased. A panel with diamond core has highest structure efficiency. It was shown that ICA is useful and competitive than the other heuristic algorithms because of direct using of function values in some problems which was required to the total optimization.

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The present study proposes an analytical solution for the axisymmetric/asymmetric buckling analysis of thin circular/annular nanoplates under uniform radial compressive in-plane load. In order to consider small scale effects, nonlocal elasticity theory of Eringen is employed. To ensure the efficiency and stability of the present methodology, the results are compared with other presented in literature. Material properties including Young’s modulus, density, Poison’s ratio are assumed to be constant through the body of nanoplate. In addition, the effect of small scales on critical buckling loads for different parameters such as radius of the FG nanoplate, boundary condition, mode number and geometry parameters are investigated. In order to obtain the critical buckling load, the asymmetric modes as well as axisymmetric modes are considered. The thin nanoplate is modeled using Kirchhoff plate theory.

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In this paper, thermal effect on deflection, critical buckling load and vibration of nonlocal Euler-Bernoulli beam on Pasternak foundation using Ritz method is proposed. Equations of motion Euler-Bernoulli beam on Pasternak elastic foundation under thermal load is achieved by using energy method. Ritz method is used to solve the governing equations of motion. By this method, mass, stiffness and hardness buckling matrices are obtained. In this study, the effects of thermal, various boundary conditions, Winkler-type spring constant, Pasternak-type shear constant, non-local parameter on dimensionless deflection, critical buckling load, and natural frequency of Euler-Bernoulli beam theory are assessed. The obtained results indicate that with an increase of Winkler and Pasternak constants, the dimensionless natural frequency and critical buckling load increase, while the dimensionless deflection decreases. However, with increasing the temperature change in nonlocal Euler-Bernoulli beam on Winkler–Pasternak elastic foundation, the dimensionless natural frequency and critical buckling load decrease, while the dimensionless deflection increases. Moreover, with considering Winkler and Pasternak constants, the lower mode shape are removed and replaced with higher mode shapes.

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The main purpose of this study is to investigate nonlinear bending and buckling analysis of radially functionally graded annular plates subjected to uniform in-plane compressive loads by Dynamic Relaxation method. The mechanical properties of plates assumed to vary continuously along the radial direction by the Mori–Tanaka distribution. The nonlinear formulations are based on first order shear deformation theory (FSDT) and large deflection von Karman equations. The dynamic relaxation (DR) method combined with the finite difference discretization technique is employed to solve the equilibrium equations. Due to the lack of similar research for the bending and buckling of functionally graded annular plates with material variation in the radial direction, some results are compared with the ones obtained by the Abaqus finite element software. Furthermore, some comparison study is carried out to compare the current solution with the results reported in the literature for annular isotropic plates. The achieved good agreements between the results indicate the accuracy of the present numerical method. Finally, numerical results for the maximum displacement and critical buckling load for various boundary conditions, effects of grading index, thickness-to-radius ratio and inner radius -to-outer radius ratio are presented.

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In the present work, creep buckling of linear viscoelastic plate was studied. Pseudo-transient or Dynamic Relaxation method with finite element discritization was used for solving the nonlinear governing equations of the plate. The displacements were based on first order shear deformation theory. Von Karman assumptions were considered for strains, including initial imperfection of the plate. Central deflections of the rectangular PMMA plate as well as end-shortenings were obtained during the loading of the plates with simply supported and clamped edges. The results compared well with commercial finite element code ANSYS.

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In this paper, exact closed-form solutions in explicit forms are presented to investigate small scale effects on the buckling of Lévy-type rectangular nanoplates based on the Reddy’s nonlocal third-order shear deformation plate theory. Two other edges may be restrained by different combinations of free, simply supported, or clamped boundary conditions. Hamilton’s principle is used to derive the nonlocal equations of motion and natural boundary conditions of the nanoplate. Two comparison studies with analytical and numerical techniques reported in literature are carried out to demonstrate the high accuracy of the present new formulation. Comprehensive benchmark results with considering the small scale effects on buckling load ratios and non-dimensional buckling loads of rectangular nanoplates with different combinations of boundary conditions are tabulated for various values of nonlocal parameters, aspect ratios and thickness to length ratios. Due to the inherent features of the present exact closed-form solution, the present findings will be a useful benchmark for evaluating the accuracy of other analytical and numerical methods, which will be developed by researchers in the future. Also, the present study may be useful for static and dynamic analysis of thicker nano scale plate-like structures, multi-layer graphene and graphite as composite or sandwich structures.

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In this paper, the governing equations for a vibratory beam with moderately large deflection are derived using the first order shear deformation theory. These equations which are a system of nonlinear partial differential equations with constant coefficients are solved analytically with the perturbation technique and the natural frequencies and the buckling load of the system are determined. A parametric study is performed and the effects of the geometrical and material properties on the natural frequency and buckling load are investigated and the effect of normal transverse strain and axial load on natural frequency are examined. Some results based on the first order shear deformation theory are consistent with classic theories of beams and some yield different results. Formulation presented to calculate the transverse frequency, determines the axial frequency too. Also, the natural frequencies and buckling load are calculated with the finite elements method by applying one and three-dimensional elements and the results are compared with the analytical solution.

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In this paper, multi-objective optimization of sandwich panels with open and prismatic core has been studied. Naming these panels is based on the number of corrugations (n) of the core. The panel is considered as a heat exchanger that is loaded under longitudinal loading simultaneously. Multi-objective particle swarm optimization (MOPSO) is used by considering weight and heat transfer index as objective function. Optimization is carried out so that the panel has minimum weight and maximum heat transfer index simultaneously, moreover it will not suffer from yielding and buckling in face and core plates. The results showed that two panels, i.e. n=1 and n=7 are very suitable in one-objective and two-objective optimizations. Also, maximum of heat transfer index obtained by a certain panel is nearly the same in various loadings. Pareto diagrams achieved out of two-objective optimization have two separate areas where in one area weight increase may cause an intense increase in heat transfer index and in another area this index remains almost constant. The diagrams are helpful in selecting suitable panel and its geometric dimensions based on significance of each objective functions. Comparing the results indicate efficiency of PSO method in one-objective and two-objective optimization of the panels.

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Buckling and vibration characteristics of thin symmetrically laminated elliptical composite plates under initial in-plane edge loads and resting on Winkler-type elastic foundation are presented based on the classical laminated plate theory. The governing equations are obtained from the variational approach and solved by the Ritz method. Extensive numerical data are provided for the first three natural frequencies as a function of in-plane load for various classical edge conditions (free, clamped and simply supported). Moreover, the effects of fiber orientation on the natural frequencies and buckling loads of laminated angle-ply plates with stacking sequence of [(β /-β / β /-β)]s, are studied for chosen foundation parameter. Also, selected deformation mode shapes are illustrated. The accuracy of calculations is checked by performing good convergence studies, and the correctness of results is established by comparison with the existing results in the literature as well as FEM data.

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In this paper, buckling and energy absorption behavior of stainless steel semi-sphere, cylindrical and conical shells under axial loading are studied. Every shell with the same mass and different shapes with and without groove is designed. In this paper the effect of shape, thickness, height, groove of shells and distance between grooves, on buckling and energy absorption were investigated. In experimental test, Samples had same mass and thickness and also grooves had same depth and distance. Experimental tests were performed by a servo-hydraulic INSTRON 8802 machine. Numerical analysis is carried out by ABAQUS software and is validated with experimental results.

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In this paper, the buckling of rectangular plates subjected to non-uniform in-plane loading is investigated. At first the equilibrium equations of plate based on the first order shear deformation theory have been extracted. The kinematic relations have been assumed based on the von-Karman model and the Hook’s law has been considered as the constitutive equations. The adjacent equilibrium method has been used for deriving the stability equations. The equilibrium equations which are related to the prebuckling stress distribution, have been solved using the differential equations theory. To determine the buckling load of a simply supported plate, the Galerkin method has been used for solving the stability equations which are a system of differential equations with variable coefficients. In this paper, four types of in-plane loading, including the uniform, parabolic, cosine and triangular loading, have been considered and the effects of the plate aspect ratio and thickness on the buckling load has been investigated and the results have been compared with the finite element method and the classical plate theory. The comparison of the results show that for all loading cases, the buckling load computed by the classical plate theory is higher than the value obtained based on first order shear deformation theory.

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In this article, an analytical procedure is presented for prediction of linear buckling load of a waffle cylinder stiffened by an array of equilateral triangles. The grid stiffened shell is subjected to axial loading condition. The shell has simply supported boundary conditions at its two edges. The equivalent stiffness of the stiffener and skin is computed by superimposing between the stiffness contributions of the stiffeners and skin with a new method. Total stiffness matrix of the shell is composed of stiffness matrix of skin and grids with special volume fractions. In this analysis, using energy method, equilibrium equations of the grid stiffened shell are extracted based on the thin shell theory of Flugge. The Navier solution is applied to solve the problem. A 3-D finite element model was also built in ANSYS software to show the accuracy and validity of the present solution. The results show that the present new approach has high accuracy and precision. The effect of various geometrical parameters on the critical buckling load is investigated. Due to the stability and accuracy, the present method can be used by many designers and engineers to improve their design quality.

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This paper describes a simple method for determined the critical buckling load of composite lattice conical structures under axially compressive load. To reveal the critical buckling strength of conical lattice structures, an analytical method based on the classical beam-column theory was applied. Characteristic equations were built according to the equilibrium equations. Furthermore, the buckling behavior of the conical composite shells under axial compression were investigated using experimental method. The specimens used in the experiment were made from glass/epoxy by winding the continuous glass fibers wetted with epoxy on a die with helical and circumferential grooves adopting a simplified manufacturing process. A relatively new flexible tool was developed for forming the grid-structures die, and the specimens were tested by using a universal testing machine. The diagrams of axial load versus displacement were recorded in real time during the tests. The experimental results describe failure modes that are present in the structures such as rib crippling, and general buckling. Axial buckling tests were carried out and the results were compared with the analytical method. The results have been summarized to verify the analytical method. Also, the proposed model has verified with the aid of finite element analysis. The proposed model suggests the possibility to improve the preliminary design solution with respect to the fully analytical approach.

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In previous experiments, practice and in some condition of loading, geometry and support configurations, a type of instability has been observed in which tension flange moves laterally which it has been addressed in design codes as “web sidesway buckling”. Web sidesway buckling is a case of instability that it was observed in beam with restrained top flange and no constraint for bottom flange. Primary studies and experiments show that web sidesway buckling is due to both local instability in the web just under loaded zone and global instability of tension flange along length of the girder. In the present paper, a concise study has been carried out on behavior and the mechanism of this instability occurrence in web sidesway and how to evaluate loading capacity of the girders in the light of experiments, then a simple model which is a modification on the existing model has been proposed. Experimental work has been conducted to investigate the effect of tension flange on the load capacity of beams. The specimen's dimensions were adjusted in order to show web sidesway buckling. In addition, the supports configuration was made compatible with this instability. The objectives of the experiment were to obtain; mechanism of instability initiation, deformation pattern, effect of tension flange width and nonlinear deformations underneath the loading point. A closer view in load-displacement behavior of test specimens shows at first, loading accompanies lateral displacement due to imperfection and then rate of displacement reduces. After reaching to maximum load, girder has still capacity for load carrying but with excessive lateral displacement in tension flange. The results of experiments also show that web sidesway buckling generally accompanied by local buckling or crippling of the web under loaded zone. Deformation initiates with lateral movement of tension flange. Then local buckling and yielding occur, and finally, web sidesway buckling develops along the beam length. From this time onwards, load capacity is approximately constant. Furthermore, it can be seen that the rate of lateral displacement is directly dependent on width of tension flange. On the other hand, the results from design equations of design codes for estimating load capacity of girders against web sidesway buckling are too conservative in comparison to the proposed model. The critical load is affected by tension flange clearly, and occurrence of this type of instability is credible in other sections such as T- shape beam but in a lower critical load with respect to the I-shape sections. Also the results from the new model are in good agreement with that of experimental data. Finally, • It seems that only the existence of an area in the web affected by a tension stress field do not cause web sidesway buckling and transformation of tension stress field into compression field determents on initiation of instability.

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One of the strengthening methods in reinforced concrete frame buildings is improving seismic behavior of such structures by means of steel bracing. When influenced by compressive stresses, traditional steel braces would buckle and are free of any ductility. As a result, efforts in order to restrain buckling problem for steel braces has led to creation of steel unbonded brace. In these braces, Eulerian buckling of central steel core is controlled by placing in a steel tube full of mortar. In this paper, RC buildings of 6, 12 and 18 stories are first designed based on standard 2800 and then controlled based on the rehabilitation regulation and the third edition of standard 2800. After analyzing and in order to improve seismic behavior, these buildings are strengthened by the use of common braces and steel unbonded braces and the columns of braced frames are also reinforced by concrete jacket. Totally, 42 models were analyzed by nonlinear static analysis (pushover analysis). The results indicate that structures with traditional braces have weakness in high level of drifts due to buckling of compressive braces and the energy absorption in 12 and 18 stories structures is even lower than non-strengthened structures. Nevertheless, this defect is removed by applying unbounded braces because of somehow identical behavior in extension and pressure as well as utilizing total capacity of these kinds of brace. Also, in comparison with structures with traditional braces and non-strengthened structures, a high level of energy absorption will be obtained. One of the strengthening methods in reinforced concrete frame buildings is improving seismic behavior of such structures by means of steel bracing. When influenced by compressive stresses, traditional steel braces would buckle and are free of any ductility. As a result, efforts in order to restrain buckling problem for steel braces has led to creation of steel unbonded brace. In these braces, Eulerian buckling of central steel core is controlled by placing in a steel tube full of mortar. In this paper, RC buildings of 6, 12 and 18 stories are first designed based on standard 2800 and then controlled based on the rehabilitation regulation and the third edition of standard 2800. After analyzing and in order to improve seismic behavior, these buildings are strengthened by the use of common braces and steel unbonded braces and the columns of braced frames are also reinforced by concrete jacket. Totally, 42 models were analyzed by nonlinear static analysis (pushover analysis). The results indicate that structures with traditional braces have weakness in high level of drifts due to buckling of compressive braces and the energy absorption in 12 and 18 stories structures is even lower than non-strengthened structures. Nevertheless, this defect is removed by applying unbounded braces because of somehow identical behavior in extension and pressure as well as utilizing total capacity of these kinds of brace. Also, in comparison with structures with traditional braces and non-strengthened structures, a high level of energy absorption will be obtained.

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In this paper, elastic-plastic symmetrical buckling of a thin solid circular plate of variable thickness, under uniform edge pressure, is investigated, based on both Incremental Theory (IT) and Deformation Theory (DT). Two kinds of simply supported and clamped boundary conditions have been considered. A power-law function was assumed for thickness variation. To minimize the integral uniqueness criterion, based on Rayleigh-Ritz method, transversal displacement was approximated by a test function which includes some unknown coefficients and satisfies geometric boundary conditions. Substituting the test function in the stability criterion and minimizing with respect to the unknown coefficients results in a homogeneous algebraic set of equations in terms of unknown coefficients. For non-trivial solution, the determinant of coefficient matrix should be equated to zero. Using this equation, critical buckling load is determined. The results of present study were compared with existing analytical solutions for circular plate of constant thickness and a good agreement was observed. This clearly shows the validity of presented analysis. Then the effect of thickness variation and boundary conditions type on the critical buckling load was investigated, for commercial aluminum and steel 1403 materials. The results show that when the thickness of circular plate center is 10% greater than its edge thickness the buckling load may increase up to 40% comparing with the circular plate for which the center thickness is 10% less than its edge thickness.