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The stability of axially functionally graded (AFG) heavy columns was analyzed. Consideration in stability analysis of the column is given to the free vibration and bucking problems. The mass density and Young's modulus of the AFG heavy column vary along the column axis through a power-law function. Unified modeling of the differential equations with the associated boundary conditions governing the deformed shape of the free vibrations and buckling of the column was developed. Using a combination of direct numerical integration method and numerical solution method of nonlinear equation, differential equations were solved to calculate the natural frequency and the critical buckling load. Calculation results for the natural frequency and buckling load compare well with the FEM results. As a result of numerical experiments, the effects of material and geometric properties on the natural frequency and the buckling load were reported and discussed in detail. [ABSTRACT FROM AUTHOR]

The paper aims to develop a unified modeling to analyze the free vibrations and buckling of laterally functionally graded material columns. The columns of rectangular cross-section, in which the mass density and Young's modulus vary along the depth as a power-law function, were considered. The differential equation governing a mode shape of a deformed column was derived with the relevant boundary conditions, including the effect of rotatory inertia. The computation results for the natural frequencies and buckling load were compared well with those available in the open scientific literature. The effects of geometrical and material properties on natural frequencies and buckling loads with the mode shapes are highlighted. [ABSTRACT FROM AUTHOR]

In the present research, the optimum paths and orientations for curvilinear and straight fibers of variable-and constant-stiffness composite cylindrical shells subjected to an external hydrostatic pressure and bending were found. For this purpose, a linear variation in the fiber orientation was considered for the curvilinear fibers. A genetic algorithm program written in the Python language was developed and linked to the ABAQUS finite-element code and used in an optimization process. The optimization was performed for several aspect ratios of the length-to-diameter of composite cylindrical shells. The buckling pressure of the variable-stiffness composite cylindrical shell increased by about 30℅ in comparison with that of the constant-stiffness composite cylindrical shell under an external hydrostatic pressure. The gaps and overlaps were modeled using a Pythonbased program and the ABAQUS software to investigate their effects on the buckling load of variable-stiffness cylindrical shells under external pressure loads. [ABSTRACT FROM AUTHOR]

For several years, kites have been representing an innovative technology in the maritime sector to reduce the fuel consumption through an auxiliary propulsion or producing energy onboard. Regarding the continuous increase in kite sizes, one of the main objectives is to determine whether a leading-edge inflatable kite and its components will be able to withstand the pressure field induced by the aerodynamic load. Therefore, an accurate identification of stress fields in them is required by designers. For this aim, a fluid-structure interaction method was developed by coupling a 3D nonlinear lifting-line model with the Abaqus™ 2017 finite-element software tools. Within this framework, a structural analysis was performed for a kite made of a woven fabric by employing the thin-layer finite-element technique for its weak bending properties. This modeling method is new and is not available in the Abaqus™. [ABSTRACT FROM AUTHOR]

The 3D nonaxisymmetric local stability loss problem is studied for a hollow cylinder, made of a viscoelastic composite material, under the axial compression. The criterion of an infinitesimal initial imperfection is employed, and the evolution of this imperfection is investigated by 3D geometrically nonlinear exact equations of viscoelasticity theory. The corresponding nonlinear problem is solved by the boundary perturbation method. The material of the cylinder is modeled as a viscoelastic transversely isotropic medium. Numerical results for the critical time and critical compressive forces are presented, discussed, and compared with those obtained by approximate shell theories. [ABSTRACT FROM AUTHOR]

To assess the stability and postbuckling behavior of thin composite panels with additional repair lap plates, it is proposed to use relations that consider the unsymmetry of the structure. An analytical solution of the geometrically nonlinear problem is presented for smooth composite panels, whose shape is close to a square, loaded by tangential flows. The initial relations of the problem consider the possible unsymmetry of the structure and include mixed stiffnesses. The boundary conditions in this case correspond to a hinged support. An explicit expression is obtained for the critical stresses of the loss of stability under the action of tangential forces. Relations for the stress-strain state of a square composite panel at its geometrically nonlinear behavior are given. Examples of determination of the critical shear forces are presented, and the expediency of consideration of unsymmetry of the structure in verification calculations of thin composite panels is shown. [ABSTRACT FROM AUTHOR]

The paper presents a review of Haar wavelet methods and an application of the higher-order Haar wavelet method to study the behavior of multilayered composite beams under static and buckling loads. The Refined Zigzag Theory (RZT) is used to formulate the corresponding governing differential equations (equilibrium/stability equations and boundary conditions). To solve these equations numerically, the recently developed Higher-Order Haar Wavelet Method (HOHWM) is used. The results found are compared with those obtained by the widely used Haar Wavelet Method (HWM) and the Generalized Differential Quadrature Method (GDQM). The relative numerical performances of these numerical methods are assessed and validated by comparing them with exact analytical solutions. Furthermore, a detailed convergence study is conducted to analyze the convergence characteristics (absolute errors and the order of convergence) of the method presented. It is concluded that the HOHWM, when applied to RZT beam equilibrium equations in static and linear buckling problems, is capable of predicting, with a good accuracy, the unknown kinematic variables and their derivatives. The HOHWM is also found to be computationally competitive with the other numerical methods considered. [ABSTRACT FROM AUTHOR]

The problem of local buckling delamination around interface edge cracks in a sandwich PZT/Metal/PZT rectangular thick plate is studied within the scope of the 3D linearized buckling instability theory. Crack faces have an insignificant initial imperfection, and the plate is compressed by uniformly distributed normal forces acting on two opposite ends of the plate. The evolution of the initial imperfection is investigated, and the critical buckling forces for the plate are found. A mathematical modeling of the problem considered is performed using the 3D exact geometrically nonlinear electroelasticity theory within the framework of a piecewise homogeneous body model. The corresponding boundary-value problems are solved numerically by employing a 3D finiteelement method. Numerical results for the critical forces and the effect problem parameters on these forces are presented and discussed. [ABSTRACT FROM AUTHOR]

Basalt-fiber-reinforced epoxy (BFRE) composite laminates fabricated using the vacuum infusion process were subjected to axial compression to assess their buckling behavior. The buckling responses of open-hole specimens were compared with those of plain ones. ABAQUS finite-element predictions of BFRE composite buckling agreed well with experimental results. A validated numerical model was used to perform a parametric investigation into the effects of open-hole specimen geometry and boundary conditions of specimens on their buckling behavior. A linear analysis was carried out to estimate the effect of geometric imperfections of specimens on their buckling. Also, glass-fiber-reinforced epoxy specimens were analyzed for their buckling response and compared with that of BFRE ones. The results of this study can be used for buckling-based designs of open-hole composite structures. [ABSTRACT FROM AUTHOR]

A new refined quasi-3D shear deformation theory for bending, buckling, and free vibration analyses of a functionally graded porous beam resting on an elastic foundation is presented. It involves only three unknown functions, against four or more ones in other shear and normal deformation theories. The stretching effect is naturally taken into account by this theory because of its 3D nature. The mechanical characteristics of the beam are assumed to be graded in the thickness direction according to two different porosity distributions. The differential equation system governing the bending, buckling, and free vibration behavior of porous beams is derived based on the Hamilton principle. The problem is then solved using the Navier solution for a simply supported beam. The accuracy of the present solution is demonstrated by comparing it with other closed-form solutions available in the literature. A detailed parametric study is presented to show the influence of porosity distribution on the general behavior of FG porous beams on an elastic foundation. [ABSTRACT FROM AUTHOR]

The optimum paths and orientations for curvilinear and straight fibers in composite cylindrical shells of variable and constant stiffness under external hydrostatic pressure are obtained and compared. The optimization was performed for several length-to-diameter ratios of the shells. Results showed that the buckling pressure of the variable-stiffness shell was by about 30℅ higher than that of the constant-stiffness one. This increase in the buckling pressure was obtained by locating fibers in the hoop direction in the middle of the cylinder and orienting the fibers toward the longitudinal direction on cylinder edges. [ABSTRACT FROM AUTHOR]

The necessity for considering both strength criteria and postbuckling effects in calculating the load-carrying capacity in compression of thin-wall composite structures with impact damage is substantiated. An original applied method ensuring solution of these problems with an accuracy sufficient for practical design tasks is developed. The main advantage of the method is its applicability in terms of computing resources and the set of initial data required. The results of application of the method to solution of the problem of compression of fragments of thin-wall honeycomb panel damaged by impacts of various energies are presented. After a comparison of calculation results with experimental data, a working algorithm for calculating the reduction in the load-carrying capacity of a composite object with impact damage is adopted. [ABSTRACT FROM AUTHOR]

In order to determine the nonlocal critical buckling loads of chiral double-walled carbon nanotubes embedded in an elastic medium, the nonlocal Timoshenko beam theory is implemented. The solution for the nonlocal critical buckling loads is obtained using governing equations of the nonlocal theory. The effect of the elastic medium, the buckling mode number, chirality, and aspect ratio on the nonlocal critical buckling loads of double-walled carbon nanotubes are studied and discussed. The Young's modulus of three types of double-walled carbon nanotubes, with armchair, zigzag, and chiral tubules, are calculated based on molecular dynamics simulations. The nonlocal critical buckling loads in relation to the chirality of double-walled carbon nanotubes, buckling mode number, and length-to-diameter (aspect} ratio, in the presence and absence of an elastic medium, are examined. [ABSTRACT FROM AUTHOR]

The paper presents results of two creep tests on pultruded open-section GFRP beams aimed to evaluate the long-term deformations, the residual deflection after unloading, and the influence of creep strains on the flexuraltorsional buckling phenomenon. Two beams were subjected to a constant load for about one year. Then one of the beams was unloaded to evaluate its residual deflection. For the other beam, the load was increased up to failure, and the residual buckling strength was compared with that of a similar beam tested up to failure. The parameters of the Findley power law are evaluated, and the experimental results are compared with those of numerical analyses and with available formulations for prediction of the time-dependent properties of composite beams. Results of the investigation testify, in particular, to a noninsignificant time-dependent increment in deflections of the beams and to a significant reduction in their buckling strength due to creep deformations. [ABSTRACT FROM AUTHOR]

The buckling of simply supported laminated composite plates is studied using various higher-order shear deformation theories. A Navier-type analytical method is used to solve the governing differential equations. The critical buckling loads of simply supported laminated composite plates under a uniaxial buckling load are calculated. The present results are compared with available published results to verify the accuracy of the higher-order shear deformation theories considered. [ABSTRACT FROM AUTHOR]

On the basis of the nonlocal elasticity theory, the Timoshenko beam model is utilized to investigate the elastic buckling of chiral single-walled carbon nanotubes (SWCNTs) under axial compression. Based on the governing equations of the nonlocal Timoshenko beam model, an analytical solution for nonlocal critical buckling loads is obtained. The influence of a nonlocal small-scale coefficient, the vibration mode number, the chirality of SWWCNTs, and their aspect ratio on the nonlocal critical buckling loads is studied and discussed. [ABSTRACT FROM AUTHOR]

The buckling behavior of a thin particle-reinforced composite plate under the influence of an unsteady temperature field and a temperature gradient across its thickness is investigated. An analytic solution for bending of the plate is obtained in the form of double trigonometric series. Based on the analytic result, a numerical test is carried out to study the thickness and time dependences of the buckling behavior of a plate made of a PVC matrix and titanium particles. [ABSTRACT FROM AUTHOR]

The buckling of a long multilayered nonlinearly elastic shell made of different materials and subject to the action of external pressure is investigated. The load is not hydrostatic and greatly varies in value and direction. Neglecting the effect of end fastening of the shell, the problem is reduced to an analysis of the loss of load-carrying ability of a ring of unit width separated from the shell. The solution is based on a variational method of mixed type formulated for heterogeneous nonlinearly elastic bodies, taking into account the geometrical nonlinearity, in a combination with the Rayleigh-Ritz method. The initial analysis is reduced to solving the Cauchy problem for a nonlinear ordinary differential equation resolved for the derivative. Numerically, using the Runge-Kutta method, the effect of the number of layers and of the parameter of nonuniformity of the external pressure on the critical buckling force is revealed. The urgency and importance of the problem are connected with the research of reserves in the saving of materials with a simultaneous possibility of increasing the load-carrying ability of a structure. [ABSTRACT FROM AUTHOR]

The nonlinear buckling and postbuckling of a shear-deformable anisotropic laminated cylindrical panel of finite length is investigated based on a boundary-layer theory for buckling. The layers of the panel are assumed to be linearly elastic. The governing equations are based on Reddy's higher-order shear deformation theory of shells and include the von Karman-type kinematic nonlinearity and extension/twist, extension/flexure, and flexure/twist couplings. The nonlinear prebuckling deformations and the initial geometric imperfections of the panel are both taken into account. The postbuckling behavior of the panel under axial compression is analyzed. A singular perturbation technique is employed to determine its buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect moderately thick anisotropic laminated cylindrical panels with different geometric parameters and stacking sequences. The new finding reveals that there arises a compressive stress along with an associate shear stress and twisting when a moderately thick anisotropic laminated cylindrical panel is subjected to axial compression. [ABSTRACT FROM AUTHOR]

The delamination buckling problem for a rectangular plate made of an orthotropic composite material is studied. The plate contains a band crack whose faces have an initial infinitesimal imperfection. The subsequent development of this imperfection due to an external compressive load acting along the crack is studied through the use of the three-dimensional geometrically nonlinear field equations of elasticity theory for anisotropic bodies. A criterion of initial imperfection is used in determining the critical forces. The corresponding boundary-value problems are solved by employing the boundary-form perturbation technique and the FEM. Numerical results for the critical force are presented. [ABSTRACT FROM AUTHOR]

The buckling of imperfect composite cylinders under concentric and eccentric compression is investigated experimentally and numerically, with particular attention given to the imperfection sensitivity of the shells. A series of glass-fiber-reinforced plastic cylinders have been tested under different load eccentricities to validate the corresponding nonlinear numerical analyses performed in this study. A good agreement between the experimental and numerical results was achieved through use of the ABAQUS/Explicit finite-element code and the introduction of initial imperfections. Both the experimental and the numerical results show that the knockdown factor increases as the loading eccentricity grows. [ABSTRACT FROM AUTHOR]

The postimpact buck ling loads of E-glass/epoxy laminates have been measured. Composite samples with the stacking sequence [+45/−45/90/0]2s were subjected to low-speed impact loadings at various energy levels. The tests were conducted on a specially developed vertical drop-weight testing machine. The main impact parameters, such as the peak load, absorbed energy, deflection at the peak load, and damage area, were evaluated and com pared. The damaged specimens were subjected to compressive axial forces, and their buckling loads were determined. The relation between the level of impact energy and buck ling loads is investigated. [ABSTRACT FROM AUTHOR]

Two new hyperbolic displacement models, HPSDT1 and HPSDT2, are used for the buckling and free vibration analyses of simply supported orthotropic laminated composite plates. The models contain hyperbolic expressions to account for the parabolic distributions of transverse shear stresses and to satisfy the zero shear-stress conditions at the top and bottom surfaces of the plates. The equation of motion for thick laminated rectangular plates subjected to in-plane loads is deduced through the use of Hamilton’s principle. Closed-form solutions are obtained by using the Navier technique, and then the buckling loads and the fundamental frequencies are found by solving eigenvalue problems. The accuracy of the models presented is demonstrated by comparing the results obtained with solutions of other higher-order models given in the literature. It is found that the theories proposed can predict the fundamental frequencies and buckling loads of cross-ply laminated composite plates rather accurately. [ABSTRACT FROM AUTHOR]

The loss of the load-carrying capacity of a nonlinearly elastic multilayer rod is investigated. The rod, whose layers have various thickness and are made of different materials, is rigidly fixed at both its ends. Rigid contact conditions between the layers are assumed. The problem posed is solved by using the variational method of mixed type in combination with the Rayleigh-Ritz method. The initial analysis is reduced to the solution of the Cauchy problem for a nonlinear ordinary differential equation solved for the first derivative. As the initial condition, the maximum initial eccentricity of the rod is assumed. In the case of zero eccentricity, the Shanley critical force for an axially compressed rod is determined. For a three-layer rod whose outer layers have equal thickness and are made of the same material, numerically, for various degrees of nonlinearity, the effect of physicomechanical and geometric parameters on the critical load of buckling instability is determined. It is found that, by matching the heterogeneity of the rod, it is possible to raise its load-carrying capacity. [ABSTRACT FROM AUTHOR]

The stability of elastic columns subjected to axial pressure is studied. An elastic multistepped column with rectangular cross sections are considered assuming that at the re-entrant corners of the column stable cracks are located. The influence of a crack on the loss of stability of the column is described by means of local flexibility and the function of compliance coupled with the stress intensity factor, which is known from the linear elastic fracture mechanics. A column with a single step is studied in more detail. The influence of crack location and length on the buckling load is assessed numerically. [ABSTRACT FROM AUTHOR]

A method is presented for determining the flexural strength of composites from tests on pinned specimens in axial compression. This scheme is close to the so-called Euler buckling model, but the load is applied eccentrically, and the bar is bent practically from the beginning of loading. An analytical model is proposed for calculating the flexural stress in longitudinal flexure of a thin bar in the case of large displacements. The problem is solved in elliptic integrals of the first and second kinds. The analytical model shows an excellent agreement with experiments. The results obtained are compared with experimental tension data. A device is also designed for testing composite bars in longitudinal flexure. The method offered has an obvious advantage over the conventional three- or four-point bending — the gage zone in this scheme is far away from the loading zone of the test specimen. [ABSTRACT FROM AUTHOR]