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Presented herein is a matrix method for buckling analysis of general frames based on the Hencky bar-chain model comprising of rigid segments connected by hinges with elastic rotational springs. Unlike the conventional matrix method of structural analysis based on the Euler–Bernoulli beam theory, the Hencky bar-chain model (HBM) matrix method allows one to readily handle the localized changes in end restraint conditions or localized structural changes (such as local damage or local stiffening) by simply tweaking the spring stiffnesses. The developed HBM matrix method was applied to solve some illustrative example problems to demonstrate its versatility in solving the buckling problem of beams and frames with various boundary conditions and local changes. It is hoped that this easy-to-code HBM matrix method will be useful to engineers in solving frame buckling problems. [ABSTRACT FROM AUTHOR]

The objective of this study is to develop and validate similitude requirements and scaling laws for studying the real characteristics of structures easily and economically, especially for large structures. The generalized similitude requirements and the scaling law of orthogonally stiffened cylindrical panels and shells for buckling and free vibration are derived by applying the similitude transformation to the total energy of the structural system directly. In practice, due to either the difficulty of satisfying all of the similitude requirements simultaneously or to save experimental cost and time, distorted models with partial similarity are necessarily employed and approximate scaling laws are proposed. The partial similitude is mainly investigated first by using specific formulas of stiffness parameters and corresponding scaling laws are given. Also discussed herein are particular models with relaxations in the material properties of stiffeners, the materials of both the skin and the stiffeners and the material properties and geometry. The obtained results indicate that the distorted models are able to accurately predict the behavior of the prototype. [ABSTRACT FROM AUTHOR]

This paper is concerned with the surface effect on the buckling behavior of double nanobeam system using the nonlocal Timoshenko beam theory. The size effect is taken into consideration by using the Eringen's nonlocal elasticity theory and the exact solution for buckling loads for simply supported boundary condition is presented. Influences of various parameters such as stiffness constant, nonlocal parameter, shear effect and buckling mode number are investigated. Also for the sake of validation, the present results are compared with those obtained from the Euler-Bernoulli model. It is shown that the proposed nonlocal model is able to produce results with high accuracy and it can be used as a benchmark in future studies on buckling of nano-sandwich structures. [ABSTRACT FROM AUTHOR]

In this paper, a discrete model of the planar Cosserat rod is presented. Based on the calculus of variations, the equilibrium equations of the model are derived for potential forces and hyperelastic material. Buckling of the structure under axial loading is thoroughly studied assuming linear elasticity. Dimensionless stiffness parameters are introduced, and analytical solutions are given for the critical loads and the corresponding buckled shapes of the model. Classification of the axially loaded structure is accomplished based on the number, sign, and physical admissibility of its buckling loads. It is revealed that the model can possess several buckling modes under tension. [ABSTRACT FROM AUTHOR]

This paper presents the Hencky bar-chain model (HBM) for buckling and vibration analyses of Euler-Bernoulli beams with elastic end restraints. The Hencky bar-chain comprises rigid beam segments (of length a = L/n where L is the total length of beam and n the number of beam segments) connected by frictionless hinges with elastic rotational springs of stiffness EI/a where EI is the flexural rigidity of the beam. The elasticity and the mass of the beam are concentrated at the hinges with rotational springs. The key contribution of this paper lies in the modeling of the elastic end restraints of the Hencky bar-chain that will simulate the same buckling and vibration results as that furnished by the first-order central finite difference beam model (FDM) which was earlier shown to be analogous to the HBM. The establishment of such a physical discrete beam model allows one to obtain solutions for beam-like structure with repetitive cells (or elements) as well as to calibrate the Eringen's coefficient e0 in the nonlocal beam theory that captures the small length scale effect. [ABSTRACT FROM AUTHOR]

Cracks in structural members lead to local changes in their stiffness and consequently their static, dynamic and stability behavior is altered. The influence of cracks on dynamic characteristics like free vibration, buckling and parametric resonance characteristics of a cracked beam with a transverse crack using finite element method (FEM) is investigated in the present work. Modal testing of beams with transverse open crack is conducted using FFT analyzer to verify the frequencies of vibration of beams. The crack is assumed to be open type and the analysis is linear based on small deformation theory neglecting damping. The loading on the beam is considered as axial with a simple harmonic fluctuation with respect to time. A two-noded Timoshenko beam element with provision of crack is used in this study. The equation of motion represents a system of second-order differential equations with periodic coefficients of the Mathieu-Hill type. The development of the regions of instability arises from Floquet's theory and the periodic solution is obtained by Bolotin's approach using FEM. It is observed that the frequencies of vibration and buckling load of the beam are influenced significantly by location and depth of cracks. It is observed that, for a given location of crack, the onset of instability occurs earlier with increase in depth of crack. As the location of crack moves from the fixed end to the free end the excitation frequency increases. The instability occurs later and the width of the instability regions reduces. When the damage is near to the free end, the instability region almost coincides with the instability region for the undamaged beam. This means that the damage near the fixed end is more severe on the dynamic instability behavior than that of the crack located at other positions. The vibration and instability results can be used as a technique for structural health monitoring or testing of structural integrity, performance and safety. [ABSTRACT FROM AUTHOR]

This paper focuses on the effect of member geometric imperfection on nonlinear geometrically buckling and seismic performance of a new style of space steel structure, suspen-dome, which is composed of a reticulated shell and cable-strut system. By supposing the initial curvature of members as half-wave sinusoids, a stiffness equation of imperfect truss elements is derived for the struts, while that of imperfect beam elements is derived for the reticulated shell members. The proposed imperfect elements are implanted into ANSYS finite element program. Three numerical examples are employed to validate the proposed imperfect elements and analysis method. An ellipsoidal suspen-dome of Changzhou gymnasium is taken as an example. The results show that the imperfection value has relatively great influence on the structural stiffness. With the increase of member imperfection, the critical load decreases in a basically linear way. Under different prestress states, the relation curves between the critical load and imperfection are basically parallel. The nonlinear seismic analysis results show that when imperfection is included, the initial state responses are different, namely, the seismic displacement increases while the stress in rods and cables decreases. The proposed imperfection analysis method can be widely used in not only suspen-dome structures, but also other kinds of prestressed space grid structures. In this way, the influence of member imperfection on structural buckling and seismic performance can be estimated. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the transverse vibration of a circular plate loaded by uniform pressure along its edge. The plate is supported by an elastic ring support being coaxial with the plate. At its edge the plate is clamped but the radial displacement is allowed. Apart from this problem, the heated plate clamped at its edge, but without the possibility of radial displacement, is also analyzed. The analytical solution of governing equation is obtained in the form of Bessel's functions. Using the analytical solution, the frequencies of transverse vibrations depending on loads, elastic ring stiffness and the location of ring are obtained. The results show that the lowest frequencies vibrations can be either symmetric or asymmetric having one or two nodal diameters. It is also shown that multiple vibration frequencies can occur for special values of load and ring stiffness. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the buckling capacity of a hybrid grid shell, which is made of quadrangular meshes diagonally stiffened by pre-tensioned thin cables. The eigenvalue buckling, geometrical nonlinear elastic buckling and elasto-plastic buckling analyses of the hybrid structure were carried out. Then the influences of the shape and scale of imperfections on the elasto-plastic buckling loads were discussed. Also, the effects of different structural parameters, such as the rise-to-span ratio, cross-section of beams, area and pre-stress of cables and boundary conditions, on the failure load were investigated. The results show that the buckling capacity is reduced when taking into account the material nonlinearity. Furthermore, the hybrid structure is highly imperfection sensitive and the reduction of the failure load due to imperfections can be considerable. The proper shape and scale of the imperfection are also important. It is also shown that there exists an optimal rise-to-span ratio resulting in a relatively high buckling capacity for a specific span. Moreover, the enlarging of the cross-section of steel beams notably improves the stability performance of the structure. However, the area and pre-stress of cables pose small effect on the structural stability. [ABSTRACT FROM AUTHOR]

Based on the nonlocal elastic theory and variational principle, new Timoshenko beam models and analytical solutions for buckling of carbon nanotubes considering nanoscale size effect and shear deformation are established. New equilibrium equations and higher-order boundary conditions are derived and the buckling behavior of carbon nanotubes is numerically investigated. The numerical solutions confirm that nanotube stiffness is enhanced by nanoscale size effect and reduced by shear deformation. It is also concluded that nanotubes with different boundary conditions show varying sensitivity to changes in nanoscale and dimension. Comparison with molecular dynamics simulation results verifies the accuracy and reliability of this new analytical nonlocal Timoshenko beam model. [ABSTRACT FROM AUTHOR]

Modern fiber placement machines allow laminates with spatially varying stiffness properties to be manufactured. In earlier research, the authors optimized variable stiffness plates for maximum buckling load, demonstrating significant improvements in load-carrying capacity. In aerospace applications, panel structures are often permitted to enter the postbuckling regime during service. It is, therefore, not only important to understand their postbuckling behavior, but also to develop fast analysis methods that can subsequently be used in a design optimization framework. The aim of the present research is to study the postbuckling behavior of the optimized plates using a perturbation method that has been developed earlier within a general-purpose finite element environment. The perturbation approach is used to compute postbuckling coefficients, which are used to make a quick estimate of the postbuckling stiffness of the panel and to establish a reduced-order model. In the present work, the postbuckling analysis of variable stiffness plates is carried out using the reduced-order model, and the potential of the approach for incorporation within the optimization process is demonstrated. [ABSTRACT FROM AUTHOR]