Nonlinear inelastic buckling of rigid-jointed frames under finite displacements

Summary A nonlinear analytical approach for establishing the precise load-carrying capacity of imperfection-sensitive frames, made from ideal elastic-plastic material, is presented. The imperfection sensitivity is due to support eccentricities of columns. Stability criteria for both modes of failure, due to elastic and inelastic buckling, are established. The failure through inelastic buckling occurs for frames exhibiting postbuckling strength or monotonically rising equilibrium paths. The inelastic analysis is approximate with a basic assumption that the overall response of the frame can be predicted by considering the elastoplastic stress distribution at only one single (the most unfavorable) cross-section. Plastic buckling is associated with a limit point instability. Simple formulas for evaluating the stress distribution at the critical sections in both the elastic and inelastic range are assessed. The proposed method is demonstrated by means of a simple two-bar frame for which the overall response from the onset of loading up to failure is determined.With 5 Figures     

Nonlinear behavior and buckling of cylindrical shells subjected to localized external pressure

Buckling loads and postbuckling behavior of cylindrical shells subjected to localized external pressure are considered. The modified extended Kantorovich method with path-tracing technique is applied to determine the buckling loads of the cylindrical shells. It is found that the load is dependent nonmonotonically on geometrical parameters of the area subjected to external pressure. Respective postbuckling shapes show correlation with the shapes corresponding to secondary bifurcation paths for the cases of a cylindrical shell under uniform external pressure and a cylindrical shell under uniform axial load.     

Nonlinear dynamic buckling of orthotropic cylindrical shells subjected to rapidly applied loads

Dynamic buckling of an orthotropic cylindrical shell which is subjected to rapidly applied compression is considered. A nonlinear differential equation of Donnell–Karman type is derived with the initial imperfection taken into account. An energy method is used to obtain the equation of motion which is then solved numerically by means of a Runge-Kutta method. These numerical results show that the critical load is increased over the corresponding static case. An analytical solution is also obtained for the problem of hydrostatic pressure.     

Nonlinear buckling analysis of two-dimensional frames composed of curved non-prismatic members

A novel finite element methodology is presented for the analysis of arbitrarily shaped two-dimensional frames composed of curved non-prismatic members. The method utilizes a hybrid-mixed approach in conjunction with an updated Lagrangian formulation. The proposed methodology goes beyond existing modelling capabilities for it enables a more realistic analysis of the nonlinear response of thin-walled frames undergoing large deflections (displacements and/or rotations) in the pre- and postbuckling range. Efficiency, accuracy and reliability of the proposed method are demonstrated on the basis of numerical experiments carried out on several typical examples.     

均匀热载荷作用下功能梯度圆板的非线性振动

基于经典板理论,研究了热载荷作用下功能梯度圆板的大幅振动问题.在经典板理论下利用物理中面概念,导出了功能梯度圆板的非线性运动方程.利用Ritz?Kantorovich方法消去时间变量,将非线性运动方程转换成了一组关于空间变量的非线性常微分方程.采用打靶法数值求解所得方程,并利用数值结果研究了热载荷作用下功能梯度圆板静态...     

Nonlinear dynamic buckling of functionally graded cylindrical shells subjected to time-dependent axial load

This paper is presented to solve the nonlinear dynamic buckling problem of a new type of composite cylindrical shells, made of ceram/metal functionally graded materials. The material properties vary smoothly through the shell thickness according to a power law distribution of the volume fraction of the constituent materials. The dynamic axial load is set in a linear increase form with regard to time. By taking the temperature-dependent material properties into account, the effect of environmental temperature rise is included. The nonlinear dynamic equilibrium equation of the shell was obtained by applying an energy method, and was then solved using the four-order Runge–Kutta method. The critical condition was eventually determined using B-R dynamic buckling criterion. Numerical results show the dynamic buckling load is higher than its static counterpart. Meanwhile, various effects of the inhomogeneous parameter, loading speed, dimension parameter, environmental temperature rise and initial geometrical imperfection on nonlinear dynamic buckling are discussed.     

Analytical study on the buckling of cylindrical shells with stepwise variable thickness subjected to uniform external pressure

This article focuses on the buckling of cylindrical shells with stepwise variable thickness subjected to uniform external pressure. First, combining the method of separation of variables, perturbation method, and Fourier series expansion, an analytical method for the buckling analysis of cylindrical shells with axisymmetric thickness variation subjected to external pressure is established. The method is verified by comparing with the previous results. Then, the stepwise variable thickness of cylindrical shells is described exactly by the arc tangent function. Finally, using the presented method, a general formula for the critical buckling load of cylindrical shells with stepwise variable thickness subjected to uniform external pressure is derived. This general formula is compared and discussed with some empirical formulae in the current design standards. This study lays a theoretical foundation for the calculation of the buckling load of cylindrical shells with stepwise variable thickness subjected to uniform external pressure. Moreover, it provides a reference and guidance for the further revision of related standards.     

集中荷载作用下弹性扭转约束层合浅拱的非线性面内稳定

该文以3D打印材料ABS-M30作为试验载体,开展了拱脚沉降下3D打印拱的非线性失稳研究。基于最小势能原理推导了失稳临界荷载的解析表达式,得到了拱脚竖向和水平变位下拱径向位移沿拱轴线的分布图;设计了可控制拱脚沉降的加载系统,试验得到了拱在加载过程中的平衡路径,并通过有限元模拟对解析与试验结果进行了验证;分析了拱脚沉降量、矢跨比和长细比对3D打印拱失稳临界荷载的影响。研究结果表明：非线性失稳临界荷载随着拱脚沉降量的增大而减小;在拱脚沉降量一定的前提下,非线性失稳荷载随着矢跨比的增大而增大,随着长细比的增大而减小,且长细比的影响最为显著。     

Dielectric behaviour of a ferrofluid subjected to a uniform magnetic field

The electric susceptibility of samples of ferrofluids subjected to a uniform magnetic fieldHwas measured. The electric susceptibilitychiis dependent on the magnitude of the magnetic field and on the relative direction between the electric fieldEand the magnetic fieldH. 1) WhenEis perpendicular toH, frac{partialchi_{perp}}{partialH} < 02) WhenEis parallel toH, frac{partialchi_{parellel}}{partialH} > 0These results have been interpreted as a magneto-electric directive effect. A model is proposed, based on the assumption that the magnetic particles are roughly ellipsoidal and conducting grains.     

Elastica buckling analysis of a simple frame

Summary A nonlinear stability analysis based on an analytical approach of elastic type is performed for the first time on a simple two-bar frame. In order to obtain an exact determination of its buckling and postbuckling behavior the effect of compressibility of the bar centroidal axis is taken into account. This effect implies very slight increase in the buckling load which can be safely ignored. Moreover, it is found that even in the most extreme cases of geometry and stiffness, the critical buckling displacements are of negligibly small magnitude contrary to existing results obtained by the nonlinear kinematic stability analysis. The two foregoing findings enable us to replace the limit point by a bifurcation point. Such a simplification, being correct in an asymptotic sense, allows the application of a stability analysis of frames by considering their bars as incompressible.A variety of numerical results shows the degree of accuracy and the range of applicability of the aforementioned nonlinear kinematic stability analysis by comparing it with the exact method of stability analysis proposed herein.With 2 Figures     

Interface cracks in layered materials subjected to a uniform temperature change

Elastic and incremental elasto-plastic analyses have been used to evaluate the driving force for interface edge-crack growth initiation in tri-layered material systems subjected to a monotonic variation in temperature. Whenever possible, closed-form solutions are derived as functions of the thermo-mechanical material properties and the geometry of the layers. Analytical expressions for the different critical temperatures at which distinct transitions occur in thermally induced deformation are presented and are correlated with the three regimes of interface fracture; elastic, partially plastic and fully plastic. Furthermore, a large-scale contact model, which predicts the shielding effect of contact in the wake of an interface crack, is also presented and the attendant reduction in the energy release rate is estimated. Finite element results, showing the influence of layer geometry and strain hardening on the energy release rate, are presented for a model Al₂O₃/Ni(Cr)/Al₂O₃ tri-layered system; these simulations confirm the bounds predicted by the theory.     

Evolution of deflagration in a cold combustible subjected to a uniform energy flux

The title problem is treated in the limit of large activation energy. It is shown that the evolutionary process takes place in a series of distinct stages, and the spatial and temporal structure of each stage is described. It is found that subsequent to thermal runaway, the behavior of the system resembles that of self-induced combustion, except that the thermal explosion is now confined to a thin surface layer.     

Propagation of waves in magneto-thermo-viscoelastic solids subjected to a uniform magnetic field

The propagation of magneto-thermo-mechanical (MTM) plane waves in electrically and thermally conductive magneto-thermo-viscoelastic (MTVE) unbounded solids is investigated with account for the mutual effects of the magnetic, thermal and strain fields. Concerning the mutual and thermo-electric effects in isotropic solids the governing equations are first linearized. In the linearization, the material is assumed to be subjected to a uniform and primary magnetic field in any direction while the material undergoes infinitesimal deformations. It is shown that the governing equations at the intermediate state are fulfilled by the presumed MTM-fields. Furthermore, the dispersion relation which allows us to consider the entire frequency range, the effect of the magnetic field and some nondimensional material parameters is obtained. Therefore, several modes of MTM-waves arise depending upon the direction of the magnetic field such as the uncoupled magnetic and mechanical S-mwaves, the coupled S-wave, the modified mechanical $\text{P}$-and thermal waves, and the modified and coupled MTM-waves. It is seen that all modes of the wave are dispersive and dissipative due to the conductivity and the viscosity of the material. Then the phase velocities and the attenuation constants for the coupling modes are obtained, and some limiting values are discussed. From the expressions follow, in particular, the results for the elastic case, the propagation of mechanical waves in nonconductive materials.     

Dynamic pulse buckling of composite shells subjected to external blast

Dynamic pulse buckling of woven E-Glass/Vinyl Ester and laminated E-Glass/Epoxy cylindrical shells subjected to uniform overpressure and asymmetric pressure pulse (side-on explosion) were examined. The solutions for the radial shell deformations were represented by Mathieu differential equations. The dynamic instability of the shells was determined from a Mathieu stability diagram. It was found that the stability of the shells depended on lay-up, aspect ratio as well as impulse distribution. The stable vibration response of the shells with side-on explosion compared well with finite element solutions using a Dynamic, Implicit analysis in ABAQUS Standard. First-ply failure of the woven E-Glass/Vinyl Ester shell with side-on explosion was predicted using a modified Hashin–Rotem failure criterion. It was shown that the thinner woven E-Glass/Vinyl Ester shells were more likely to fail by dynamic instability, whereas the thicker woven E-Glass/Vinyl Ester shells were more likely to fail by first-ply failure.     

Nonlinear buckling and postbuckling behavior of cylindrical nanoshells subjected to combined axial and radial compressions incorporating surface stress effects

In the present study, the Gurtin-Murdoch elasticity theory, as a theory capable of capturing size effects, is implemented to predict the nonlinear buckling and postbuckling response of cylindrical nanoshells under combined axial and radial compressive loads in the presence of surface stress effects. For this purpose, a size-dependent shell mode containing geometric nonlinearity is proposed within the framework of the classical shell theory. Because it is necessary to satisfy balance conditions on the surfaces of nanoshell, it is assumed that the normal stress component of the bulk varies linearly through the shell thickness. On the basis of a variational formulation using the principle of virtual work, the non-classical governing differential equations are derived. Subsequently, a boundary layer theory is employed including the nonlinear prebuckling deformations and the large deflections in the postbuckling regime. Then a two-stepped perturbation methodology is utilized to obtain the size-dependent critical buckling loads and the postbuckling equilibrium paths of nanoshells corresponding to the axial dominated and radial dominated loading cases. It is revealed that in the radial dominated loading case, a positive value of surface elastic constants leads to increase the critical buckling load but decrease the critical end-shortening of nanoshell. However, in the axial dominated loading case, surface elastic constants with positive sign causes to increase the both critical buckling load and critical end-shortening of nanoshell.     

Vibration and buckling of beam-columns subjected to non-uniform axial loads

The small-displacement free vibration of elastic Euler-Bernoulli beams subjected to non-uniform axial forces and the buckling of elastic columns are both analysed by means of various types of beam finite elements. The procedure incorporates beams and columns of varying cross-sections, such as linear tapers, inhomogeneous beams and columns, distributed axial forces, elastic end and interior restraints and point masses with linear and rotary inertias. All of these topics individually or in some combinations have been analysed by others. The purpose of this paper is to bring together under a single umbrella the various problems studied by others, and to provide the solution to one problem apparently not yet solved—the buckling and vibration of tapered columns under non-uniform axial thrust. The mass, stiffness and geometric stiffness matrices for the standard beam element are fully written out for direct incorporation into existing finite element programs. A FORTRAN subroutine for generating these matrices, and those for various higher-order beam elements, is also provided.     

Elastic-plastic buckling analysis of rectangular plates subjected to biaxial loads

In order to calculate the buckling load of a rectangular plate, the analytical approach is used in this study. The plate is assumed to be simply supported on four edges and loaded by uniform stresses along the edges. If the plate is slender, the buckling is elastic. However, if the plate is sturdy, it buckles in the plastic range. Then, the instantaneous moduli in the constitutive equations depend on the external loading. In this study, the elastic and plastic buckling equations are derived for rectangular plates under biaxial loading, and the corresponding interaction curves are presented. The influences of aspect ratios, load ratios and hardening factors on the buckling stresses are investigated for rectangular plates. From the plastic buckling analysis, the optimal combination of loads is given for the buckling strength.     

Elastic-plastic buckling analysis of rectangular plates subjected to biaxial loads

In order to calculate the buckling load of a rectangular plate, the analytical approach is used in this study. The plate is assumed to be simply supported on four edges and loaded by uniform stresses along the edges. If the plate is slender, the buckling is elastic. However, if the plate is sturdy, it buckles in the plastic range. Then, the instantaneous moduli in the constitutive equations depend on the external loading. In this study, the elastic and plastic buckling equations are derived for rectangular plates under biaxial loading, and the corresponding interaction curves are presented. The influences of aspect ratios, load ratios and hardening factors on the buckling stresses are investigated for rectangular plates. From the plastic buckling analysis, the optimal combination of loads is given for the buckling strength.     

Nonlinear analysis of portal frames

A kinematically nonlinear analysis of unbraced, rigid-jointed, portal frames, rotationally restrained at the base and subjected to eccentric concentrated and/or uniformly distributed loads, is presented. Through this analysis the complete behaviour, including the primary path and postbuckling path (whenever it exists), is evaluated. Moreover, through parametric studies, the effects of bar slenderness ratio, load eccentricity and amount of rotational restraint are assessed. Through this method it is also possible to assess the effect of member lengths and member lengths and member bending stiffnesses.