Buckling stresses of composite tubes under biaxial compressive loads

An analytical model describing the instability of specially orthotropic composite tubes with geometric imperfections subject to biaxial compressive loads and under clamped-clamped boundary conditions is developed. Furthermore, the range of validity of the present solution is clarified, and comparisons are made to some studies on isotropic cylindrical shells. Six E-glass woven fabric-epoxy composite tubes with the same internal radius and different thicknesses and longitudinal lengths were fabricated and subjected to various combinations of external hydrostatic pressure and axial compressive load simultaneously. The normalized buckling stresses were found to agree in general with the theoretical predictions at various biaxial loadings. The buckling envelopes in normalization form provide useful design data on the strength of specially orthotropic composite tubes under a realistic range of biaxial loading conditions.     

The elastic sphere under arbitrary concentrated surface loads

The elastostatic problem of a sphere subject to a concentrated surface load of arbitrary direction which is equilibrated in a very simple manner by a distribution of surface tractions is solved. Particular attention is placed in the analysis of the singularity at the point of application of the concentrated load.The solution obtained provides a means for reducing problems pertaining to a sphere under arbitrary concentrated and distributed loads to a regular second boundary-value problem for the sphere. For illustration the problem of a sphere acted by two equal, opposite and collinear loads applied at two arbitrary surface points is treated.The paper also contains an exposition and an essential extension of an integration scheme developed by Almansi. Thus, an explicit integral representation of the displacements in an elastic sphere in terms of a vector valued harmonic potential which coincides on the surface with the tractions is obtained.

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Résumé On présente la résolution du problème élastostatique d'une sphère soumise en surface à une charge ponctuelle de direction arbitraire équilibrée par une distribution trés simple de contraintes superficielles. On s'attache plus spécialement à l'analyse de la singularité au point d'application de la charge ponctuelle.La solution obtenue permet de réduire les problèmes d'une sphère soumise de manière quelconque à des charges ponctuelles et réparties, à un problème avec conditions aux limites régulières. A titre d'exemple, on traite le problème d'une sphère soumise à deux forces ponctuelles, co linéaires, égales et de sens opposé, appliquées en deux points arbitraires de la surface.L'article contient également une exposition et une extension d'un schéma d'intégration développé par Almansi. On obtient ainsi une représentation explicite, sous forme d'intégrale, des déplacements dans une sphère élastique, en termes de potentiel vecteur qui coïncide, à la surface, avec le champ de contraintes.

     

On the stability of Kelvin cell foams under compressive loads

It has been previously shown that the nonlinearity exhibited in the compressive response of open cell foams is governed by cell ligament buckling. Significant insight into this behavior can be gained by idealizing such foams as periodic, space-filling Kelvin cells assigned several of the geometric characteristics of actual foams. The cells are elongated in the rise direction; the ligaments are assumed to be straight, to have Plateau border cross sections, and nonuniform cross sectional area distribution. The mechanical response of such foams can be established using models of a characteristic cell assigned appropriate periodicity conditions. The ligaments are modeled as shear deformable beams. The periodicity of this microstructure allows the use of Bloch wave theory to conduct the search for the critical state efficiently. The method tailored to the present microstructure is outlined. It is subsequently used to establish the critical states for uniaxial and a set of triaxial loadings. A rich variety of buckling modes are identified which are affected by the anisotropy and the mutliaxiality of the applied loads. Under some loadings the critical modes have long wavelengths which are shown to lead to unstable postbuckling behavior involving localization. Under other loading conditions the modes are either local to the characteristic cell or involve an assemblage of a few such cells. For the cases analyzed local modes were found to have a stable postbuckling response.     

Effects of lateral loads and constraints on buckling of cracked thin plates under compressive edge loads

Critical buckling load is important in investigation of behaviors of thin plates or shells. The presence of cracks in these structures can affects their safety factor with respect to the common modes of failure such as buckling. Some analytical solutions were obtained for un-cracked plates with different boundary conditions. Their numerical results have good agreement with these solutions. In this paper, we also studied the effects of lateral loads and constraints on the critical buckling load of cracked plates under axial compression, experimentally and numerically. Effects of length and orientation of cracks are investigated in presence of the lateral loads. Finally, tests data are compared with the results of numerical calculations.     

Unilateral contact buckling of lightly profiled skin sheets under compressive or shearing loads

Thin, profiled steel sheets forming the skin of concrete-filled composite wall panels and similar members benefit from the unilateral (tensionless) restraint provided by fill of sufficient elastic modulus. This paper investigates the buckling of such skin sheets in panels subjected to compressive or shearing loads. The profiled skins are modelled as infinite, thin orthotropic plates resting on tensionless rigid foundations, allowing the local buckling response to be simulated by the single-wave buckling mode of an unrestrained plate section of appropriate aspect ratio. Solution of the governing differential equations leads to the determination of the plate buckling coefficients. Simplified formulas for the buckling coefficients in terms of the parameters describing the skin sheets are developed and shown to agree well with published results and finite element analyses for particular limiting cases.     

The suspended elastic cable under the action of concentrated vertical loads

This investigation treats the static response of a single elastic cable which is suspended between two points that are not necessarily at the same level. The cable is loaded by its self-weight and any number of concentrated vertical loads which may be arbitrarily placed along its length. The analysis presented uses a Lagrangian approach. For the strained cable profile, the tension and displacements are given as functions of a single Lagrangian co-ordinate. A specific application of the general analysis is made and compared with a simple experiment.     

Nonlinear deformation and buckling of elastic inhomogeneous shells under thermomechanical loads

The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling, and postbuckling behavior of thin thermoelastic inhomogeneous shells with complex-shaped midsurface, geometrical features throughout the thickness, or multilayer structure under complex thermomechanical loading. The method is based on the geometrically nonlinear equations of three-dimensional thermoelasticity and the moment finite-element scheme. The method is justified numerically. Results of practical importance are obtained in analyzing poorely studied classes of inhomogeneous shells. These results provide an insight into the nonlinear deformation and buckling of shells under various combinations of thermomechanical loads     

Interactive buckling of an inflated envelope under mechanical and thermal loads

This paper elucidates the interactive buckling behaviors of an inflated envelope under coupled mechani-cal and thermal loads, especially the longitudinal wrinkling bifurcation and hoop ovalization buckling. The longitudi-nal bending buckling process of the inflated envelope can be divided into three continuous stages, which are global buckling, interactive global-local buckling, and kink. A vari-ety of hoop ovalization buckling modes are observed under coupled mechanical-thermal load. Unlike the mechanical case, thermal load leads to a hoop negative ovalization buck-ling. In addition, it can accelerate the longitudinal coupled bifurcation and resist the hoop coupled ovalization buckling. Moreover, the bending resistance of the inflated envelope will be improved when the length of the structure is increased, resulting in the difficulty of it to become wrinkled. These results provide a new insight into the buckling behaviors of an inflated envelope under coupled external loads, and give a reference for the design of the inflated envelope.     

Upper and lower bounds for constitutive relation of crack-weakened rock masses under dynamic compressive loads

A micro-mechanics-based model is proposed to investigate the rate-dependent constitutive relation for crack-weakened rock masses subjected to dynamic compressive loads. The present micro-mechanical model reveals that the nucleation, growth and coalescence of sliding cracks dominate the failure and macroscopic properties of crack-weakened rock masses subjected to dynamic compressive loads. The interactions among multiple parallel sliding cracks in crack-weakened rock masses subjected to dynamic compressive loads are examined asymptotically in an explicit and quantitative manner in order to reveal fully their so-called shielding and magnification effects on the stress–strain relation. Based on the micro-mechanical framework and the asymptotic analysis, analytical upper and lower bounds are proposed for the rate-relation for rock masses containing multiple rows of echelon cracks subjected to dynamic compressive loads. The factors that affect the rate-dependent properties of crack-weakened rock masses have been analyzed. The strain energy density factor approach, which is related to crack growth velocity and dynamic fracture toughness of rock material, is employed in the analysis. The rate-dependent constitutive relation of crack-weakened rock masses is derived from micro-mechanical framework and the asymptotic analysis. The closed-form explicit expression for the rate-dependent constitutive relation of rock masses containing echelon cracks subjected to dynamic compressive loads is obtained. Finally, the present model is used to analyze the complete stress–strain relation and strength for jointed rock masses at shiplock slope of the Three Gorges Dam.     

Analysis of sloping elastic pile under arbitrary loads by line-loaded integral equation method

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Dynamics of an elastic half-space with a reinforced cylindrical cavity under moving loads

Partial separation of variables and reexpansion of cylindrical and plane waves are used to find the solution describing the uniform motion of a load along a thin circular cylindrical shell in an elastic half-space with the free surface parallel to the axis of the shell. This is a model problem for studying the dynamics of tunnels and shallow-buried pipelines under transport loads. Dispersion curves for the cases of sliding and tight contact between the shell and the half-space are plotted and analyzed. The effect of the shell parameters on the stress–strain state of the half-space is examined     

Nonlinear vibrations and stability of elastic and viscoelastic systems under random stationary loads

The paper deals with numerical analysis of nonlinear vibrations of viscoelastic systems under a stochastic action in the form of a Gaussian stationary process with rational spectral density. The analysis is based on numerical simulation of the original stationary process, numerical solution of the differential equations describing the motion of the system, and computation of the maximum Lyapunov exponent if the stability of this motion is studied. An example of a plate subjected to a random stationary load applied in its plane is used to consider specific issues concerning the application of the proposed method and the peculiarities of the behavior of geometrically nonlinear elastic and viscoelastic stochastic systems. Special attention is paid to the interaction of a deterministic periodic action and a stochastic action from the viewpoint of stability of the system motion. It is shown that in some cases imposing a “colored” noise may stabilize an unstable system subjected to a periodic load.     

A crack in a piezoelectric layer bonded to a dissimilar elastic layer under transient load

Summary  A piezoelectric layer bonded to the surface of an elastic structure is considered. The piezoelectric and the elastic layers are infinite along the x-axis and have finite thickness in the y-direction. The polarization direction of the piezoelectric material is along the y-axis. By means of the method of singular integral equations, the solution in a Laplace transform plane is demonstrated. Laplace inversion yields the results in the time domain. Numerical values of the crack tip fields under in-plane transient electromechanical loading are obtained. The influence of layers thickness on stress and electric displacement intensity factors is investigated. Received 16 March 2000; accepted for publication 16 August 2000     

Dynamic characteristics of multi-span spinning beams with elastic constraints under an axial compressive force

A theoretical model for the multi-span spinning beams with elastic constraints under an axial compressive force is proposed. The displacement and bending angle functions are represented through an improved Fourier series, which ensures the continuity of the derivative at the boundary and enhances the convergence. The exact characteristic equations of the multi-span spinning beams with elastic constraints under an axial compressive force are derived by the Lagrange equation. The efficiency and ac...