Static buckling appraisal of an echinodome

The buckling behavior of an underwater shell of revolution structure of optimum form—an echinodome—is examined under axisymmetric and symmetric point loads both experimentally and theoretically. For the concentrated loadings, experimental predictions of critical buckling are based on the Southwell technique and a possible alternative method is suggested. Bifurcation and nonlinear collapse buckling analyses are described theoretically. Within the bifurcation investigation both linear and nonlinear approaches are included. The effects of base fixity on the instability of the structure are considered. Comparisons are made with earlier external-pressure loading effects and the relative significance of the two forms of loading are discussed.     

Two instructive instabilities in non-linear elasticity: Biaxially loaded membrane,and rubber balloons

Elastic bodies buckle under compressive loads, i.e. solutions become non-unique, they bifurcate and the body becomes unstable. Similar phenomena occur in tension as is evidenced here by the symmetric biaxial loading of a square membrane. Symmetry breaking removes the non-uniqueness. Under non-symmetric loading the load-deformation curves become non-monotone, consequently a hysteresis occurs which is the reflection of a fold-type catastrophy. This instructive instability was discovered by Kearsley [1]. Here we investigate it more fully and present some additional aspects.Balloons have non-monotone pressure-radius relations which suggest non-trivial stability properties. A stability analysis is presented for two interconnected balloons. In this we follow — and expand on — the analyses presented by Dreyer et al. [2] and Kitsche et al. [3].General Invited Lecture presented at AIMETA '95 — 12th Congress of the Italian Association of Theoretical and Applied Mechanics, Napoli, 3–6 October, 1995.     

The equilibrium field near the tip of a crack for finite plane strain of incompressible elastic materials

This investigation is concerned with the deformations and stresses in a slab of all-around infinite extent containing a traction-free plane crack, under conditions of plane strain. The analysis is carried out within the framework of the fully nonlinear equilibrium theory of homogeneous and isotropic incompressible elastic solids. For a fairly wide class of such materials and general loading conditions at infinity, assymptotic estimates appropriate to the various field quantities near the crack-tips are deduced. For a subclass of the materials considered, these results — in contrast to the analogous predictions of the linearized theory — lead to the conclusion that the crack opens up in the neighborhood of its tips even if the applied loading is antisymmetric about the plane of the crack, (e.g., Mode II loading). It is shown further that the non-linear global crack problem corresponding to such a loading in general cannot admit an antisymmetric solution.The results communicated in this paper were obtained in the course of an investigation supported in part by Contract N00014-75-C-0196 with the Office of Naval Research in Washington, D.C.     

Dependence of the Critical Load on the Geometric Characteristics of a Hinged Plate with a Crack

The plane problem of three-dimensional stability of a hinged plate with a central crack under uniaxial loading along the crack is considered. The net approach is used to solve the problem. The variational difference and gradient methods are used, respectively, to construct a difference scheme and to solve difference problems. The dependence of the critical load on two parameters — the crack length and the thickness ratio — is derived. Formulas for calculation of the critical load are given     

Stability Problems for Plates with Short-Term Damageability

The problem on stability of plates with microdamages simulated by hollow randomly dispersed micropores is considered. Two approaches are proposed to investigate the stability of plates weakened by microdamages. These approaches are based on models well known from the theory of stability of elastoplastic bodies — the concepts of tangent-modulus loading and continuous loading     

Microslip and macroslip in bolted joints

The dynamic forces which occur in structures whose jointed parts may slide during dynamic loading are associated with energy dissipation. The high-strength friction grip bolted joint (HSFGBJ) is a structural element which under certain circumstances may dissipate a large amount of vibrational energy. This energy is an increasing function of the frictional force and of the magnitude of slip of the joint. However, in a joint with a relatively large number of bolts, the amount of slip cannot be large, as the bolt holes are not much larger than the bolt diameter. Thus, some bolts of the joint may be sheared at the beginning of the full-slip stage of loading. In this paper, mathematical equations for the frictional force and slip in both stages of loading—partial slip and full slip—are established, and the dissipation of energy is evaluated. It is shown that if the joint is designed so that the magnitude of slip is at the border partial slip/full slip, the joint may dissipate a large amount of vibrational energy.     

Wave propagation in inhomogeneous elastic media; normal loading of spherical and cylindrical surfaces

The propagation of waves in inhomogeneous elastic media with spherical or cylindrical symmetry, when the curved surface of the solid is given a uniform normal loading — the stress and displacement components within the solid then may be assumed to depend on one space coordinate and time alone —, is considered. The particular case in which the elastic parameters are proportional to (radius) ⁿ is considered as a special case.Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No.: DA-31-124-ARO-D-462.     

Nonlinear Antiplane Deformation of an Elastic Body

The antiplane elastic deformation of a homogeneous isotropic prestretched cylindrical body is studied in a nonlinear formulation in actual–state variables under incompressibility conditions, the absence of volume forces, and under constant lateral loading along the generatrix. The boundary–value problem of axial displacement is obtained in Cartesian and complex variables and sufficient ellipticity conditions for this problem are indicated in terms of the elastic potential. The similarity to a plane vortex–free gas flow is established. The problem is solved for Mooney and Rivlin—Sonders materials simulating strong elastic deformations of rubber–like materials. Axisymmetric solutions are considered.     

A simple model of the mechanical behavior of ceramic-like materials

This paper presents a macroscopic mechanical theory for ceramic-like materials undergoing isothermal deformations. The proposed model describes an elastic brittle material which is damageable only under tensile loading. The damage lowers the elastic stiffness in traction simulating hence the softening and the fracture (zero stillness) of the material. The basic idea is to consider the continuum as a mixture of two phases—a linear elastic phase and a masonry phase (which shows a linear elastic behavior under compression but cannot hold tractive loads at all). The damage is then related to the volume fraction β of the clastic constituent. The constitutive relations are derived from macroscopic thermodynamics with the volume fraction β and its gradient β taken as state variables.     

Investigation of the Effect of Axial Loads on the Transverse Vibrations of a Vertical Cantilever with Variable Parameters

The method of influence function is applied to the solution of the boundary-value problem on the free transverse vibrations of a vertical cantilever and a bar subjected to axial loads. To demonstrate the capabilities of the method, a cantilever with the free end under two types of loading — point forces (conservative and follower) and a load distributed along the length (dead load) — is analyzed. A characteristic equation in the general form, which does not depend on the cantilever shape and on the type of axial load, is given. The Cauchy influence function depends on the cantilever shape and the type of axial load. As an example, a tapered cantilever subjected to conservative and follower forces and an elastically supported bar under the dead load are considered in detail. The characteristic equation derived allows one to evaluate the natural frequencies and the Euler critical loads. It is shown that the calculated natural frequencies and critical forces are in a good agreement with the exact values when several terms are retained in the characteristic series. The high accuracy of the method is also confirmed     

On the buckling of a girder, elastically supported and elastically clamped in a number of equidistant points

Summary Lately the authors have been engaged in an inquiry with respect to the safety of scaffolding constructions, as used in the erection and the repair of large buildings. A question of detail was presented by the determination of the buckling load of a prismatic girder, elastically supported and elastically clampled in a number of equidistant points. The present paper gives an answer to this problem with the understanding that the endpoints of the girder — though elastically clamped — are fixedly supported.     

Problems and trends in mathematical modeling

Main problems and trends in mathematical modeling — a new line of research into various processes and phenomena — are formulated. The status and future prospects are analyzed using as an example the mechanics of continuous media. Emphasis is on two stages of modeling — the selection of physicomathematical models of the mechanics of continuous media and numerical algorithms of solution.     

Hybrid Electromagnetic System for Acceleration of Solids

The electroexplosive and electrothermal mechanisms and the principles of conduction and induction electrodynamics are used simultaneously to convert electromagnetic energy to the kinetic energy of projectiles. This approach is implemented on the basis of the well–known configuration of a coaxial pinch accelerator. It is established that there is an active lengths of the barrel on which the system ensures launching with nearly constant acceleration. For a barrel length of 340 mm and a barrel diameter of 17 mm, bodies with a mass of 1—12 g are accelerated to velocities of 3.4—1.45 km/sec with an energy conversion efficiency of 25—29% at a capacitive storage voltage of 1.75 kV and a discharge current of up to 150 kA. Bodies with a mass of 40—80 g (barrel diameter 25 mm are accelerated to velocities of 1.3—1.0 km/sec with an efficiency of 28—20% at a voltage of 3.5 kV and a current of up to 220 kA.     

Experimental snap-through boundaries for acoustically excited,thermally buckled plates

This paper presents some recent experimental results on the dynamic snap-through behavior of a clamped, rectangular plate subject to thermal loading and intense acoustic excitation. The likelihood of snap-through oscillations is characterized in terms of boundaries separating regions of snap-through and no snap-through in the parameter space. Two scenarios are considered. First, using tonal inputs, the regions of snap-through are mapped in the sound pressure level—input frequency domain ((SPL, ) plane). Second, random acoustic inputs are used, and the effect of varying the overall sound pressure level and frequency bandwidth are investigated ((SPL, ) plane). Several nonlinear characteristics are evident and discussed.     

Nonaxisymmetric Thermoviscoelastoplastic Deformation of Shells of Revolution

An analysis is made of the basic results obtained at the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine in developing a theory and methods for thermoviscoelastic stress—strain analysis of flexible laminated shells of revolution with a thickness variable in two directions under nonaxisymmetric nonisothermal deformation along rectilinear and slightly curved paths, with the loading history taken into account     

Motion of soil-working tool under impact loading

The cyclic process of penetration of soil by a tool under periodic impact loading was described mathematically. The analysis was based on a piecewise-linear approximation of the dependence of the soil frontal resistance force on tool displacement—an approximation reflecting modern views on the principles of soil-tool interaction.Different intervals in the cycle of steady-state motion of the tool, and different interaction regimes were considered. The mean tool velocity for borehole forming was determined. Conditions for a minimum energy requirement in the cyclic process were formulated, and the influence of frequency on the laws governing the interaction was established.     

Yield behavior of wood under combined static axial force and torque

We have examined the yield behavior of wood (Japanese cypress and Japanese beech) under combined static axial force and torque. In order to take the anisotropy of the wood into consideration, the specimen had a rectangular cross-section with one of its major axis lying in the fiber (longitudinal) direction. The axial force was applied in the fiber direction (along L) and torque was applied on an axis lying in the same direction as L. A combined loading test was performed according to the proportional deformation loading method. The results obtained are summarized as follows. (1) The yield condition of wood under combined axial-shear stress can be expressed by several well-known yield criteria. (2) The determinations of yield points are more influenced by torsion than axial force. (3) Japanese cypress deforms elastically compared with Japanese beech. (4) It is suggested that the equivalent stress-equivalent strain relation could be used at the determination of the yield point.     

A maximum principle for the analysis of elastic-plastic systems

Summary We consider an elastic-plastic body subjected to a specific programme of static loading. In the analysis of the behaviour of the body in the course of the individual steps of the loading programme some difficulties arise if the variational principles of the theory of plasticity are applied. We then propose a maximum principle which appears suitable for the formulation of simple and direct computing procedures. For an elastic-perfectly plastic material the function to be maximized represents the differential energy dissipated in the single infinitesimal step starting from the elastic solution. In that function the variables are the plastic distortions. Since the energy dispersed by the effect of these latter must at every point be positive or zero, the maximum in question is a field maximum and therefore the property is not variational.The principle is demonstrated both for elastic-perfectly plastic materials and for elastic—work-hardening materials. Materials with regular yield surfaces are at first considered; the demonstration is then extended to the case of singular yield surfaces.First published in Rendiconti dell'Istituto Lombardo, Classe di Scienze, A 99, 125–140, 1965.     

On loading,yield and quasi-yield hypersurfaces in plasticity theory

In the context of the author's previously published “simple” theory of plasticity[1] in which no loading or yield surfaces are assumed to exist, it is shown that (a) loading surfaces must exist for a plastic material as a result of Caratheodory's theorem on Pfaffian forms, and that (b) a yield hypersurface in state space may be defined as the boundary of the region in which no loading surfaces exist (the elastic region) if this region has a positive volume, otherwise this region degenerates into the quasi-yield hypersurface. The significance of loading and yield (or quasi-yield) hypersurfaces is further explored for one-component loadings, with particular attention to the Bauschinger effect and kinematic hardening.     

穿斗式木框架受力性能研究

为研究西南地区穿斗式木结构的承载能力和变形特征,设计了单榀足尺穿斗式木框架进行水平静力单调加载试验,获得了木框架水平荷载-位移曲线关系以及木框架的整体破坏形态等,并采用ABAQUS 软件对木框架进行数值分析．研究表明木框架破坏形式表现为框架整体的严重倾斜,柱与枋本身较为完好;木框架柱顶侧移随着加载位移的增加呈线性增长关系,对称的左右立柱和瓜柱柱顶侧移基本一致;不同节点榫头同步拔出,拔榫量峰值相差较小,表现出较好的协调性;暗销节点的变形主要表现为榫头的挤压凹陷,榫头横纹方向较早地进入塑性变形阶段．卯口受压变形较小,处于弹性变形阶段．