Strain distribution within compressed circular cylinders

A theoretical solution has been obtained for the stress distribution throughout a cylindrical specimen loaded in compression, which takes into account different degrees of friction at the end surfaces. To check the solution experimentally, a cylindrical model was constructed from epoxy sheets, with electrical-resistance strain gages embedded between the sheets and also bonded to the cylindrical surface. With the specimen under axial compression, strain measurements were recorded within the elastic range of the epoxy. Reasonable agreement with the theoretical solution was observed for the two types of end conditions. In one case the cylinder was in direct contact with the platens of the testing machine, in the other case a Teflon sheet was placed between the two surfaces.     

提高PIV片光源质量的研究

根据高斯光束的性质,本文设计了一种利用普通连续激光器产生较高质量PIV片光源的光路系统。整个光路分为两部分,第一部分为原始光束优化光路,第二部分为片光分光光路。原始光束优化光路通过一系列凸凹透镜有序布置,将原来直径大于2mm的光斑在PIV实验区间控制到1mm以下。优化光路能有效集中激光能量,提高片光亮度。片光分光光路使用鲍威尔棱镜将激光光束分为扇形片光,再用平凸柱面镜将扇形片光汇聚为矩形片光。鲍威尔棱镜分得片光的能量在宽度方向分布较常规双凹柱面镜均匀。平凸柱面镜将扇形光源中分散在极宽区域的能量集中在固定宽度里,使得激光能量的有效利用率提高,有利于PIV实验。     

Shaping a thin-walled cylindrical shell on a three-roll bending machine

We use the Bernoulli-Euler kinematic hypothesis to model the steady-state process of shaping a thin-walled cylindrical shell by bending an elastoplastic strengthening parent sheet on a three-roll bending machine. We determine the curvilinear shape of the moving parent sheet in the bending area and the displacement of the central roll axis needed to obtain the prescribed curvature of the cylindrical shell when leaving the bending area. One- and multitransition shell shaping processes are considered. The computational model is in satisfactory agreement with experiments.     

Study of nonlinear deformation and stability of reinforced shells under combined loading by a bending moment and a transverse boundary force

We present a finite-element statement for the solution of stability problems for reinforced elliptic cylindrical shells with moment properties and nonlinearity in their precritical stressstrain state taken into account. Integrating the equations obtained by equating the linear strain components with zero, we find explicit expressions for the displacements of elements of noncircular cylindrical shells as rigid bodies. Using these expressions, we construct the shape functions of a fourangle finite element of natural curvature and develop an effective algorithm for studying nonlinear deformation and stability of shells. We study the stability of reinforced elliptic cylindrical shells under combined loading by a transverse boundary force and a bending moment and investigate how the ellipticity of the shells and the nonlinearity of deformation at the precritical stage affect the shell stability.     

Puncturing a thin elastic sheet

We use membrane theory to analyze the puncturing of a thin solid circular isotropic elastic sheet by a rigid axisymmetric indenter. A solution is obtained in which a hole is formed at the center of the sheet with an interior annulus in frictionless contact with the cylindrical surface. The contacting part is in a state of pure hoop stress with the corresponding hoop stretch exhibiting a strong singularity at the origin. Conditions are given ensuring that the solution has finite total energy and it is shown to be energetically favored over unpunctured states for transverse indenter displacements exceeding a finite critical value.     

Study of a drawing-quality sheet steel. I: Stress/strain behaviors and Lankford coefficients by experiments and micromechanical simulations

The sheet-metal industry uses Lankford coefficients and the forming-limit curve, FLC, as standards for characterizing a sheet’s ability to be stretched and deep drawn. Investigators have recently made significant advances in computer codes that predict these measures of formability. However, complete experimental data sets that provide input properties and verification data for the simulations rarely exist for a single material. The current investigation focused on obtaining such data for a single drawing-quality steel sheet. Measurements intended for the calibration and initial verification of the simulation code include uniaxial-tension tests, through-thickness and plane-strain compression experiments, and quantitative texture – orientation distribution function – evaluations, while a comparison between measured and simulated Lankford coefficients, Part I, and an FLC, Part II, provide a rigorous verification of the computer simulations. In order to initially verify the simulations, we performed through-thickness and plane-strain compression measurements. A key experimental result was that the flow curve in free, through-thickness compression – an experiment that corresponds to biaxial stretching – lies 18% above the uniaxial tensile data. The plane-strain compression curve is another 11% above the free-compression stress/strain data. We measured the Lankford coefficients, as a function of angle to the rolling direction, for the same steel sheet, finding the maximum values in and at 90° to the rolling direction, 1.59 and 1.89 respectively. A minimum Lankford coefficient of 1.19 was measured at 45° to the rolling direction. For calibrating a rate-dependent visco-plastic self-consistent polycrystal model we needed only to measure the material’s initial texture and to fit power-law and saturation-hardening laws to our tensile data. This kept the set of adjustable parameters to a minimum. Without other adjustments to the model, we predicted the correct stress levels in the free and channel-die compression experiments as well as values of Lankford coefficients. These successes indicate that the polycrystal model should be capable of simulating the entire FLC, Part II.     

Dynamic stability of nearly cylindrical orthotropic shells of revolution subjected to meridional forces

We study the natural vibrations and the dynamic stability of nearly cylindrical orthotropic shells of revolution subjected to meridional forces uniformly distributed over the shell ends. We consider shells of medium length for which the shape of the midsurface generatrix is described by a parabolic function. Using the theory of shallow shells, we obtain the resolving equation for the vibrations of the corresponding prestressed shell. In the isotropic case, this equation differs from the well-known equation [1] by an additional term, which can be of the same order as the other terms taken into account. We consider shells of both positive and negative Gaussian curvature. We assumed that the shell ends are freely supported. The formulas and universal curves describing the dependence of the minimum frequency, the wave generation shape, and the dynamic instability domain boundaries on the orthotropy parameters, the preliminary stress, the Gaussian curvature, and the amplitude of the shell deviation from the cylinder are given in dimensionless form. We find that in the case of prestresses the orthotropy parameters and the shell deviation from the cylinder (of the order of thickness) can significantly change the least frequencies, the wave generation shape, and the dynamic instability domain boundaries of the corresponding prestressed orthotropic cylindrical shell.In this case, we note that for convex shells under preliminary compression the influence of the elastic parameter in the axial direction is stronger than the influence of the elastic parameter in the circular direction, while the situation is opposite in the case of concave shells. In the case of preliminary extension, the leading role of any orthotropy parameter can vary depending on the value of the preliminary stress and the Gaussian curvature.     

Electromagnetic disturbance created by an expanding conducting cylinder in a magnetic field

We examine the electromagnetic disturbance created by a linearly expanding, ideally conducting cylinder in an external uniform magnetic field with account for effects of order v/c (v is the boundary velocity).The problem of uniform magnetic field compression in a contracting cylindrical cavity with ideally conducting walls with radius decreasing linearly with time was solved in [1]. As far as we know the corresponding external problem has not been investigated.     

Torsional,flexural, and torsional-flexural buckling modes of a cylindrical shell under combined loading

Stability problems for cylindrical shells under various loading modes were considered in numerous papers. A detailed analysis of such problems can be found, e.g., in the monograph [1]. We refer to the solutions presented in this monograph as classical.For long cylindrical shells in axial compression, one of the buckling modes is the purely beam flexural mode similar to the classical buckling mode of a straight rod. It is well known that it can be studied by using the nonlinear or linearized equations of the membrane theory of shells. In [2], it was shown that, on the basis of such equations constructed starting from the noncontradictory version of geometrically nonlinear elasticity relations in the quadratic approximation [3], under the separate action of the axial compression, external pressure, and torsion, there are also previously unknown nonclassical buckling modes, most of which are shear ones.In the present paper, we show that the use of the above equations for cylindrical shells under compression and external pressure with simultaneous pure torsion or bending permits revealing the earlier unknown torsional, beam flexural, and beam torsional-flexural buckling modes, which are nonclassical, just as those found in [2]. The second of these buckling modes is realized when axially compressing forces are formed in the shell with simultaneous torsion, and the third of them is realized under compression combined with pure bending.It was found that, earlier than the classical buckling modes, the torsional buckling modes can be realized for relatively short shells with small shear rigidity in the tangent plane, while the second and third buckling modes can be realized for relatively long shells.     

圆柱壳轴向流固冲击屈曲与塑性失效的实验研究

通过对三种不同径厚比圆柱壳进行的流固冲击实验，分析了它们在流固冲击载荷下的动力响应特点，并与相应的高速撞击与静力屈曲实验作了简单的比较，分析了它们之间的异同点。同时文中对极值冲击倒塌特性进行了详细分析     

Stability analysis of fluid flow over a nonlinearly stretching sheet

We discuss the stability of solutions to a class of nonlinear third-order ordinary differential equations arising in the viscous flow over a nonlinearly stretching sheet. In particular, we consider solutions over the semi-infinite interval [0, ∞). These results complement the available existence and uniqueness results in the literature. We find that, in general, there is one stable solution branch and one unstable solution branch. Furthermore, it is observed that the stable solution becomes more stable with an increase in the nonlinearity due to the stretching sheet, while the unstable solution branch becomes more unstable given such an increase in the nonlinearity. The stable solution is the physically meaningful solution.     

Circumferential strain measurement for a concrete cylinder in uniaxial compression by a fiber optic sensor

This paper deals with circumferential strain measurement for concrete in uniaxial compression by using a fiber optic sensing system. A fiber optic sensing system was employed to measure the elongation of the optical fiber for a cylindrical concrete specimen in uniaxial compression by using white light interferometry. A theoretical model describing the relationship between the elongation of the fiber glass and the circumferential strain of cylindrical concrete specimen in uniaxial compression is proposed. Some tests were performed to verify the measurement method. The results indicate that the proposed method is valid.     

The secondary deformation of a compressible isotropic sheet under torsion

This work investigates the second order deformation of a uniformly thick compressible isotropic elastic sheet with an axial cylindrical hole. The sheet is clamped at infinity and is subjected to a constant angular deformation on the interior boundary of the hole. The mathematical solution is formulated in terms of Weber-Orr transforms which are then numerically inverted.     

Creep and long-time fracture of a cylindrical shell under external pressure in the presence of an aggressive medium

We consider the process of deformation and fracture of an oval ring modeling the behavior of a long cylindrical shell subjected to distributed external pressure. The shell deformation is studied in both the presence and absence of an aggressive medium. The hypothesis of nonlinear viscosity with a singular component is taken for the constitutive relation used to estimate the metal characteristics. This relation allows for the difference between the tensile and compression strength of the material. The singularity permits taking into account not only the nonlinear viscosity but also instantaneous fracture characteristics. We show that an aggressive medium can substantially decrease the shell operation life.     

Wave field of a directed explosion

We consider an underwater gas explosion in a cylindrical tank which is open at the bottom. The pressure field in the water is a toroidal compression wave with gradually increasing pressure behind the wave front. In the linear approximation the pressure shock occurs only under the cylinder with the gas. Filling of the lower portion of the cylinder with water alters the compression wave profile.The results obtained may be used in marine seismological prospecting for developing sources for exciting elastic vibrations which are not hazardous to the fish population, in explosive cleaning of filters in water wells, etc.     

轴向应力波作用下圆柱壳塑性轴对称动力屈曲

运用有限元特征值分析方法对应力波作用下圆柱壳塑性轴对称动力失稳问题进行了研究。基于应力波理论和相邻平衡准则导出了圆柱壳轴对称动力失稳时的特征方程,在分析中同时考虑了应力波效应及横向惯性效应,把圆柱壳塑性动力失稳问题归结为特征值问题。通过引入圆柱壳动力失稳时的波前约束条件实现了此类问题的有限元特征值解法。计算结果揭示了圆柱壳塑性轴对称动力屈曲变形发展的机理,以及轴向应力波和屈曲变形的相互作用规律。     

轴向应力波作用下圆柱壳弹性轴对称动力失稳有限元特征值分析

本文运用有限元特征值分析方法对应力波作用下圆柱壳弹性轴对称动力失稳问题进行了研究。基于应力波理论和相邻平衡准则导出了圆柱壳轴对称动力失稳时的有限元特征方程,在此方程中考虑了应力波效应及横向惯性效应,把圆柱壳弹性动力失稳问题归结为特征值问题。通过引入圆柱壳动力失稳时的波前约束条件实现了此类问题的有限元特征值解法。计算结果揭示了圆柱壳弹性轴对称动力屈曲变形发展的机理,以及轴向应力波和屈曲变形的相互作用规律。     

Novel stacked folded cores for blast-resistant sandwich beams

Recent research has established the effectiveness of sandwich structures with metallic cellular cores for blast mitigation. The choice of core architecture can enhance sandwich performance, dissipating energy through plastic core compression and exploiting fluid–structure interaction effects to reduce the momentum imparted to the structure by the blast. In this paper we describe the first analysis of a novel sandwich core concept for blast mitigation: the stacked folded core. The core consists of an alternating stacked sequence of folded sheets in the Miura (double-corrugated) pattern, with the stack oriented such that the folding kinematics define the out-of plane compressive strength of the core. It offers a number of distinct characteristics compared to existing cellular cores. (i) The kinematics of collapse of the core by a distinctive folding mechanism give it unique mechanical properties, including strong anisotropy. (ii) The fold pattern and stacking arrangement is extremely versatile, offering exceptional freedom to tailor the mechanical properties of the core. This includes freedom to grade the core properties through progressive changes in the fold pattern. (iii) Continuous manufacturing processes have been established for the Miura folded sheets which make up the core. The design is therefore potentially more straightforward and economical to manufacture than other metallic cellular materials. In this first investigation of the stacked folded core, finite element analysis is used to investigate its characteristics under both quasi-static and dynamic loading. A dynamic analysis of an impulsively loaded sandwich beam with a stacked folded core reveals the versatility of the concept for blast mitigation. By altering the fold pattern alone, the durations of key phases of the dynamic sandwich response (core compression, beam bending) can be controlled. By altering both fold pattern and sheet thickness in the core, the same is achieved without altering the density of the core or the mass distribution of the sandwich beam.     

Establishing experiments in tensor nonlinear theories of continuum mechanics

A basic scheme of establishing experiments to find three material functions of tensor nonlinear constitutive relations in continuum mechanics is described. These material functions depend on the three invariants of a stress state. It is proposed to use long hollow cylindrical specimens suitable to implement any combination of the following realizable stress states: uniaxial tension, torsion, longitudinal shear, and uniform compression.     

The Equations of Motion of a Plate with Residual Stress

We consider a three-dimensional body which is at rest in a cylindrical configuration of height 2ε. We assume that the material is residually stressed and that it responds elastically to deformations from the reference configuration. Under appropriate assumptions on the data, and using weak-convergence methods, we determine the limit, as ε goes to zero, of the elasto-dynamic problem. The plate problem obtained, as in the case without residual stress, splits into two problems: one governing the in-plane displacement and the other determining the out-of-plane motion.