共查询到20条相似文献,搜索用时 15 毫秒
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Wrinkling can affect the functionality of thin membranes subjected to various loadings or boundary conditions. The concept of relaxed strain energy was studied for isotropic, hyperelastic, axisymmetric membranes pressurized by gas or fluid. Non-intuitive instabilities were observed when axisymmetric wrinkled membranes were perturbed with angle dependent displacement fields. A linearized theory showed that static equilibrium states of pressurized membranes, modelled by a relaxed strain energy formulation, are unstable, when the wrinkled surface is subjected to pressure loadings. The theory is extended to the non-axisymmetric membranes and it is shown that these instabilities are local phenomena. Simulations for the pressurized cylindrical membranes with non-uniform thickness and hemispherical membranes support the claims in both theoretical and numerical contexts including finite element simulations. 相似文献
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The torsion of a composite,nonlinear-elastic cylinder with an inclusion having initial large strains
Vladimir A. Levin Leonid M. Zubov Konstantin M. Zingerman 《International Journal of Solids and Structures》2014
This article considers a static problem of torsion of a cylinder composed of incompressible, nonlinear-elastic materials at large deformations. The cylinder contains a central, round, cylindrical inclusion that was initially twisted and stretched (or compressed) along the axis and fastened to a strainless, external, hollow cylinder. The problem statement and solution are based on the theory of superimposed large strains. An accurate analytical solution of this problem based on the universal solution for the incompressible material is obtained for arbitrary nonlinear-elastic isotropic incompressible materials. The detailed investigation of the obtained solution is performed for the case in which the cylinders are composed of Mooney-type materials. The Poynting effect is considered, and it is revealed that composite cylinder torsion can involve both its stretching along the axis and compression in this direction without axial force, depending on the initial deformation. 相似文献
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The problem of a thin rod moving longitudinally along the axis of symmetry of a cylindrical vessel is examined for Newtonian and non-Newtonian liquids. For non-Newtonian fluids, the inelastic power-law type solution predicts the experimental results particularly well. On account of wall effects, the induced pressure gradients are much greater for a Newtonian fluid than for a viscoelastic fluid. In fact, in the latter case, they may be considered negligible when the radius of the inner cylinder is small compared to the one of the outer cylinder. 相似文献
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The paper presents an analytical estimate for an area of contact for a thin-walled noncircular cylindrical shell placed between two parallel rigid plates with an initial gap and then pressurized hydrostatically up to the contact appearance. The Euler–Bernoulli beam is used to model the shell deformation under the plane strain assumption. Such a simplification allows one to obtain the simplest closed-form estimate for the contact zone area. The first approximation is obtained neglecting the deformation of the curvilinear segments of the flat oval shell cross-section while the solution for the curved beam loaded by the homogeneous pressure is considered as a second approximation. The accuracy of the proposed analytical solutions as well as their usability in the preliminary design of thin-walled elements of various cooling systems is validated by the results of both numerical simulations and experimental tests. 相似文献
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对曲边柱壳受轴向非均匀内压作用下的大转动几何非线性3-D动力学行为进行了研究.基于Nayfeh and Pai[1]非线性壳体理论,给出了考虑几何非线性的3-D混合型(含内力与位移)动力学模型.为了克服该强非线性模型难以求解的问题,依据分析获得的结构静动态变形关系,采用Lagrange方程推导建立了基于结构静态解的曲边柱壳多自由度3-D动力学方程,并对其进行了线性化与降阶处理,结合差分法获得了一套高效的求解算法.与LS-DYNA有限元结果的吻合,验证了本文方法的正确性.最后分析了单元数和计算时间步分别对有限元模型和本文方法的影响,发现求解精度随着计算时间步的减小不断提高直至趋于稳定.同时对采用本文方法获得的曲边柱壳动态变形模式的分析表明:结构动态响应与其所受内压载荷沿轴向的分布形式关系紧密,可以通过改变或者设计内压轴向分布形式来影响以及控制结构的动态变形模式,从而应用于曲边柱壳结构设计及优化的工程实际中. 相似文献
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The rectilinear deformation of an incompressible, isotropic clastic solid is, in general, characterized by the two planar fields of pressure and displacement magnitude, and these are, in turn, restricted by the three, generally independent, differential equations of equilibrium. The over-determined nature of this situation suggests the possibility that transverse deformations may accompany rectilinear shear—a possibility not supported by the linear theory. Within this context we consider the class of equilibrium non-linear clasticity problems which is associated with cylindrical domains whose various boundaries each are displaced rigidly along their generators. An approximation scheme is developed for determining the cross sectional deformation and a specific example for a cylinder with eccentric circular cross section is given. 相似文献
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热超弹性圆筒的不稳定性 总被引:1,自引:1,他引:1
应用有限变形弹性理论分析了受内压和轴向拉伸作用的不可压热超弹性圆筒发生非均
匀变形的不稳定性问题. 受内压和轴向拉力作用的薄壁圆筒,当内压较小时,圆筒发生稳定
的均匀膨胀变形;当内压大于某一临界值时,圆筒产生复杂的非均匀变形,其一部分膨胀变
形很大,形如``灯泡'状,而另一部分仅仅是轻微膨胀,且此时的变形是不稳定的. 但对厚
壁圆筒而言,不论压力如何,总是发生稳定的均匀膨胀变形. 根据圆筒的变形曲线,给出了
圆筒可以发生不稳定变形的临界厚度. 同时,讨论了轴向拉伸和温度场对圆筒变形的影响. 相似文献
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A. M. Kovrizhnykh 《Mechanics of Solids》2012,47(2):234-241
The ideal plasticity model based on the Tresca-Saint-Venant criterion is used to solve one-dimensional problems of deformation
and fracture of solids with circular boundaries. A thickwalled cylinder and a hollow sphere under pressure, cylindrical and
hollow cavities in an unbounded body, and uniform extension at infinity of a plate with a free circular hole are considered.
In simple elastoplastic problems, the proposed approach allows one to determine the value of the maximum external load at
the fracture initiation and the motion of the fracture front for a given displacement of points of the contour on which this
load acts. 相似文献
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The stress distribution in a pressurized elastomer confined by a hollow cylinder is of interest in various applications of material testing and manufacturing. A relatively accurate closed form solution for the pressure distribution inside an elastomer confined by a rigid hollow cylinder was presented by Yu et al. (2001). But in many practical applications the assumption of a rigid hollow cylinder is not appropriate, because the cylinder deformations have a significant influence on the stresses inside the elastomer. Thus in this paper a solution for an elastomer confined by a deformable hollow cylinder is derived. Both axial and radial deformations of the hollow cylinder are taken into account, while the bending stiffness of the cylinder wall is neglected, i.e. the cylinder wall is treated according to the membrane theory. The accuracy of the proposed closed form solution is verified by a parametric finite element simulation. 相似文献
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Quasi-static cylindrical cavity expansion in an elastoplastic compressible Mises solid 总被引:1,自引:0,他引:1
The self-similar elastoplastic field induced by quasi-static expansion of a pressurized cylindrical cavity is investigated for Mises solids under the assumption of plane-strain. Material behavior is modeled by the elastoplastic J2 flow theory with the standard hypoelastic version. The theory accounts for elastic-compressibility and allows for arbitrary strain-hardening (or softening) in the plastic range. A formulation of the exact governing equations is presented and analyzed in detail for the remote elastic field and for asymptotic plastic behavior near the cavity wall, along with numerical investigations for the entire deformation zone. An analytical solution was obtained under the axially-hydrostatic assumption (axial stress coincides with hydrostatic stress) within an error of about 2% or less as compared to the exact, numerically evaluated, value of cavitation pressure. Two ad-hoc compressibility approximations for cavitation pressure are suggested. These relations, which give very accurate results, appear to provide tight lower and upper bounds on the exact value of cavitation pressure within an error of less than 0.5%. 相似文献
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The present paper describes the dynamic process of a vapour bubble moving in a non-uniform flow field. The coupling between
the bubble moving as a whole and the deformation of the bubble surface is considered. The effect of the pressure gradient
on the bubble movement is analysed. For a given flow field the numerical calculation is carried out until the vapour bubble
is split by a micro-jet. 相似文献
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A theory is formulated for the finite deformation of a thin membrane composed of homogeneous elastic material which is isotropic in its undeformed state. The theory is then extended to the case of a small deformation superposed on a known finite deformation of the membrane. As an example, small deformations of a circular cylindrical tube which has been subjected to a finite homogeneous extension and inflation are considered and the equations governing these small deformations are obtained for an incompressible material. By means of a static analysis the stability of cylindrically symmetric modes for the inflated and extended cylinder with fixed ends is determined and the results are verified by a dynamic analysis. The stability is considered in detail for a Mooney material. Methods are developed to obtain the natural frequencies for axially symmetric free vibrations of the extended and inflated cylindrical membrane. Some of the lower natural frequencies are calculated for a Mooney material and the methods are compared. 相似文献
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An analytical method for the three-dimensional vibration analysis of a functionally graded cylindrical shell integrated by two thin functionally graded piezoelectric (FGP) layers is presented. The first-order shear deformation theory is used to model the electromechanical system. Nonlinear equations of motion are derived by considering the von Karman nonlinear strain-displacement relations using Hamilton’s principle. The piezoelectric layers on the inner and outer surfaces of the core can be considered as a sensor and an actuator for controlling characteristic vibration of the system. The equations of motion are derived as partial differential equations and then discretized by the Navier method. Numerical simulation is performed to investigate the effect of different parameters of material and geometry on characteristic vibration of the cylinder. The results of this study show that the natural frequency of the system decreases by increasing the non-homogeneous index of FGP layers and decreases by increasing the non-homogeneous index of the functionally graded core. Furthermore, it is concluded that by increasing the ratio of core thickness to cylinder length, the natural frequencies of the cylinder increase considerably. 相似文献
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A perturbation solution is obtained for the local stress-strain fields in an axially cracked cylindrical shell. The tenth-order differential equations are used that take into account the transverse shear deformation. The perturbation of a curvature parameter, λ, is employed, where
. The stress intensity factors for finite size cylindrical shells subjected to bending and internal pressure are evaluated. Sufficient accuracy can be obtained without using fine mesh sizes in regions near the crack tip. Also analyzed are the influence of cylinder diameter and shearing stiffness on bulging. 相似文献
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The present paper is devoted to the study of finite inflation of a hyperelastic toroidal membrane on a cylindrical rim under uniform internal pressure. Both compliant and rigid frictionless rims have been considered. The compliant cylindrical rim is modeled as a linear distributed stiffness. The initial cross-section of the torus is assumed to be circular, and the membrane material is assumed to be a homogeneous and isotropic Mooney–Rivlin solid. The problem is formulated as a two point boundary value problem and solved using a shooting method by employing the Nelder–Meads search technique. The optimization function is constructed on a two (three) dimensional search space for the compliant cylinder (rigid cylinder). The effect of the inflation pressure, material properties and elastic properties of the rim on the state of stretch and stress, and on the geometry of the inflated torus have been studied, and some interesting results have been obtained. The stability of the inflated configurations in terms of occurrence of the impending wrinkling state in the membrane has also been studied. 相似文献
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D. Ieşan 《International Journal of Solids and Structures》2011,48(3-4):573-583
This paper is concerned with the linear theory of porous Cosserat elastic solids. We study the equilibrium of a cylindrical bar which is subjected to resultant forces and resultant moments on the ends, to body loads and to surface tractions on the lateral surface. The Almansi problem, where the body loads and the surface loading on the lateral surface are polynomials in the axial coordinate, is considered. The bar is made of an inhomogeneous and isotropic material whose constitutive coefficients are independent of the axial coordinate. The problem is reduced to the study of two-dimensional problems. The results are used to study two practical applications concerning the deformation of a circular rod. It is shown that a uniform pressure on the lateral surface produces an extension, a uniform change of the porosity, and a plane deformation. The bending by terminal couples produces a non-uniform variation of the porosity and a microrotation of the material particles. 相似文献