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V. P. Shevchenko 《International Applied Mechanics》2007,43(7):707-725
This paper deals with fundamental-solution methods applied to stress-concentration problems for thin elastic shells. Publications
concerned with the relevant division of the theory of plates and shells are reviewed. The theories behind the methods are
described, and specific results for static and dynamic concentrated loads are presented. The capabilities of the methods are
illustrated by fracture problems for orthotropic shells with notches and holes under mechanical loading and for isotropic
shells with notches under thermal loading
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 3–25, July 2007. 相似文献
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Complex equations of flexible circular ring shells overall-bending in a meridian plane and general solution for the slender ring shells 总被引:1,自引:0,他引:1
IntroductionEquationsforcircularringshellsaredifficulttosolve.Theresearchofthisproblemstartedatthebeginningofthiscentury.Inthelate1970sandearly1980s,W.Z.Chien(1979,1980,1981)[1~3]rebuiltthecomplexequationsofaxis_symmetricallyloadedringshellspresented… 相似文献
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In order to clarify the mechanism of loading and unloading, buckling growth, and strain-reversal occurrence in elastic–plastic cylindrical shells that are impacted axially, non-linear dynamic equations in incremental form are derived and solved by using the finite difference method. The validity of the developed theory is verified by comparing theoretical and experimental results. From the calculation results, it is found that, at the initial stage of the impact process, the effective stress related to the middle-surface stresses in the part near the impacted end rises with time, and exhibits plastic loading. The radial restraints on the impacted end have obvious influence on the strain reversal occurrence at an early stage of the impact process. The effective modulus controls the post-buckling deformation of the shell, which contrasts with the situation for the bar to be impacted axially. 相似文献
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A. Z. Galishin 《International Applied Mechanics》2001,37(2):271-278
A method is developed to determine the axisymmetric geometrically nonlinear thermoelastoviscoplastic stress–strain state of branched laminated medium-thickness shells of revolution. The method is based on the hypotheses of a rectilinear element for the whole set of layers. The shells are subject to loads that cause a meridional stress state and torsion. They can consist of isotropic layers, which deform beyond the elastic limit, and elastic orthotropic layers. The relations of thermoviscoplastic theory, which describe simple processes of loading, are employed as the equations of state for the isotropic layers. The solution of the problem is reduced to numerical integration of systems of differential equations. The geometrically nonlinear elastoplastic state of a two-layer corrugated shell of medium thickness is calculated as an example 相似文献
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H. Altenbach O. Morachkovsky K. Naumenko A. Sychov 《Archive of Applied Mechanics (Ingenieur Archiv)》1997,67(5):339-352
Summary A phenomenological constitutive model for characterization of creep and damage processes in metals is applied to the simulation
of mechanical behaviour of thin-walled shells and plates. Basic equations of the shell theory are formulated with geometrical
nonlinearities at finite time-dependent deflections of shells and plates in moderate bending. Numerical solutions of initial/boundary-value
problems have been obtained for rectangular thin plates (two-dimensional case) and axisymmetrically loaded shells of revolution
(one-dimensional case). Based on the numerical examples for the two problems, the influence of geometrical nonlinearities
on the creep deformation and damage evolution in shells and plates is discussed.
Accepted for publication 30 October 1996 相似文献
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R. Heuer 《Nonlinear dynamics》1994,5(1):25-38
A dynamic nonlinear theory for layered shallow shells is derived by means of the von Karman-Tsien theory, modified by the generalized Berger-approximation. Moderately thick shells with polygonal planform composed of multiple perfectly bonded layers are considered. The shell edges are assumed to be prevented from in-plane motions and are simply supported. A distributed lateral force loading is applied to the structure, and additionally, the influence of a static thermal prestress, corresponding to a spatial distribution of cross-sectional mean temperature, is taken into account. In the special case of laminated shells made of transversely isotropic layers with physical properties symmetrically distributed about the middle surface, a correspondence to moderately thick homogeneous shells is found. Application of a multi-mode expansion in the Galerkin procedure to the governing differential equation, where the eigenfunctions of the corresponding linear plate problem are used as space variables, renders a coupled set of ordinary time differential equations for the generalized coordinates with cubic as well as quadratic nonlinearities. The nonlinear steady-state response of shallow shells subjected to a time-harmonic lateral excitation is investigated and the phenomenon of primary resonance is studied by means of the perturbation method of multiple scales. A unifying non-dimensional representation of the nonlinear frequency response function is presented that is independent of the special shell planform. 相似文献
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Internal resonance in nonlinear vibration of functionally graded (FG) circular cylin- drical shells in thermal environment is studied using the Hamiltonian dynamics formulation. The material properties are considered to be temperature-dependent. Based on the Karman-Donnell's nonlinear shell theory, the kinetic and potential energy of FG cylindrical thin shells are formu- lated. The primary target is to investigate the two-mode internal resonance, which is triggered by geometric and material parameters of shells. Following a secular perturbation procedure, the underlying dynamic characteristics of the two-mode interactions in both exact and near resonance cases are fully discussed. It is revealed that the system will undergo a bifurcation in near resonance case, which induces the dynamic response at high energy level being distinct from the motion at low energy level. The effects of temperature and volume fractions of composition on the exact resonance condition and bifurcation characteristics of FG cylindrical shells are also investigated. 相似文献
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The paper presents a technique for thermoelastoplastic stress–strain analysis of flexible laminated shells of revolution under complex axisymmetric loading. The constitutive deformation equations are used to describe loading along arbitrary plane paths. The problem is solved by the method of successive approximations. A numerical example is given 相似文献
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圆柱壳在侧向非对称冲击载荷下的塑性动力屈曲 总被引:2,自引:1,他引:2
采用塑性动力屈曲能量准则,对圆柱壳非均匀局部径向冲击下的塑性动力屈曲进行了研究。文中分别采用弹性的角弹簧和位移弹簧模拟非屈曲部分对屈曲部分的影响,推导了有关模态和临界速度的冲击公式,并与有关的实验结果进行了比较,分析了两种边界对塑性动力屈曲的影响。 相似文献
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Results obtained on the basis of linearized functionals in the theory of nonlinearly elastic composite shells are analyzed and generalized. The Kirchhoff-Love and Timoshenko hypotheses are used. Possible membrane or shear locking is taken into account. New approaches are proposed to improve the convergence of numerical solution for new classes of nonlinear problems for thin and nonthin shells with a curvilinear (circular, elliptical) hole. The stress-strain state of shells is analyzed using different versions of shell theory. The influence of the nonlinear properties and orthotropy of composite materials on the stress distribution in structural members is studied.Translated from Prikladnaya Mekhanika, Vol. 40, No. 11, pp. 45–84, November 2004.This revised version was published online in April 2005 with a corrected cover date. 相似文献
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Non-linear vibrations of free-edge shallow spherical shells are investigated, in order to predict the trend of non-linearity (hardening/softening behaviour) for each mode of the shell, as a function of its geometry. The analog for thin shallow shells of von Kármán's theory for large deflection of plates is used. The main difficulty in predicting the trend of non-linearity relies in the truncation used for the analysis of the partial differential equations (PDEs) of motion. Here, non-linear normal modes through real normal form theory are used. This formalism allows deriving the analytical expression of the coefficient governing the trend of non-linearity. The variation of this coefficient with respect to the geometry of the shell (radius of curvature R, thickness h and outer diameter 2a) is then numerically computed, for axisymmetric as well as asymmetric modes. Plates (obtained as R→∞) are known to display a hardening behaviour, whereas shells generally behave in a softening way. The transition between these two types of non-linearity is clearly studied, and the specific role of 2:1 internal resonances in this process is clarified. 相似文献
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双曲率壳是飞机、汽车以及船舶上常见的薄壁结构,其中性面可看作是一条动曲线沿着另一条曲线扫掠所形成的曲面.双曲率壳的非线性理论不断更新推动着双曲率壳力学行为的研究.随着工程实际应用的不断改进,如功能梯度材料(FGM),加筋壳,弹性地基模型等的引入,双曲率壳在强度、变形和稳定性等方面的研究得到了进一步促进.本文首先回顾了双曲率壳结构非线性力学基本理论发展过程,主要阐述了经典的二维板壳理论,如Donnell 薄壳理论,一阶剪切变形壳理论,高阶剪切变形壳理论,和三维板壳理论的理论体系及基本公式,并对几种理论之间的联系和应用进行了总结和讨论,简述了近几十年来国内外学者在双曲率壳非线性弯曲、稳定性和振动等方面的最新研究成果,最后对双曲率壳体研究目前的局限性和未来的研究方向进行了探讨. 相似文献
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《International Journal of Solids and Structures》2014,51(3-4):894-903
In this paper, an analytical method is presented to investigate the nonlinear buckling and expansion behaviors of local delaminations near the surface of functionally graded laminated piezoelectric composite shells subjected to the thermal, electrical and mechanical loads, where the mid-plane nonlinear geometrical relation of delaminations is considered. In examples, the effects of thermal loading, electric field strength, the stacking patterns of functionally graded laminated piezoelectric composite shells and the patterns of delaminations on the critical axial loading of locally delaminated buckling are described and discussed. Finally, the possible growth directions of local buckling for delaminated sub-shells are described by calculating the expanding forces along the length and short axis of the delaminated sub-shells. 相似文献
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This paper applied the simplified theory for multilayer sandwich shells undergoing moderate/small rotations in Ref. [1] to
shallow shells. The equilibrium equations and boundary conditions of large deflection of orthotropic and the special case,
isotropic shells, are presented. 相似文献
17.
D. I. Chernopiskii 《International Applied Mechanics》1999,35(9):917-925
A method for determining the principal curvatures of medium-thickness shells through the vector representation of local bases
is proposed based on the parametrization of the base median surface of a shell and its front surfaces. Repeated partial derivatives
of vector functions with respect to variable Gaussian coordinates, which is a standard practice in theory of shells when calculating
the curvatures as coefficients of the second quadratic form, are not used. Such an approach allows us to accurately account
for the geometry of the front surfaces of the shell in determining its stress-strain state.
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika,
Vol. 35, No. 9, pp. 58–65, September, 1998. 相似文献
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本文用薄壳理论导出了壁厚线性变化的锥壳在承受轴对称截荷时的复变量方程,在薄壳理论误差范围内求得了齐次方程的渐近解和工程实用载荷的非齐次解,并给出了算例。 相似文献