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Placido Cicala 《Meccanica》1985,20(1):43-48
Summary A general scheme encompassing expansion methods for the sleeve is presented: one homogeneous condition for each contour portion
establishes real eigenvalues ensuring orthogonality to Fourier-Bessel expansions. Solutions by integral equations may be regarded
as limiting cases, with summations replaced by integrations. Special attention is devoted to the alternative use of complex
eigensolutions, subjected to two homogeneous conditions on the cylindrical boundary.
Sommario Si presenta uno schema generale che inquadra i metodi di risoluzione attraverso sviluppi, per cilindri cavi: imponendo una condizione omogenea su ciascuna parte, piana o cilindrica, di contorno, si definiscono le autosoluzioni reali, ortogonali, per gli sviluppi in serie di Fourier-Bessel. Rientrano come casi particolari quelli di lunghezza o raggio infinito. Si esamina inoltre l'uso di autosoluzioni complesse, definite da due condizioni omogenee sul contorno cilindrico.相似文献
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Summary Presented in this paper are the solutions to several plate bending problems as governed by a recent theory developed by Green and Naghdi, into which couple-stress is incorporated. Specifically, each problem considered is subjected to boundary conditions emanating from a singular load distribution acting on the free edge of a semi-infinite plate. The method of integral transforms is applied in the solutions.In general, it is found that the singularities in the shear and moment resultants are of the same order as those given in Reissner's plate theory, however the detailed structures of these singular functions are altered. The present theory also suggests that, in most cases, the maximum magnitudes of the moment resultants are diminished as compared to the corresponding results given in Reissner's theory.Also discussed is the exact relationship between the Green-Naghdi theory and Reissner's theory.
This research is sponsored by the U. S. Navy under Contract Nonr-610(06) with the Office of Naval Research in Washington, D. C. 相似文献
Sommario In questa memoria sono presentate le soluzioni di alcuni problemi relativi a piastre inflesse studiati in base ad una teoria recentemente sviluppata da Green e Naghdi, in cui si considerano distribuzioni di coppie di volume.In ogni problema considerato le condizioni al contorno presentano una singolarità nella distribuzione di carico agente su un bordo libero di una piastra semi-indefinita. Per la risoluzione è applicato il metodo delle trasformate integrali.In generale risulta che le singolarità nel taglio e nel momento sono dello stesso ordine di quelle date dalla teoria delle piastre di Reissner, benchè gli andamenti di queste funzioni singolari siano diversi. La teoria sviluppata porta inoltre a valutare, nella maggior parte dei casi, momenti massimi più piccoli di quelli corrispondenti ottenuti in base alla teoria di Reissner.Si discute inoltre l'esatta relazione tra le teorie di Green-Naghdi e di Reissner.
This research is sponsored by the U. S. Navy under Contract Nonr-610(06) with the Office of Naval Research in Washington, D. C. 相似文献
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Cornelius O. Horgan 《International Journal of Solids and Structures》1974,10(8):837-852
Energy-decay inequalities are applied in investigating the decay of end effects in a transversely isotropic circular cylinder subject to torsionless axisymmetric end loads. A lower bound (in terms of the elastic constants) is obtained for the rate of exponential decay of stresses and this is compared with results of other authors. For a highly anisotropic medium, a slow decay rate is predicted thus anticipating disagreement with Saint-Venant's principle in this case. 相似文献
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《International Journal of Solids and Structures》2003,40(1):105-123
By virtue of the separation of variables technique, the axisymmetric plane strain electroelastic dynamic problem of hollow cylinder is transferred to an integral equation about a function with respect to time, which can be solved successfully by means of the interpolation method. Then the solution of the displacements, stresses, electric displacements and electric potentials are finally obtained. The present method is suitable for the hollow cylinder with arbitrary thickness subjected to arbitrary mechanical and electrical loads. Numerical results are also presented. 相似文献
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The three-dimensional theory of elasticity is used to study the free vibrations of an anisotropic hollow cylinder with different
boundary conditions at the ends. The relevant problem is solved by a numerical-and-analytic method. Spline approximation and
collocation is used to reduce the partial differential equations of elasticity to a boundary-value problem for a system of
ordinary differential equations of high order for the radial coordinate, which is solved using the stable discrete-orthogonalization
and incremental-search methods. The calculated results for an orthotropic inhomogeneous cylinder with boundary conditions
of several types are presented
Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 74–85, October 2008. 相似文献
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《International Journal of Solids and Structures》2003,40(10):2355-2380
This paper presents an analysis of the thermomechanical behavior of hollow circular cylinders of functionally graded material (FGM). The solutions are obtained by a novel limiting process that employs the solutions of homogeneous hollow circular cylinders, with no recourse to the basic theory or the equations of non-homogeneous thermoelasticity. Several numerical cases are studied, and conclusions are drawn regarding the general properties of thermal stresses in the FGM cylinder. We conclude that thermal stresses necessarily occur in the FGM cylinder, except in the trivial case of zero temperature. While heat resistance may be improved by sagaciously designing the material composition, careful attention must be paid to the fact that thermal stresses in the FGM cylinder are governed by more factors than are its homogeneous counterparts. The results that are presented here will serve as benchmarks for future related work. 相似文献
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Singular integral equations are used to formulate the torsion problem of a circular cylinder containing a polygonal opening and a line crack. The formulation is based on degenerating a system of connecting line cracks to that of a polygon, the sides of which coincides with the cracks. Considered, in particular, is the torsion of a circular cylinder with a rectangular hole and a nearby slanted line crack. Mode III stress intensity factors are computed at both ends of the crack to reflect their relative position to the rectangular hole in addition to change in the dimensions of the crack relative to the other geometric variables. Recognizing that the singular behavior of the stresses near a reentrant's corner differs from that of the crack tip, intensification of the local stresses at the corners of the rectangular hole is also examined. The results show the influence of the crack size and position. 相似文献
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A deformation plasticity model is used to implement the elastic compensation (iterative use of linearly elastic models to approximate elastic/plastic response) simulation of small axisymmetric circular plate deformations by the finite element method. Representative numerical results are presented graphically and used to demonstrate the utility of the approach. 相似文献
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Hai QING 《应用数学和力学(英文版)》2022,43(5):637-652
Previous studies have shown that Eringen's differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates. Based on the nonlocal integral models along the radial and circumferential directions, we propose nonlocal integral polar models in this work. The proposed strainand stress-driven two-phase nonlocal integral polar models are applied to model the axisymmetric bending of circular microplates. The governing differential equations and boundary conditions (BCs) as well as constitutive constraints are deduced. It is found that the purely strain-driven nonlocal integral polar model turns to a traditional nonlocal differential polar model if the constitutive constraints are neglected. Meanwhile, the purely strain-and stress-driven nonlocal integral polar models are ill-posed, because the total number of the differential orders of the governing equations is less than that of the BCs plus constitutive constraints. Several nominal variables are introduced to simplify the mathematical expression, and the general differential quadrature method (GDQM) is applied to obtain the numerical solutions. The results from the current models (CMs) are compared with the data in the literature. It is clearly established that the consistent softening and toughening effects can be obtained for the strain-and stress-driven local/nonlocal integral polar models, respectively. The proposed two-phase local/nonlocal integral polar models (TPNIPMs) may provide an e-cient method to design and optimize the plate-like structures for microelectro-mechanical systems. 相似文献
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Yin Chang-yan 《应用数学和力学(英文版)》1989,10(6):563-570
In the present paper by using complex variable methods in linear elasticity and by means of analytic continuation, the author obtains for this problem a complex torsional function, shear stress components, displacement components,the torsional rigidity and shear stresses on boundaries expressed in terms of series. 相似文献
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Yong-Gang Wang Wen-Hui Lin Chang-Ling Zhou 《Archive of Applied Mechanics (Ingenieur Archiv)》2014,84(3):391-400
The present study proposes a nonclassical Kirchhoff plate model for the axisymmetrically nonlinear bending analysis of circular microplates under uniformly distributed transverse loads. The governing differential equations are derived from the principle of minimum total potential energy based on the modified couple stress theory and von Kármán geometrically nonlinear theory in terms of the deflection and radial membrane force, with only one material length scale parameter to capture the size-dependent behavior. The governing equations are firstly discretized to a set of nonlinear algebraic equations by the orthogonal collocation point method, and then solved numerically by the Newton–Raphson iteration method to obtain the size-dependent solutions for deflections and radial membrane forces. The influences of length scale parameter on the bending behaviors of microplates are discussed in detail for immovable clamped and simply supported edge conditions. The numerical results indicate that the microplates modeled by the modified couple stress theory causes more stiffness than modeled by the classical continuum plate theory, such that for plates with small thickness to material length scale ratio, the difference between the results of these two theories is significantly large, but it becomes decreasing or even diminishing with increasing thickness to length scale ratio. 相似文献
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Janusz Murzewski 《International Journal of Non》1968,3(4):483-493
Cylindrical shell beams of mono-symmetrical closed profile, stiffened by stringers and frames, are under consideration for a limit state of bending. Alternative systems of internal forces acting on the frame are determined for the cases:
1. (i) simultaneous deformations of the frame and the shell profile, provided that the sheet remains elastic, smooth and continuous with the frame,
2. (ii) when a second-order effect arises when a plastic hinge of the sheet is formed around the frame and the panel forces are no longer normal to the plane of the frame.
Comments on the buckling of the frame and collapse of the cylinder are added. 相似文献