Elastic deformation of composite cylinders with cylindrically orthotropic layers

This paper provides explicit analytical expressions for displacement and stress fields in a multilayered composite cylinder with cylindrically orthotropic layers subjected to homogeneous boundary conditions. The solutions are derived in the assumption of perfect bonding between layers. The components of displacement, strain and stress are expressed in terms of the integration constants found from boundary conditions by utilizing the transfer matrix approach. Several examples are considered. The approach is validated by comparing with previously known solutions.     

Residual-stress measurement in orthotropic materials using the hole-drilling method

The hole-drilling method is used here to measure residual stresses in an orthotropic material. An existing stress-calculation method adapted from the isotropic case is shown not to be valid for orthotropic materials. A new stress-calculation method is described, based on the analytical solution for the displacement field around a hole in a stressed orthotropic plate. The validity of this method is assessed through a series of experimental measurements. A table of elastic compliances is provided for practical residual-stress measurements in a wide range of orthotropic materials.     

Analysis of residual stresses in bars and tubes of cylindrically orthotropic materials

One of the most frequently used techniques of determining residual stresses in cylindrical bodies of elastically isotropic materials is the Mesnager-Sachs boring-out method. This method is adequate for many engineering materials; however, certain materials possess elastic properties which vary with direction. Materials having one fairly common kind of directional variation are known as cylindrically orthotropic materials. Heretofore, no means has been available for determining the residual stresses from strain data taken after successive borings of members made of such materials. This paper gives the derivation of equations for this purpose along with graphs depicting the error to be expected if the data had been reduced by the Sachs equations.     

Acoustoelastic determination of stress in slightly orthotropic materials

A method is proposed to determine stresses in acoustoelasticity by making use of orthotropic stress-acoustic relations and the equations of equilibrium. It is derived theoretically that shear stress is determined ny ultrasonic data ofB and ?, which denote a magnitude of acoustic birefringence and its principal direction, respectively. Other stress components are obtained by numerical integration of the equilibrium equation with the shear stress thus determined. Experiments were carried out to show the validity and usefulment of the method. This method was applied to the measurement of stress field on a plate with a circular hole subjected to axial tension. Ultrasonic measurements were made by a Y-cut quartz transducer with 5-MHz fundamental frequency. The specimen was cut out from 1100 aluminum plate of 4-mm thickness, which shows a slight orthotropy due to roll working. The values ofB and ? were measured in both stressed and unstressed state. Then, stress distributions were determined by the method proposed here, and are compared with the known theoretical distributions.     

Elastoplastic analysis of cylindrically orthotropic composite thick-walled tube

In the present paper, Tsai-Hill Yield Criterion in a state of plane strain is derived for incompressible and compressible materials respectively. the elastoplastic stress and displacement fields of cylindrically orthotropic composite thick-walled tube under uniform radial pressure are studied. The formulas of the yield pressure, limit pressure and region of shakedown are obtained.     

Analysis of transient thermal stress in cylindrically orthotropic tubes

IntroductionCylindricallyorthotropictubesarenowwidelyappliedinengineering ,theresearchofthestressesfieldhasattractedalotofattentionfromscientistsandengineers .ConsiderableworksonstressfieldduetomechanicalloadinghavebeendonebyLehknitskii[1],Sherrer[2 ]andPagano[3].KalamandTauchert[4 ],HyerandCooper[5 ]studiedthethermalstressesinorthotropiccylindersduetosteaky_statetemperaturegradient.TheproblemoftransientthermalstressesinaholloworthotropiccircularcylinderwasfirstlyproposedandtreatedbyKardoma…     

Nonlinear dynamic buckling of symmetrically laminated cylindrically orthotropic shallow spherical shells

Summary In this paper, a model of cusped catastrophe at nonlinear dynamic buckling of a symmetrically laminated cylindrically orthotropic shallow spherical shell is presented. The shell is subjected to an axisymmetrical load. Effects of transverse shear are taken into account. Effects of the shear modulus, geometry and parameters of the material on the nonlinear dynamic buckling are discussed. Received 2 April 1997; accepted for publication 27 November 1997     

An investigation of meterial properties of non-homogeneous cylindrically orthotropic circular plates

It has been been reported that the reduced stiffness of non-homogeneous cylindricallyorthotrpic circular plate varing exponentially with radius r is obtained by using thebending theory of a simple beamThe aim of this paper is to verify the effect of radius on the materal properties According to the flat stress-strain relation the values of material properties E_r E_a and v_θr which are the functions of radius r are obtained.Compared with the experimentalvalues the analytical values of the material properties are in essential agreement withtem.     

On the nonlinear stability of symmetrically laminated cylindrically orthotropic shallow spherical shells

In this paper,the large deflection theory of symmetrically laminated cylindricallyorthotropic shallow spherical shells is established.Based on this theory,applying themodified iteration method,the analytic solution for critical buckling loads of the shells withrigidly clamped edges under actions of uniform pressure has been obtained.     

Analysis of residual stresses in cylindrically anisotropic materials

Metal-forming operations leave residual stresses in formed parts due to nonuniform deformation occurring during the process. An exact method of determining the longitudinal, radial and circumferential (tangential) residual stresses in axisymmetric specimens was proposed by Mesnager¹ and further developed by Sachs². The boring-out technique can be complemented by a similar procedure in which strains are measured on the inner surface of the tube when material is removed from the outer surface.The work proposed in this paper extends previous analyses of residual stresses to the case where the material exhibits cylindrical elastic anisotropy, i.e., the principal axes of anisotropy correspond to the longitudinal, radial and circum-ferential directions of the tube. In addition, the present analysis considers the case in which a residual-shear stress, developed by twisting the tube about its axis, exists in the tube. When such shearing stresses are present, the principal axes of the residual-stress distribution are not parallel to the principal axes of the tube.     

Thermal buckling of axisymmetrically laminated cylindrically orthotropic shallow spherical shells including transverse shear

The nonlinear thermal buckling of symmetrically laminated cylindrically orthotropic shallow spherical shell under temperature field and uniform pressure including transverse shear is studied. Also the analytic formulas for determining the critical buckling loads under different temperature fields are obtained by using the modified iteration method. The effect of transverse shear deformation and different temperature fields on critical buckling load is discussed.     

Anti-plane wave motion in a cylindrically orthotropic elastic solid containing a stress-free crack

A cylindrically orthotropic elastic solid is excited by a point impulsive body force. The solid contains a semi-infinite stress-free crack. The resulting wave motion is anti-plane. An eigenfunction solution to the problem is obtained in the form of an infinite series. The series is summed into two parts. The first part contains the incident and reflected wave pulses while the second part gives the diffraction integral. Wave front patterns are presented with an application to wood.     

Residual-stress determination through combined use of holographic interferometry and blind-hole drilling

Holographic interferometry is used to determine in-plane radial displacements due to release of residual stresses by hole drilling. A method is derived for relating radial displacements measured in three directions of illumination to the state of residual stress, analogous to relations used in the conventional strain-rosette technique. Residual stress is produced by an interference fit of two circular tubes. Agreement between stress determined holographically with a computed value and with that determined by the conventional technique is good. Advantages of the holographic technique in overcoming various shortcomings of the conventional technique are discussed. A modification of the holographic technique involving data collection in only two directions of illumination is described.     

Elastoplastic analysis of cylindrically orthotropic composite lamina with a circular hole under uniform pressure

This paper presents the standard parametric representation of the Tsai-Hill yieldcriterion in a state of plane stress and the equations governing the stress distribution in acylindrically orthotropic composite lamina with a circular hole under uniform pressure forthe three cases: (a) elastic state.(b) limit state and (c) elastoplastic state. The formulasfor the yield pressure and the limit pressure have been obtained.     

THE PROBLEMS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULAR PLATE（II）

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THE PROBLEMS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULA RPLATE（I）

ＴＨＥＰＲＯＢＬＥＭＳＯＦＴＨＥＮＯＮＬＩＮＥＡＲＵＮＳＹＭＭＥＴＲＩＣＡＬＢＥＮＤＩＮＧＦＯＲＣＹＬＩＮＤＲＩＣＡＬＬＹＯＲＴＨＯＴＲＯＰＩＣＣＩＲＣＵＬＡＲＰＬＡＴＥ（Ｉ）ＱｉｎＳｈｅｎｇ－Ｉｉ（秦圣立）ＨｕａｎｇＪｉａ－ｙｉｎ（黄家寅）（Ｑｕｆ...     

The nonaxisymmetric elastoplastic state of isotropic and cylindrically orthotropic solids of revolution under nonisothermal loading

A technique for numerical analysis of the nonaxisymmetric elastoplastic stress-strain state of laminated isotropic and cylindrically orthotropic bodies of revolution under nonisothermal loading with allowance for its history is stated. The strain of isotropic materials is described by the equations of the theory of strain along small-curvature trajectories, while Hooke's law is used to describe the strain of orthotropic materials. The necessity of accounting for the loading history is shown by an example of a nonaxisymmetrically heated sandwich solid of revolution. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 2, pp. 83–90, February, 2000.