Exact piezothermoelastic solution of simply-supported orthotropic circular cylindrical panel in cylindrical bending

Summary This work presents an exact piezothermoelastic solution of infinitely long, simply supported, cylindrically orthotropic, piezoelectric, radially polarised, circular cylindrical shell panel in cylindrical bending under thermal and electrostatic excitation. The general solution of the governing differential equations is obtained by separation of variables. The displacements, electric potential and temperature are expanded in appropriate Fourier series in the circumferential coordinate to satisfy the boundary conditions at the simply-supported longitudinal edges. The governing equations reduce to Euler-Cauchy type of ordinary differential equations. Their general solution involves six constants for each Fourier component. These are solved from the algebraic equations obtained by satisfying the boundary conditions at the lateral surfaces. The solution of the inverse problem of inferring the applied temperature field from the given measured distribution of electrical potential difference between the lateral surfaces of the shell has also been presented. Numerical results are presented for typical thermal and electrostatic loadings for various values of radius to thickness ratio.     

General solution for the coupled equations of transversely isotropic magnetoelectroelastic solids

IntroductionMechanicsandphysicsofmediapossessingsimultaneouslypiezoelectric ,piezomagneticandmagnetoelectriceffects ,namely ,magnetoelectroelasticsolids,haveattractedmoreandmoreattentionduetotheirgreatpotentialapplicationsinthetechnologiesofsmartandadaptivematerialsystem[1] .Sometheoreticalinvestigationsappearedintheliteratureinclude :1)Theexistenceproblemofsurfacewavesinsemi_infiniteanisotropicmagnetoelectroelasticmediawithvariousboundaryconditions[2 ,3 ] ;2 )Green’sfunctions[4～ 7] ;3)Inho…     

Complete general solution of Stokes equations for plane boundaries

The completeness of a representation for a solution of Stokes equations is proved which is suitable for solving problems which involve plane boundaries. We discuss two theorems for Stokes flow past a plane boundary with different boundary conditions and illustrate them with examples.     

General solutions of coupled thermoelastic problem

ＩｎｔｒｏｄｕｃｔｉｏｎＷｈｅｎｔｈｅｈｅａｔｃｏｎｄｕｃｔｉｏｎｅｑｕａｔｉｏｎｉｎｖｏｌｖｅｓｔｈｅｔｅｒｍｏｆｄｅｆｏｒｍａｔｉｏｎａｎｄｔｈｅｒｍｏｅｌａｓｔｉｃｅｑｕａｔｉｏｎｓｃｏｎｔａｉｎｔｅｍｐｅｒａｔｕｒｅ,ｔｈｉｓｋｉｎｄｏｆｐｒｏｂｌｅｍｉｓｃａｌｌｅｄｃｏｕｐｌｅｄｔｈｅｒｍｏｅｌａｓｔｉｃｐｒｏｂｌｅｍ,ｗｈｉｃｈｔｅｍｐｅｒａｔｕｒｅｆｉｅｌｄａｎｄｅｌａｓｔｉｃｆｉｅｌｄｍｕｓｔｂｅｓｏｌｖｅｄｓｉｍｕｌｔａｎｅｏｕｓｌｙ[1,2].Ｉｎｇｅｎｅｒａｌ,ｔｈｅｅｑｕａｔｉｏ…     

热弹性通解完备性的一个新证明

关于线性各向同性热弹性问题,M.A.Biot提供了一个通解表达式,A.Verruijt证明了这个通解式的完备性。但是此证明十分冗长.本文提供一个完备性证明,这个证明比[2]的证明要简明得多.     

Thermoelastic problems in the half space—An application of the general solution in elasticity

In this paper, some thermoelastic problems in the half space are studied by using the general solutions of the elastic equations. The method presented here is extremely effective for the axisymmetric problems of the half space as well as the half plane problems.     

各向异性矩形薄板弯曲问题的一般解

给出了各向异性矩形薄板弯曲问题微分方程的一般解。可以求解任意载荷作用下各种边界的弯曲问题。以四边固支的正方形板为例进行了数值计算。     

ON THE GENERAL SOLUTION OF CYLINDRICAL SHELL EQUATIONS

ＯＮ　ＴＨＥ　ＧＥＮＥＲＡＬ　ＳＯＬＵＴＩＯＮ　ＯＦ　ＣＹＬＩＮＤＲＩＣＡＬ　ＳＨＥＬＬ　ＥＱＵＡＴＩＯＮＳＰｅｔｅｒＹｉＸｕｅ（薛毅）；ＸｕｅＤａｗｅｉ（薛大为）（ＲｅｃｅｉｖｅｄＯｃｔ．１６，１９９５）Ａｂｓｔｒａｃｔ：Ｉｔｉｓｐｒｏｖｅｄｍａｔ...     

Constructions of the general solution for a system of partial differential equations with variable coefficients

Solving partial differential equations has not only theoretical significance,but alsopractical value.In this paper.by the property of conjugate operator.we give a method toconstruct the general solutions of a system of partial differential equations.     

A general solution and the application of space axisymmetric problem in piezoelectric material

ＡＧＥＮＥＲＡＬＳＯＬＵＴＩＯＮＡＮＤＴＨＥＡＰＰＬＩＣＡＴＩＯＮＯＦＳＰＡＣＥＡＸＩＳＹＭＭＥＴＲＩＣＰＲＯＢＬＥＭＩＮＰＩＥＺＯＥＬＥＣＴＲＩＣＭＡＴＥＲＩＡＬＷａｎｇＺｉ－ｋｕｎｇ（王子昆）ＣｈｅｎＧｅｎｇ－ｃｈａｏ（陈庚超）（ＸｉａｎＪｉａｏ...     

Three-dimensional solution for a hybrid cylindrical shell under axisymmetric thermoelectric load

Summary An exact axisymmetric piezothermoelastic solution is presented for a simply-supported hybrid cylindrical shell made of cross-ply composite laminate and piezoelectric layers. Numerical results for hybrid shells are presented for sinusoidal and central band thermal and electrical loads. The effect of the loading, the radius-to-thickness ratio, the span-to-radius ratio and the number of layers of the substrate on the response is investigated. The interface between the substrate and the actuated piezoelectric layer has been found to be subjected to high shear stress. It has been shown that the maximum values of the deflection and the stresses, due to thermal load, can be appreciably reduced by appropriate application of actuation potential. Accepted for publication 13 October 1996     

Numerical-analytical solution of plane problems in thermoelasticity

The scaled-boundary method is used as a numerical-analytical method to solve problems of thermoelasticity. As an example, the stress intensity factor for a heated thin circular orthotropic disk with an internal crack is evaluated __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 122–126, December 2007.     

Exact solution for in-plane static problems of circular beams made of functionally graded materials

Exact analytical solutions of in-plane static problems of circular beams with uniform cross-section made of functionally graded material (FGM) are obtained. Material properties are assumed to be varying arbitrarily through the thickness. The effects of axial extension and shear deformations are considered. The differential equation system is solved exactly using the initial values method. The circumferential stress distribution on the cross-section is also obtained. The results are compared with those of rather complex approaches in the literature, such as elasticity approach, and the comparison shows an excellent agreement. Effects of power law exponent and radius-to-height ratio of the beam on circumferential stress distribution and displacements are investigated.     

The general solution for axial symmetrical bending of nonhomogeneous circular plates resting on an elastic foundation

In this paper,a new method,the exact analytic method,is presented on the basis of stepreduction method.By this method,the general solution for the bending of nonhomogenouscircular plates and circular plates with a circular hole at the center resting,on an elastfcfoundation is obtained under arbitrary axial symmetrical loads and boundary conditions.The uniform convergence of the solution is proved.This general solution can also be applieddirectly to the bending of circular plates without elastic foundation.Finally,it is onlynecessary to solve a set of binary linear algebraic equation.Numerical examples are givenat the end of this paper which indicate satisfactory results of stress resultants anddisplacements can be obtained by the present method.     

A general method for the incremental solution of elastic-plastic problems

Summary A general iterative method for the incremental solution of elastic-plastic problems is described. The convergence of the procedure on the rigorous solution is demonstrated.

---

Sommario Si espone un procedimento iterativo generale per la soluzione incrementale dei problemi elasto-plastici. Si dimostra la convergenza del procedimento verso la soluzione effettiva.

---

---

The results presented in this paper were obtained in the course of research sponsored by the C.N.R., Gruppo Plasticità     

Nonlocal coupled thermoelastic wave propagation band structures of nano-scale phononic crystal beams based on GN theory with energy dissipation: An analytical solution

This paper deals with the band structures of thermoelastic waves in nano-scale phononic crystal or metamaterial beams considering nano-size effects. The nonlocal coupled thermoelastic governing equations are derived using the Green–Naghdi theory of the generalized coupled thermoelasticity with energy dissipation and Eringen’s nonlocal theory. The derived governing equations are analytically solved and the field quantities including the temperature and the deflection are obtained in the closed forms. Using the proposed analytical solution, the transfer matrix between two unit-cells are obtained using the thermal and mechanical continuity conditions on the interfaces between the unit-cells and between the two sections of each unit-cell. The band structures of the phononic crystals are obtained using the Bloch–Floquet theorem. The detailed discussions are presented for the band structures of nonlocal thermoelastic waves in nano-scale aluminum/epoxy phononic crystal or metamaterial beams. Also, the effects of the small-scale parameter and the thickness of the epoxy layers on the band structures are studied and discussed by using the derived analytical solution.     

A note on general solution of Stokes equations

Li et al. (2015) claim that it is sufficient to use two harmonic functions to express the general solution of Stokes equations. In this paper, we demonstrate that this is not true in a general case and that we in fact need three scalar harmonic functions to represent the general solution of Stokes equations (Venkatalaxmi et al., 2004).     

Towards the solution of finite plane-strain problems for compressible elastic solids

A new approach to the solution of finite plane-strain problems for compressible Isotropie elastic solids is considered. The general problem is formulated in terms of a pair of deformation invariants different from those normally used, enabling the components of (nominal) stress to be expressed in terms of four functions, two of which are rotations associated with the deformation. Moreover, the inverse constitutive law can be written in a simple form involving the same two rotations, and this allows the problem to be formulated in a dual fashion.For particular choices of strain-energy function of the elastic material solutions are found in which the governing differential equations partially decouple, and the theory is then illustrated by simple examples. It is also shown how this part of the analysis is related to the work of F. John on harmonic materials.Detailed consideration is given to the problem of a circular cylindrical annulus whose inner surface is fixed and whose outer surface is subjected to a circular shear stress. We note, in particular, that material circles concentric with the annulus and near its surface decrease in radius whatever the form of constitutive law within the given class. Whether the volume of the material constituting the annulus increases or decreases depends on the form of law and the magnitude of the applied shear stress.     

A general solution of the axisymmetric contact problem for biphasic cartilage layers

A unilateral axisymmetric contact problem for articular cartilage layers is considered. The articular cartilages bonded to subchondral bones are modeled as biphasic materials consisting of a solid phase and a fluid phase. It is assumed that the subchondral bones are rigid and shaped like bodies of revolution with arbitrary convex profiles. The obtained closed-form analytical solution is valid over time periods compared with the typical diffusion time and can be used for increasing loading.