Exact solutions for variable-thickness inhomogeneous elastic plates under various boundary conditions

In this paper, an exact solution to the governing equations of the bending of a variable-thickness inhomogeneous rectangular plate is presented. The procedure is applicable to variable-thickness inhomogeneous rectangular plates with two opposite edges simply supported. The remaining ones subjected to a combination of clamped, simply supported, and free boundary conditions and between these two edges the plate may have varying thickness. The procedure is valuable in view of the fact that tables of deflections and stresses cannot be presented for variable-thickness inhomogeneous orthotropic plates as for uniform-thickness homogeneous isotropic plates even for commonly encountered loads because the results depend on the inhomogeneity coefficient and the orthotropic material properties instead of a single flexural rigidity. Numerical results, useful for the validation or otherwise of approximate solutions, are tabulated. The influences of the degree of the inhomogeneity, aspect ratio, thickness parameter and degree of non-uniformity on the deflections and stresses are investigated. This paper is partially supported by the Deanship of Scientific Research at King AbdulAziz University (Grant no. 172/427).     

Large deflection analysis of the moderately thick general theta ply laminated plates on nonlinear elastic foundation with various boundary conditions

This paper presents a powerful method i.e. the kinetic Dynamic Relaxation for analyzing general theta ply laminated plates, resting on nonlinear elastic foundation with different boundary conditions. Comprehensive comparison and parametric studies prove accuracy and efficiency of the proposed approach with interesting specifications such as fully vector calculations, independency to configuration, situation and angle of plies so that general theta ply laminated plate with simultaneous coupling between membrane, bending and shear strains could be analyzed as simple as analyzing of symmetric cross ply plate. Moreover, the proposed technique could simply satisfy complicated boundary conditions such as free and movable edges.     

非线性随动强化条件下的安定定理

基于经典的安定理论与随动强化模型的一般性质,将结构在强化过程中的背应力计入Von Mises屈服准则,建立了随动强化条件下结构的静力安定定理;将背应力与对应的塑性应变率的点积在一个载荷循环内的积分计入塑性耗散功,建立了随动强化条件下结构的机动安定定理,扩展了经典安定理论的应用范围。针对两种定理的存在格式进行了理论证明,并以推论形式给出了结构在随动强化条件下静力安定和机动安定另外两种存在格式。结果表明,随动强化材料的安定状态和安定极限不受强化过程的影响,只取决于材料的初始屈服应力和最终屈服应力。     

Existence and uniqueness of periodic solutions for fourth-order nonlinear periodic systems

In this paper, we study the existence, uniqueness and stability of the periodic solutions for fourth-order nonlinear nonhomogeneous periodic systems with slowly changing coefficients by using the method of Liapunor Function. We obtain some sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions of these systems and estimate the extent to which the coefficients are allowed to change.     

Geometrically nonlinear vibration of laminated composite cylindrical thin shells with non-continuous elastic boundary conditions

The geometrically nonlinear forced vibration response of non-continuous elastic-supported laminated composite thin cylindrical shells is investigated in this paper. Two kinds of non-continuous elastic supports are simulated by using artificial springs, which are point and arc constraints, respectively. By using a set of Chebyshev polynomials as the admissible displacement function, the nonlinear differential equation of motion of the shell subjected to periodic radial point loading is obtained through the Lagrange equations, in which the geometric nonlinearity is considered by using Donnell’s nonlinear shell theory. Then, these equations are solved by using the numerical method to obtain nonlinear amplitude–frequency response curves. The numerical results illustrate the effects of spring stiffness and constraint range on the nonlinear forced vibration of points-supported and arcs-supported laminated composite cylindrical shells. The results reveal that the geometric nonlinearity of the shell can be changed by adjusting the values of support stiffness and distribution areas of support, and the values of circumferential and radial stiffness have a more significant influence on amplitude–frequency response than the axial and torsional stiffness.

     

Bending of elastic plates with a physically nonlinear inclusion

An infinite elastic isotropic plate with an elliptical, physically nonlinear inclusion loaded at infinity by uniformly distributed moments is considered. Surface loads are absent. The problem of the stress-strain state of the plate is solved in a closed form. It is shown that, for reasonably general stress-strain relations for the inclusion, the bending-moment field (and the corresponding curvatures) in the inclusion is homogeneous. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 152–157, November–December, 2006.     

Vibrations of polygonal plates with various boundary conditions

The bending vibrations of polygonal (L-shaped) plates with different shapes and boundary conditions are studied. The natural frequencies are calculated using the inverse-iteration and Kantorovich-Vlasov methods. To take the configuration of the domain into account, the fictitious domain method and an analog of the force method of structural mechanics are used. Different trends in the dependence of the lowest natural frequency of an L-shaped plate on its geometry are illustrated for different boundary conditions.Acorrelation between the extreme values of the bending frequency and some relations for the energy characteristics of the plate is established __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 63–72, May 2007.     

Existence of solutions for nonlinear elliptic boundary value problems

IntroductionInRef.[1 ]KannanandLockergivetheexistenceofatleastonesolutionofTy-h(t,y ,… ,y(n- 1) )y=f(t,y ,… ,y(n- 1) )　　 (a相似文献   

APPROXIMATION THEORY OF THREE DIMENSIONAL ELASTIC PLATES AND ITS BOUNDARY CONDITIONS WITHOUT USING KIRCHHOFF－LOVE ASSUMPTIONS

ＡＰＰＲＯＸＩＭＡＴＩＯＮＴＨＥＯＲＹＯＦＴＨＲＥＥＤＩＭＥＮＳＩＯＮＡＬＥＬＡＳＴＩＣＰＬＡＴＥＳＡＮＤＩＴＳＢＯＵＮＤＡＲＹＣＯＮＤＩＴＩＯＮＳＷＩＴＨＯＵＴＵＳＩＮＧＫＩＲＣＨＨＯＦＦ－ＬＯＶＥＡＳＳＵＭＰＴＩＯＮＳＣｈｉｅｎＷｅｉ－ｚａｎｇ（...     

Analytical solutions for thermal vibration of nanobeams with elastic boundary conditions

A nonlocal Euler beam model with second-order gradient of stress taken into consideration is used to study the thermal vibration of nanobeams with elastic boundary.An analytical solution is proposed to investigate the free vibration of nonlocal Euler beams subjected to axial thermal stress.The effects of the nonlocal parameter,thermal stress and stiffness of boundary constraint on the vibration behaviors of nanobeams are revealed.The results show that natural frequencies including the thermal stress are lower than those without the thermal stress when temperature rises.The boundary-constrained springs have significant effects on the vibration of nanobeams.In addition,numerical simulations also indicate the importance of small-scale effect on the vibration of nanobeams.     

On the boundary conditions for transversely isotropic piezoelectric plates

By invoking the theorem of work reciprocity for piezoelectric media, necessary conditions, which the prescribed edge data of the plate must fulfill in order that it should generate a decaying state within the plate, are established through generalizing the method proposed by Gregory and Wan. These decaying state conditions for the case of axisymmetric deformation of a transversely isotropic piezoelectric circular plate when stress and electric displacement conditions are imposed on the plate edge are derived explicitly, which are then used for the formulation of boundary conditions for the plate theory solution (or the interior solution). Also an analytical solution of the axisymmetric decaying state of transversely isotropic piezoelectric circular plates is derived. Furthermore, the corresponding necessary conditions for the axisymmetric deformation of elastic circular plates are indeed reproduced directly.     

Existence of solutions for periodic boundary value problems for second-order integro-differential equations

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔ(Ｅ,｜·｜)ｂｅａｒｅａｌＢａｎａｃｈｓｐａｃｅｗｉｔｈａｐａｒｔｉａｌｏｒｄｅｒｉｎｔｒｏｄｕｃｅｄｂｙａｒｅｇｕｌａｒｃｏｎｅＫｏｆＥ.Ｉｎｔｈｉｓｐａｐｅｒ,ｔｈｅｅｘｉｓｔｅｎｃｅｏｆｓｏｌｕｔｉｏｎｓｏｆｔｈｅｆｏｌｌｏｗｉｎｇｐｅｒｉｏｄｉｃｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓ(ＰＢＶＰ)ｗｉｌｌｂｅｉｎｖｅｓｔｉｇａｔｅｄ:　　(Ⅰ)ｕ″=ｆ(ｔ,ｕ,Ｔｕ)　ａ.ｅ.ｔ∈Ｊ,ｕ(0)=ｕ(ａ),ｕ′(0)=ｕ′(ａ),ｗｈｅｒｅｆ∈Ｃ(Ｊ×Ｅ×Ｅ,Ｅ),Ｊ=[0,ａ](ａ>0),ａｎｄ(Ｔ…     

EXISTENCE THEOREMS OF EXTREMAL SOLUTIONS FOR A CLASS OF NONLINEAR INTEGRO－DIFFERENTIAL EQUATIONS

ＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＳＯＦＥＸＴＲＥＭＡＬＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＩＮＴＥＧＲＯ－ＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＳｏｎｇＧｕａｎｇｘｉｎｇ（宋光兴）（ＲｅｃｅｉｖｅｄＭａｙ４，１９９５；Ｃｏｍ...     

Singular limit of equations for linear viscoelastic fluids with periodic boundary conditions

We consider a one-parameter family of problems, governing, for any fixed parameter, the motion of a linear viscoelastic fluid in a two-dimensional domain with periodic boundary conditions. The asymptotic behavior of each problem is analyzed, by proving the existence of the global attractor. Moreover, letting the parameter go to zero, since the memory effect disappears, we obtain a limiting problem, given by the Navier-Stokes equations. For any fixed parameter, we construct an exponential attractor. The resulting family is robust, meaning that these exponential attractors converge, in an appropriate sense, to an exponential attractor of the limiting problem.