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991.
The paper proposes a modification of the mixed variational principle from which stationarity conditions are derived in the
form of a mixed system of equations resolved for the first derivatives of the displacement and stress components acting in
a plane perpendicular to one of the coordinate axes. The variational principle allows decreasing the dimension of the problem
of elasticity thus reducing the system of equations to a canonical form. The modified mixed principle helps immediately obtain
a canonical system of equations for various applied theories. This possibility is demonstrated with the example of the Timoshenko
theory of plates
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 55–62, May 2007. 相似文献
992.
David J. Steigmann 《International Journal of Non》2007,42(2):233-240
Non-linear plate theory for thin prismatic elastic bodies is obtained by estimating the total three-dimensional strain energy generated in response to a given deformation in terms of the small plate thickness. The Euler equations for the estimate of the energy are regarded as the equilibrium equations for the thin plate. Included among them are algebraic formulae connecting the gradients of the midsurface deformation to the through-thickness derivatives of the three-dimensional deformation. These are solvable provided that the three-dimensional strain energy is strongly elliptic at equilibrium. This framework yields restrictions of the Kirchhoff-Love type that are usually imposed as constraints in alternative formulations. In the present approach they emerge as consequences of the stationarity of the energy without the need for any a priori restrictions on the three-dimensional deformation apart from a certain degree of differentiability in the direction normal to the plate. 相似文献
993.
994.
S 《International Journal of Solids and Structures》2007,44(25-26):8407-8423
The three matrices L(v), S(v) and H(v), appearing frequently in the investigations of the two-dimensional steady state motions of elastic solids, are expressed explicitly in terms of the elastic stiffness for general anisotropic materials. The special cases of monoclinic materials with a plane of symmetry at x3 = 0, x1 = 0, and x2 = 0 are all deduced. Results for orthotropic materials appearing in the literature may be recovered from the present explicit expressions. 相似文献
995.
G. deBotton I. Hariton E.A. Socolsky 《Journal of the mechanics and physics of solids》2006,54(3):533-559
The response of a transversely isotropic fiber-reinforced composite made out of two incompressible neo-Hookean phases undergoing finite deformations is considered. An expression for the effective energy-density function of the composite in terms of the properties of the phases and their spatial distribution is developed. For the out-of-plane shear and extension modes this expression is based on an exact solution for the class of composite cylinder assemblages. To account for the in-plane shear mode we incorporate an exact result that was recently obtained for a special class of transversely isotropic composites. In the limit of small deformation elasticity the expression for the effective behavior agrees with the well-known Hashin-Shtrikman bounds. The predictions of the proposed constitutive model are compared with corresponding numerical simulation of a composite with a hexagonal unit cell. It is demonstrated that the proposed model accurately captures the overall response of the periodic composite under any general loading modes. 相似文献
996.
Maria Luisa Tonon 《Journal of Elasticity》2002,69(1-3):15-39
This paper deals with the propagation of acceleration waves in constrained linear elastic materials, within the framework
of the so-called linearized finite theory of elasticity, as defined by Hoger and Johnson in [12, 13]. In this theory, the
constitutive equations are obtained by linearization of the corresponding finite constitutive equations with respect to the
displacement gradient and significantly differ from those of the classical linear theory of elasticity. First, following the
same procedure used for the constitutive equations, the amplitude condition for a general constraint is obtained. Explicit
results for the amplitude condition for incompressible and inextensible materials are also given and compared with those of
the classical linear theory of elasticity. In particular, it is shown that for the constraint of incompressibility the classical
linear elasticity provides an amplitude condition that, coincidently, is correct, while for the constraint of inextensibility
the disagreement is first order in the displacement gradient. Then, the propagation condition for the constraints of incompressibility
and inextensibility is studied. For incompressible materials the propagation condition is solved and explicit values for the
squares of the speeds of propagation are obtained. For inextensible materials the propagation condition is solved for plane
acceleration waves propagating into a homogeneously strained material. For both constraints, it is shown that the squares
of the speeds of propagation depend by terms that are first order in the displacement gradient, while in classical linear
elasticity they are constant.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
997.
本文从轴对称板壳理论的基本方程出发,通过建立Green函数,导出了轴对称线载荷下解的一般表述式,由此可以求出任意轴对称载荷下的解,然后本文分别讨论了圆板和扁球壳受线载问题的解,文中的结果适用于各种边界条件。 相似文献
998.
The complementary energy momentum tensor, expressed in terms of the spatial gradients of stress and couple-stress, is used to construct the and conservation integrals of infinitesimal micropolar elasticity. The derived integrals are related to the release rates of the complementary potential energy associated with a defect translation or rotation. A nonconserved integral is also derived and related to the energy release rate that is associated with a self-similar cavity expansion. The results are compared to those obtained on the basis of the classical energy momentum tensor, expressed in terms of the spatial gradients of displacement and rotation, and the release rates of the potential energy. It is shown that the evaluation of the complementary conservation integrals is of similar complexity to that of the classical conservation integrals, so that either can be effectively used in the energetic analysis of the mechanics of defects. The two-dimensional versions of the dual conservation integrals are then derived and applied to an out-of-plane shearing of a long cracked slab. 相似文献
999.
The Mullins effect in the small amplitude transverse vibration of a rubber cord is investigated. The fundamental frequency is determined for a specific class of stress-softening materials. Analytical relations for the cord vibration frequency are illustrated graphically for three phenomenological models. These results demonstrate the role of the material parameters and exhibit response characteristic of those reported in experiments by others and subsequently described here in new experiments. Frequency versus stretch results for two kinds of non-Gaussian molecular network models for rubber elasticity are compared with experimental data for four varieties of rubber cords, for each of which only three experimentally determined material constants are needed. It is shown that the theoretical predictions stand in excellent agreement with test data. 相似文献
1000.
The problem of the curved bar subjected to an arbitrarily distributed loading on the surfacesr=a andr=b is solved by using the method of complex functions and expanding the boundary conditions atr=a andr=b into Fourier series. Then another paradox in the two-dimensional theory of elasticity is discovered, i. e., the classical solution becomes infinite when the curved bar is subjected to a uniform loading or when the angle included between the two ends of the curved bar 2 is equal to 2 and the curved bar is subjected to a sine or cosine loading. In this paper the paradox is resolved successfully and the solutions for the paradox are obtained. Moreover, the modified classical solution which remains bounded as 2 approaches 2 is provided. 相似文献