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11.
12.
The purpose of this research is to investigate the effects of material inhomogeneity on the response of linearly elastic isotropic solid circular disks or cylinders, rotating at constant angular velocity about
a central axis. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e., materials
with spatially varying properties tailored to satisfy particular engineering applications. The analog of the classic problem
for a homogeneous isotropic rotating solid disk or cylinder is considered. The special case of a body with Young"s modulus depending on the
radial coordinate only, and with constant Poisson"s ratio, is examined. For the case when the Young"s modulus has a power-law
dependence on the radial coordinate, explicit exact solutions are obtained. It is shown that the stress response of the inhomogeneous disk (or cylinder) is significantly different from that of the homogeneous body. For example, the maximum radial and hoop
stresses do not, in general, occur at the center as in the case for the homogeneous material. Furthermore, for the case where the Young"s
modulus increases with radial distance from the center, it is shown that radially symmetric solutions exist provided the rate of growth of
the Young"s modulus is, at most, cubic in the radial variable. It is also shown for the general inhomogeneous isotropic case how the material inhomogeneity may
be tailored so that the radial and hoop stress are identical throughout the disk.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
13.
Upper and lower bounds are derived for the shear stress as it is determined by Saint-Venant's theory of flexure, and used to establish the asymptotic character of the classical Strength of Materials formula in the limit of vanishing thickness.
Résumé On dérive des limites supérieures et inférieures des contraintes tangentielles suivant la théorie de la flexion de Saint-Venant, que l'on utilise aux fins d'établir le caractère asymptotique de la formule de la Résistance des Matériaux dans le cas limite d'une épaisseur extrêmement petite.相似文献
14.
The purpose of this research is to investigate the simple torsion problem for a solid circular cylinder composed of isotropic
hyperelastic incompressible materials with limiting chain extensibility. Three popular models that account for hardening at
large deformations are examined. These models involve a strain-energy density which depends only on the first invariant of
the Cauchy–Green tensor. In the limit as a polymeric chain extensibility tends to infinity, all of these models reduce to
the classical neo-Hookean form. The main mechanical quantities of interest in the torsion problem are obtained in closed form.
In this way, it is shown that the torsional response of all three materials is similar. While the predictions of the models
agree qualitatively with experimental data, the quantitative agreement is poor as is the case for the neo-Hookean material.
In fact, by using a global universal relation, it is shown that the experimental data cannot be predicted quantitatively by
any strain-energy density which depends solely on the first invariant. It is shown that a modification of the strain energies
to include a term linear in the second invariant can be used to remedy this defect. Whether the modified strain-energies,
which reflect material hardening, are a feasible alternative to the classic Mooney–Rivlin model remains an open question which
can be resolved only by large strain experiments.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
15.
The axial decay of Saint-Venant end effects is investigated for anti-plane shear deformations of semi-infinite generally laminated
anisotropic strips. Imperfect bonding conditions are imposed at the interfaces. The analytical approach, using a displacement
field which decays exponentially in the axial direction, gives rise to a transcendental equation for the real eigenvalues.
The decay rate for the stresses is given in terms of the smallest positive eigenvalue. Laminated strips with periodic layout
are then considered. In the presence of imperfect bonding, the effective shear elastic moduli, computed through a homogenization
method, depend on the total number of slipping interfaces in the laminate. Numerical examples confirm that the decay lengths
computed with effective shear moduli represent the asymptotic values (for an increasing number of layers) for those of periodically
laminated strips.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
16.
A bifurcation problem for a compressible nonlinearly elastic medium: growth of a micro-void 总被引:8,自引:0,他引:8
In this paper, we carry out an explicit analysis of a bifurcation problem for a solid circular cylinder composed of a particularcompressible nonlinearly elastic material. This problem is concerned with the bifurcation of a solid body into a configuration involving an internal cavity. A discussion of its physical interpretation is then carried out. In particular, it is shown that this model may be used to describe the nucleation of a void from apre-existing micro-void. 相似文献
17.
The purpose of this research is to further investigate the effects of material inhomogeneity on the decay of Saint-Venant
end effects in linear isotropic elasticity. This is carried out within the context of anti-plane shear deformations of an
inhomogeneous isotropic elastic solid. The mathematical issues involve the effects of spatial inhomogeneity on the decay rates
of solutions to Dirichlet or Neumann boundary-value problems for a second-order linear elliptic partial differential equation
with variable coefficients on a semi-infinite strip. In previous work [1], the elastic coefficients were assumed to be smooth
functions of the transverse coordinate so that the material was inhomogeneous in the lateral direction only. Here we develop
a new technique, based on a change of variable, to study generally inhomogeneous isotropic materials. The governing partial
differential equation is transformed to a Helmholtz equation with a variable coefficient, which facilitates analysis of the
influence of material inhomogeneity on the diffusion of end effects. For certain classes of inhomogeneous materials, an explicit
optimal decay estimate is established. The results of this paper are applicable to continuously inhomogeneous materials and,
in particular, to functionally graded materials.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
18.
The design of a semi-infinite fillet for efficient stress transmission is considered. The problem is treated within the context of anti-plane shear deformations of a homogeneous, isotropic, linearly elastic solid. Under a remote state of simple shear, it is desired to determine the shape of the traction-free lateral boundaries of a symmetric plane domain so that the shear stress distribution on the finite end is as uniform as possible. A semi-inverse approach for a particular class of semi-infinite profiles is used to examine this issue. 相似文献
19.
A. Donnachie R. R. Horgan P. V. Landshoff 《Zeitschrift fur Physik C Particles and Fields》1981,10(1):71-76
We explore the validity of using nonrelativistic wave functions for lightly-bound states in relativistic situations. This is shown to be acceptable for scattering problems, but not necessarily for those involving a decay. In the latter case the wave function would need to have special properties. These do not occur for a deuteron-like wave function but do occur for a positronium-like system, the crucial features being that positronium is bound by zero mass exchange. 相似文献
20.