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51.
This paper investigates the problem of an axisymmetric penny shaped crack embedded in an infinite functionally graded magneto electro elastic medium. The loading consists of magnetoelectromechanical loads applied on the crack surfaces assumed to be magneto electrically impermeable. The material’s gradient is parallel to the axisymmetric direction and is perpendicular to the crack plane. An anisotropic constitutive law is adopted to model the material behavior. The governing equations are converted analytically using Hankel transform into coupled singular integral equations, which are solved numerically to yield the crack tip stress, electric displacement and magnetic induction intensity factors. A similar problem but with a different crack morphology, that is a plane crack embedded in an infinite functionally graded magneto electro elastic medium, was considered by the authors in a previous work (Rekik et al., 2012) [25]. While the overall solution schemes look similar, the axisymmetric problem resulted in more mathematical complexities and let to different conclusions with respect to the influence of coupling between elastic, electric and magnetic effects. The main focus of this paper is to study the effect of material non-homogeneity on the fields’ intensity factors to understand further the behavior of graded magnetoelectroelastic materials containing penny shaped cracks and to inspect the effect of varying the crack geometry. 相似文献
52.
Tungyang Chen 《Mechanics Research Communications》2011,38(1):68-71
A novel class of graded cylinders is proposed as neutral inclusions inside host shafts of arbitrary cross-section under Saint-Venant's torsion. The graded cylinder is made of cylindrically orthotropic materials with position varying quantities. The profiles of the two distinct shear moduli in the radial and tangential directions follow specific forms based on an arbitrarily selected function along the radial distance. We show that this type of graded cylinders can serve as universal neutral inclusions within host shafts of arbitrary cross-sections. In addition, we find that the associated warping fields can be exactly determined in terms of simple exponents of the selected function. This suggests that, by tuning the gradation parameter, one can manipulate the warping field of the inserted cylinder without disturbing the fields inside the host shaft. This finding is an original contribution to the existing solvable configurations of composite shafts under torsion. 相似文献
53.
李珍珠 《数学的实践与认识》2004,(4)
引进了分次 wn -模 ,讨论了具有有限分次 FP-自内射维数的 gr凝聚环和分次 wn -模的自反性 .所得的结果推广了 Stentr m,Bass和黄兆泳等人的若干结果 . 相似文献
54.
Mutsuhisa Furukawa Yukinori Hamada Ken Kojio 《Journal of Polymer Science.Polymer Physics》2003,41(20):2355-2364
Functionally graded polyurethane elastomers (FGPUEs) were prepared with two molds fixed at different temperatures (30 and 150 °C). The effects of the molar ratio of the curing agent (60/40, 75/25, or 97/3 1,4‐butane diol/1,1,1‐trimethylol propane) and the molecular weight of the polymer glycol (number‐average molecular weight = 2000 or 3000) on the molecular aggregation state and mechanical properties of the FGPUEs were investigated with differential scanning calorimetry, polarized optical microscopy, dynamic viscoelastic measurements, and tensile tests. The aggregation state of the FGPUEs was changed continuously from the one side (lower temperature side) to the other side (higher temperature side); for example, the glass‐transition temperature gradually increased in this direction. Also, the number of spherulites formed in the FGPUEs increased in the same manner. In the mechanical tests, the tensile strength and elongation at break of the lower temperature side were higher than those of the higher temperature side. This was correlated with the strong phase separation of the lower temperature side. The poly(oxytetramethylene glycol)‐based FGPUE with a chain extender of 75 wt % showed the largest degree of the temperature gradient. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2355–2363, 2003 相似文献
55.
We develop a simple theory of André-Quillen cohomology for commutative differential graded algebras over a field of characteristic zero. We then relate it to the homotopy groups of function spaces and spaces of homotopy self-equivalences of rational nilpotent CW-complexes. This puts certain results of Sullivan in a more conceptual framework. 相似文献
56.
A comprehensive treatment of fracture of functionally graded materials (FGMs) is provided. It is assumed that the material
properties depend only on the coordinate perpendicular to the crack surfaces and vary continuously along the crack faces.
By using a laminated composite plate model to simulate the material non-homogeneity, an algorithm for solving the system based
on Laplace transform and Fourier transform techniques is presented. Unlike earlier studies that considered certain assumed
property distributions and a single crack problem, the current investigation studies multiple crack problem in the FGMs with
arbitrarily varying material properties. Transient thermal stresses are presented.
Project supported by the National Natural Science Foundation of China (Nos 10102004 and 19902003). 相似文献
57.
This paper presents a translation of a theorem of Cartan into an equivariant setting. This work is largely based on the study
of the homotopical algebra in the sense of Quillen of the category of simplicial objects over the category of rationalO
g-vector spaces. The application is a solution to the equivariant commutative cochain problem. This solution is slightly better
than the solution obtained earlier by Triantafillou in that the transformation groupG need not be finite. 相似文献
58.
Locking-free DGFEM for elasticity problems in polygons 总被引:1,自引:0,他引:1
The h-version of the discontinuous Galerkin finite element method(h-DGFEM) for nearly incompressible linear elasticity problemsin polygons is analysed. It is proved that the scheme is robust(locking-free) with respect to volume locking, even in the absenceof H2-regularity of the solution. Furthermore, it is shown thatan appropriate choice of the finite element meshes leads torobust and optimal algebraic convergence rates of the DGFEMeven if the exact solutions do not belong to H2. 相似文献
59.
60.
《Journal of Pure and Applied Algebra》2023,227(6):107311
The present paper, though inspired by the use of tensor hierarchies in theoretical physics, establishes their mathematical credentials, especially as genetically related to Lie algebra crossed modules. Gauging procedures in supergravity rely on a pairing – the embedding tensor – between a Leibniz algebra and a Lie algebra. Two such algebras, together with their embedding tensor, form a triple called a Lie-Leibniz triple, of which Lie algebra crossed modules are particular cases. This paper is devoted to showing that any Lie-Leibniz triple induces a differential graded Lie algebra – its associated tensor hierarchy – whose restriction to the category of Lie algebra crossed modules is the canonical assignment associating to any Lie algebra crossed module its corresponding unique 2-term differential graded Lie algebra. This shows that Lie-Leibniz triples form natural generalizations of Lie algebra crossed modules and that their associated tensor hierarchies can be considered as some kind of ‘lie-ization’ of the former. We deem the present construction of such tensor hierarchies clearer and more straightforward than previous derivations. We stress that such a construction suggests the existence of further well-defined Leibniz gauge theories. 相似文献