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51.
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
52.
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
53.
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
54.
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
55.
Zhi CHENG Yu YE 《数学学报(英文版)》2007,23(6):965-972
We introduce the category of t-fold modules which is a full subcategory of graded modules over a graded algebra. We show that this subcategory and hence the subcategory of t-Koszul modules are both closed under extensions and cokernels of monomorphisms. We study the one-point extension algebras, and a necessary and sufficient condition for such an algebra to be t-Koszul is given. We also consider the conditions such that the category of t-Koszul modules and the category of quadratic modules coincide. 相似文献
56.
57.
《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
58.
具有不同功能梯度分布函数的板件的三维分析 总被引:1,自引:0,他引:1
发展了一种新颖的功能梯度结构分析的细观元法。细观元法对结构的常规有限单元内部设置密集细观单元以反映材料特性梯度变化,又通过协调条件将各细观元结点自由度转换为同一常规有限元自由度,再上机计算。这种细观元法既能充分反映材料功能梯度变化特性;而其计算单元又和常规有限元一样,是一种针对功能梯度结构分析的有效数值方法。文中通过细观元技术进行计算、分析,给出了具有不同功能梯度分布函数板件的力学量三维分布形态。 相似文献
59.
60.
In this paper, based on the theory of multiple scattering of elastic waves, employing wave functions expansion method, multiple scattering and strain energy density in semi-infinite functional graded materials with a circular cavity are investigated, the analytical solution of the problem is derived, and the numerical solution of the strain energy density factors around the cavity is also presented. The effects of the distance between the cavity and the edge of the materials, the wave number and the non-homogeneous parameter of materials on strain energy density factors are analyzed. From analysis, it can be seen that when the non-homogeneous parameter of materials is less than zero, it has less influence on the maximum strain energy density factor around the cavity; however, it has greater influence on the distribution of strain energy density factors around the cavity. When the non-homogeneous parameter of materials is greater than zero, it has greater influence on both the maximum strain energy density factor and the distribution of strain energy density factor around the cavity, especially in the case that the distance between the cavity and the edge is comparatively little. 相似文献