On Choosing Effective Symmetry Classes for Elasticity Tensors
نویسندگان
چکیده
منابع مشابه
Symmetry Classes for Even-order Tensors
The purpose of this article is to give a complete and general answer to the recurrent problem in continuum mechanics of the determination of the number and the type of symmetry classes of an even-order tensor space. This kind of investigation was initiated for the space of elasticity tensors. Since then, different authors solved this problem for other kinds of physics such as photoelectricity, ...
متن کاملOn the Dimensions of Cyclic Symmetry Classes of Tensors
The dimensions of the symmetry classes of tensors, associated with a certain cyclic subgroup of $m which is generated by a product of disjoint cycles is explicitly given in terms of the generalized Ramanujan sum. These dimensions can also be expressed as the Euler φ-function and the Möbius function.
متن کاملNon-Vanishing and Orthogonal Basis of Symmetry Classes of Tensors
By Cayley’s theorem, any finite group G of order n can be regarded as a subgroup of the symmetric group $n. Let χ be any irreducible complex character of G and let V n χ (G) denote the symmetry classes of tensors associated with G and χ. In this paper assuming the Cayley representation of G, we obtain a formula for the dimension of V n χ (G) and discuss its non-vanishing in general. A necessary...
متن کاملOn effective transversely isotropic elasticity tensors based on Frobenius and L2 operator norms
Abstract A generally anisotropic elasticity tensor, which might be obtained from physical measurements, can be approximated by a tensor belonging to a particular material-symmetry class; we refer to such a tensor as the effective tensor. The effective tensor is the closest to the generally anisotropic tensor among the tensors of that symmetry class. The concept of closeness is formalized in the...
متن کاملinduced operators on symmetry classes of polynomials
in this paper, we give a necessary and sufficient condition for the equality of two symmetrized decomposable polynomials. then, we study some algebraic and geometric properties of the induced operators over symmetry classes of polynomials in the case of linear characters.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Quarterly Journal of Mechanics and Applied Mathematics
سال: 2010
ISSN: 0033-5614,1464-3855
DOI: 10.1093/qjmam/hbq023