ISSN:
1573-2681
Keywords:
elasticity
;
anisotropic
;
Green's function.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
Notes:
Abstract The three Barnett-Lothe tensors H, L, S appear often in the Stroth formalism of two-dimensional deformations of anisotropic elastic materials [1–3]. They also appear in certain three-dimensional problems [4, 5]. The algebraic representation of H, L, S requires computation of the eigenvalues pv(v=1,2,3) and the normalized eigenvectors (a, b). The integral representation of H, L, S circumvents the need for computing p v(v=1,2,3) and (a, b), but it is not simple to integrate the integrals except for special materials. Ting and Lee [6] have recently obtained an explicit expression of H for general anisotropic materials. We present here the remaining tensors L, S using the algebraic representation. They key to our success is the obtaining of the normalization factor for (a, b) in a simple form. The derivation of L and S then makes use of (a, b) but the final result does not require computation of (a, b), which makes the result attractive to numerical computation. Even though the tensor H given in [6] is in terms of the elastic stiffnesses Cμ v while the tensors L, S presented here are in terms of the reduced elastic compliances s′ μv , the structure of L, S is similar to that of H. Following the derivation of H, we also present alternate expressions of L, S that remain valid for the degenerate cases p 1 p 2 and p1=p2 = p 3. One may want to compute H, L, S using either C μv or s′ μv v, but not both. We show how an expression in Cμ v can be converted to an expression in s′ μv v, and vice versa. As an application of the conversion, we present explicit expressions of the extic equation for p in Cμ v and s′ μv v.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1007394313111
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