Abstract
A thin-walled structure is homogeneously embeddable if it can be obtained by carving it out of a homogeneous material block or, in other words, if it is materially defect-free. Explicit analytic and geometric conditions for the embedded homogeneity of plane linearly elastic beams are derived and discussed. In the geometric setting, a prominent role is played by the properties of the hodograph of uniaxial material tensor fields defined on the beam axis.
Keywords
Get full access to this article
View all access options for this article.
References
1.
Wang
C-C
. Material uniformity and homogeneity in shells . Arch Ration Mech Anal 1972 ; 47 : 343 –368 .
2.
Epstein
M
De León
M
. On uniformity of shells . Int J Sol Struct 1998 : 35 (17 ): 2173 –2182 .
3.
Steigmann
D
. Fluid films with curvature elasticity . Arch Ration Mech Anal 1999 : 150 (2 ): 127 –152 .
4.
Eremeyev
VA
Pietraszkiewicz
W
. Local symmetry group in the general theory of elastic shells , J Elasticity 2006 ; 85 (2 ): 125 –152 .
5.
Šilhavý
M
. The Mechanics and Thermodynamics of Continuous Media . New York : Springer-Verlag , 1997 .
6.
Jordan
C
. Sur la théorie des courbes dans l’espace àn dimensions , C R Acad Sci Paris 1874 ; 79 : 795 –797 .
7.
8.
Nalty
K
. Curves of constant curvatures in four dimensional spacetime , www.kurtnalty.com/ThreeCurvatures.pdf, pp.1 –31 , 2011 .
9.
Ozdamar
E
Hacisalihoglu
HH
. Characterization of spherical curves in Euclidean n -space , Comm Fac Sci Univ Ankara 1974 ; 23A : 122 –124 .