TY - JOUR

T1 - Initial supercritical behavior of buckled transversely isotropic elastic medium

AU - Morozov, N. F.

AU - Tovstik, P. E.

PY - 2011/3

Y1 - 2011/3

N2 - The paper is concerned with a transversely isotropic homogeneous elastic medium subjected to uniform compression in the isotropy plane. The medium becomes unstable in the sense of Hadamard [1] at a definite level of initial strain. The critical strain is established to be uniquely determinate from the system of equations of bifurcation of equilibrium; however, there are many modes of buckling corresponding to this strain. A solution of the system of equations of bifurcation is built in the form of doubly periodic functions sinr 1x 1sinr 2x 2. The uncertainty of the mode of buckling consists in the fact that the wave numbers r 1 and r 2 remain arbitrary. In order to determine the relationship between the wave numbers we examine the initial supercritical behavior of the material. It turns out that the only possible modes are the chess-board mode (with r 1 = r 2) and the corrugation-type mode (when one of the wave numbers r 1 or r 2 vanishes). The initial supercritical equilibrium is shown as being stable.

AB - The paper is concerned with a transversely isotropic homogeneous elastic medium subjected to uniform compression in the isotropy plane. The medium becomes unstable in the sense of Hadamard [1] at a definite level of initial strain. The critical strain is established to be uniquely determinate from the system of equations of bifurcation of equilibrium; however, there are many modes of buckling corresponding to this strain. A solution of the system of equations of bifurcation is built in the form of doubly periodic functions sinr 1x 1sinr 2x 2. The uncertainty of the mode of buckling consists in the fact that the wave numbers r 1 and r 2 remain arbitrary. In order to determine the relationship between the wave numbers we examine the initial supercritical behavior of the material. It turns out that the only possible modes are the chess-board mode (with r 1 = r 2) and the corrugation-type mode (when one of the wave numbers r 1 or r 2 vanishes). The initial supercritical equilibrium is shown as being stable.

KW - Hadamard stability

KW - supercritical strain

KW - transversely isotropic elastic material

UR - http://www.scopus.com/inward/record.url?scp=84859728181&partnerID=8YFLogxK

U2 - 10.3103/S1063454111010110

DO - 10.3103/S1063454111010110

M3 - Article

AN - SCOPUS:84859728181

VL - 44

SP - 44

EP - 50

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -