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Extra info for Stability Loss and Buckling Delamination: Three-Dimensional Linearized Approach for Elastic and Viscoelastic Composites

Example text

78). 0 Compare the values of t3D:cr: with the corresponding ones calculated with employing critical deformation method (Gerard and Gilbert 1958). Remind that the critical deformation method has been explained in the previous subsection. 15. These . values ð1Þ are calculated for the various a in the case where q ¼ 0:1; Eð2Þ E0 ¼ 5; h=Rþ ¼ 0:5 and x ¼ 0:5. At the same time, in this table the corresponding values 0 0 of t3D:cr: (upper number) are also illustrated. The comparison the values of tcdm:cr: 0 with corresponding values of t3D:cr: shows that the critical deformation method does not acceptable for determination of the critical time for the stability loss of the hollow cylinder made from viscoelastic composite material.

36) coincide with the corresponding equations of the TDLTS. Therefore, to solve the obtained equation systems, according to the monograph (Guz 1999), in the cylindrical system of coordinates we can use the following representations. 1 o o2 1 1 o2 ð1Þ wÀ v; " uh ¼ À w À v; r oh r r ohoz oroz    2 À Ã Á "Ã D 1 þ G " þG " Ã À1 A " Ã þ rð0Þ o v; ¼ A 13 11 zz oz2 " uðr1Þ ¼ " uðz1Þ D1 ¼ ð2:37Þ o2 1 o 1 o2 þ þ : or 2 r or r oh2 The functions w and v are determined from the equations. 33) we find the solution to the Eq.

14) can also be determined as the values of the first approximation by taking the obvious changes into account. However, as follows from the structure of the Eq. 18), for stability loss problems, the consideration of only the zeroth and first approximation is sufficient, because accounting the second and subsequent approximation does not change the values of the critical parameters. The original of the south values is determined by employing the method (Schapery 1962, 1978), according to which, for instance, the original of the displacement uðr1Þ ðr; h; t3 ; tÞ is determined through the expression    uðr1Þ ðr; h; t3 ; tÞ % s" uðr1Þ ðr; h; t3 ; tÞ  : ð2:43Þ s¼1=ð2tÞ Now we consider the selection of the stability loss criterion.

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