zbMATH — the first resource for mathematics

The buckling of cross-ply laminated non-homogeneous orthotropic composite conical thin shells under a dynamic external pressure. (English) Zbl 1064.74101
Summary: We study the buckling of cross-ply laminated orthotropic truncated circular conical thin shells with variable Young’s moduli and densities in the thickness direction, subjected to a uniform external pressure which is a power function of time. After obtaining the dynamic stability and compatibility equations, we reduce both of them to a time-dependent ordinary differential equation with variable coefficient by using Galerkin method. The critical dynamic and static loading, the corresponding wave numbers, the dynamic factors, critical time and critical impulse are found analytically by applying a Ritz-type variational method. The dynamic behavior of cross-ply laminated truncated conical shells is investigated with: (a) lamina that present variations in the Young’s moduli and densities, (b) different numbers and ordering of layers, (c) variable semi-vertex angles, and (d) external pressures which vary with different powers of time. It is concluded that all these factors contribute to appreciable effects on critical parameters of the problem in question.

74H60 Dynamical bifurcation of solutions to dynamical problems in solid mechanics
74K25 Shells
74E30 Composite and mixture properties
PDF BibTeX Cite
Full Text: DOI