The Nonlinear Instability Modes of Dished Shallow Shells under Circular Line Loads

Abstract

This paper investigated the nonlinear stability problem of dished shallow shells under circular line loads. We derived the dimensionless governing differential equations of dished shallow shell under circular line loads according to the nonlinear theory of plates and shells and solved the governing differential equations by combing the free-parameter perturbation method (FPPM) with spline function method (SFM) to analyze the nonlinear instability modes of dished shallow shell under circular line loads. By analyzing the nonlinear instability modes and combining with concrete computational examples, we obtained the variation rules of the maximum deflection area of initial instability with different geometric parameters and loading action positions and discussed the relationship between the initial instability area and the maximum deflection area of initial instability. The results obtained from this paper provide some theoretical basis for engineering design and instability prediction and control of shallow-shell structures.

Efficient Analytical Model for Long‐Term Performance of Laminated Tube with Viscoelastic Interlayer by Quasi‐Elastic Approximation

“…Generally, a laminated tube is composed of two or more subcomponents of diferent materials, and the adjacent members are usually connected discontinuously by studs, nails, and dowels or continuously glued by adhesives [8]. Due to the characteristics of the constituent materials, practical problems exist for the laminated structure under diferent external conditions [9][10][11][12]. One of them is that the interfacial slip is inevitable to occur because the kinds of connections can hardly be rigid.…”