`Mathematical Problems in EngineeringVolume 2011 (2011), Article ID 793798, 21 pagesdoi:10.1155/2011/793798`
Research Article

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

1College of Civil Engineering, Chongqing University, Chongqing 400045, China
2Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China
3Chongqing Vocational College of Architectral Engineering, Chongqing 400039, China
4Internal Trade Engineering and Research Institute, Beijing 100069, China

Received 17 August 2010; Revised 14 February 2011; Accepted 15 February 2011

Academic Editor: E. E. N. Macau

Copyright © 2011 Liu Chang-Jiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### 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.