Rezaiefar, Ali ORCID: https://orcid.org/0000-0001-8018-6498
(2021)
*Large Displacement Analysis and Design of Stiffened Plates with Parallel Ribs in Large Industrial Ducts.*
PhD thesis, Concordia University.

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## Abstract

The structural design of stiffened plates of the walls of rectangular-sectioned industrial ducts and similar structures is conventionally based on the linear beam theory assuming that the displacements are small and the membrane forces that generate in the panel plate are negligible. The design of such stiffened plates is divided into two main steps where the panel plate and the rib stiffener are designed sequentially. Depending on the nature of the loads applied to the industrial duct, a third step might involve determining the vibration frequency of the panel plates for resonance verifications.

In the first phase of this thesis, the conventional design method for the panel plate is studied in order to examine the effects of large displacements on the behaviour of the structure and ultimately present a new design approach accordingly. Two different sets of formulas are presented based on Finite Element analysis of rectangular plates with relatively long aspect ratios that estimate the maximum stress and deformation in the typical and edge panels of stiffened plates. These formulae are then applied to establish empirical design equations for the panel plates. The new design approach is capable of reducing the panel plate thickness significantly in comparison with the conventional method.

In the second phase of the thesis, the structural design of the rib stiffeners is evaluated through a comparison between the conventional design which is based on Modelling the stiffened plate using an Equivalent Beam Analogy (EBA) and calculating the geometrical cross-sectional properties of it in linear beam theory, and FE analysis of the stiffened plate using shell elements with and without the consideration of large displacement effects. It is shown that the EBA and linear beam theory, as well as the FE using small displacements, are not relevant for the analysis and design of stiffened plates. In this phase, it is shown that the load-displacement behaviour of stiffened plates with parallel ribs could be different under positive and negative pressures as the membrane forces generated in the panel plate would affect the overall behaviour of the stiffened plate differently.

The third phase of the thesis provides means for obtaining the first three significant vibration modes for rectangular plates based on mass participation ratios. A non-dimensional frequency parameter is presented which results in the vibration frequency of rectangular plates at each of these three significant modes. Various aspect ratios and four combinations of boundary conditions at the plate edges are studied, and a correlation between the nonlinear load-deformation behaviour of the panel plate and its vibrational behaviour is also presented accordingly. It is demonstrated that the vibration frequency of the studied rectangular plates increases significantly upon increasing the applied lateral pressure if the large deformation effects are considered in the analysis. The easy-to-follow method of frequency calculation presented in this paper is useful for assessing the dynamic characteristics of rectangular plates with or without lateral pressure that are subject to vibration.

Divisions: | Concordia University > Gina Cody School of Engineering and Computer Science > Building, Civil and Environmental Engineering |
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Item Type: | Thesis (PhD) |

Authors: | Rezaiefar, Ali |

Institution: | Concordia University |

Degree Name: | Ph. D. |

Program: | Civil Engineering |

Date: | 13 April 2021 |

Thesis Supervisor(s): | Galal, Khaled |

Keywords: | FE Analysis, Rectangular plates, Stiffened plates, Industrial ducts, Large displacement analysis |

ID Code: | 988563 |

Deposited By: | ALI REZAIEFAR |

Deposited On: | 29 Nov 2021 17:00 |

Last Modified: | 29 Nov 2021 17:00 |

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