Structural Engineering and Mechanics

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Nonlinear primary resonance of multilayer FG shallow shell with an FG porous core reinforced by oblique stiffeners

  • Kamran Foroutan (Industrial Systems Engineering, University of Regina) ;
  • Liming Dai (Industrial Systems Engineering, University of Regina)
  • Received : 2024.05.16
  • Accepted : 2024.08.16
  • Published : 2024.09.10
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Abstract

The present research examines the primary resonance (PR) behaviors of oblique stiffened multilayer functionally graded (OSMFG) shallow shells featuring an FG porous (FGP) core under an external excitation. The research considers two distinct types of FGP cores: one characterized by uniform porosity distribution (UPD) and the other by non-uniform porosity distribution (NPD) along the thickness direction. Furthermore, the study explores two types of shallow shells: one with external oblique stiffeners and one with internal oblique stiffeners, which might have angles that are similar or different from each other. Using the stress function alongside the first-order shear deformation theory (FSDT), the research establishes a nonlinear model for OSMFG shallow shells. The strain-displacement relationships are obtained utilizing FSDT and von-Kármán's geometric assumptions. The Galerkin approach is utilized to discretize the nonlinear governing equations, allowing for the analysis of stiffeners at varied angles. To validate the obtained results, a comparison is made not only with the findings of previous research but also with the response of PR obtained theoretically with the method of multiple scales, using the P-T method. Renowned for its superior accuracy and reliability, the P-T method is deemed an apt selection within this framework. Additionally, the study investigates how differences in material characteristics and stiffener angles affect the system's PR behaviors. The results of this study can be used as standards by engineers and researchers working in this area, and they can offer important information for the design and evaluation of the shell systems under consideration.

Keywords

Acknowledgement

The authors greatly appreciate the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) to the present research. The supports of the University of Regina are also acknowledged.

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