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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 867079, 33 pages
Research Article

Mixed Static and Dynamic Optimization of Four-Parameter Functionally Graded Completely Doubly Curved and Degenerate Shells and Panels Using GDQ Method

1DICAM-Department, School of Engineering, University of Bologna, viale del Risorgimento 2, 40136 Bologna, Italy
2DIN-Department, School of Engineering, University of Bologna, viale del Risorgimento 2, 40136 Bologna, Italy

Received 14 February 2013; Accepted 2 April 2013

Academic Editor: Abdelouahed Tounsi

Copyright © 2013 Francesco Tornabene and Alessandro Ceruti. 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.


This study deals with a mixed static and dynamic optimization of four-parameter functionally graded material (FGM) doubly curved shells and panels. The two constituent functionally graded shell consists of ceramic and metal, and the volume fraction profile of each lamina varies through the thickness of the shell according to a generalized power-law distribution. The Generalized Differential Quadrature (GDQ) method is applied to determine the static and dynamic responses for various FGM shell and panel structures. The mechanical model is based on the so-called First-order Shear Deformation Theory (FSDT). Three different optimization schemes and methodologies are implemented. The Particle Swarm Optimization, Monte Carlo and Genetic Algorithm approaches have been applied to define the optimum volume fraction profile for optimizing the first natural frequency and the maximum static deflection of the considered shell structure. The optimization aim is in fact to reach the frequency and the static deflection targets defined by the designer of the structure: the complete four-dimensional search space is considered for the optimization process. The optimized material profile obtained with the three methodologies is presented as a result of the optimization problem solved for each shell or panel structure.