Geometrically nonlinear free vibration of composite skewed stiffened paraboloidal panels

Abstract

Laminated composites are lucrative construction materials for civil engineers. The material is lightweight, resistant to atmospheric decay and fire hazards and possesses a high strength to weight ratio and high stiffness to weight ratio. The doubly curved panels are stiff and architecturally pleasing geometry. These shells made of laminated composite materials, which is a popular choice among the practicing civil engineers to cover large areas with minimal columns, which are found in shopping complex, stadiums, auditoriums, railway stations and airport tenninal buildings. The skewed forms can satisfy the architectural requirements of industrial applications with minimum supports. The skewed panels are generally applied in industrial applications in moderately thin configurations. These panels are susceptible to in stability when the transverse load is applied. The stiffened and skewed panels can address this issue. The literature review shows that there are no research reports available on skewed stiffened elliptical and hyperbolic paraboloidal panels, especially using the geometrically nonlinear approach. Therefore, an attempt has been made in this research investigation to study the free vibration of clamped and simply supported skewed panels for different skew angles, laminations, eccentricity and stiffener orientations which can provide meaningful design guidelines to the practicing civil engineers. A CJ finite element formulation is proposed which models the skewed panels using eight noded doubly curved panel elements and stiffeners by three noded elements. Geometrically nonlinear strains, Lagrange's equation of motion and Hamilton's principle are combined for the governing equation. The transverse shear strains are taken as constant with proper correction factors. Closed form solutions and experimental results act as benchmarks to check correctness of the proposed code. The orientation, number and depth of stiffener are also varied. The findings indicate that the performance improves as the skewness of panels increases.