Static and vibration analyses of thick, generally laminated deep curved beams with different boundary conditions

Abstract

A rigorous first order shear deformation theory is employed along with modified ABD parameters to analyze static and free vibration behavior of generally laminated deep curved beams. The deepness term (1 + z/R) is exactly integrated into ABD parameters formulation and equivalent modulus of elasticity is used instead of traditional stiffness terms to account for deepness and material coupling of the beam structures, respectively. Static as well as free vibration analyses were performed and the results for deflection, moment resultants, and natural frequencies were obtained. The exact solution for simply supported boundary condition as well as numerical solutions using GDQ for other boundary conditions are presented. Results are compared with those obtained using accurate three dimensional finite element simulations using commercial software. It has been shown that when considering more accurate stiffness parameter, FSDT can accurately predict static and free vibration behaviors of composite deep beams of any lamination and boundary condition.

Introduction

Composite materials offer higher strength and stiffness to weight ratios than most metallic materials and have the possibility to tailor the design for specific purposes using different laminations. This led to their extensive and increasing use. Among composite structures, curved beam components constitute a frequently encountered element of aerospace, marine and other structures.

Since all beam theories are based on three dimensional (3D) elasticity, 3D-based analyses (including finite element analyses, FEA) are the most accurate analytical ones. However, 3D FEA is a very expensive procedure demanding expensive machines and/or longer computational times if used for large scale structures. This is particularly the case when one dimension is significantly larger than the other two. For these structures, beam models are very efficient provided that they are built on accurate models and are verified against accurate 3D analyses. Several researchers have worked on the analysis of composite beam structures. Kapania and Raciti [1], [2] published a review on advances in the analysis of laminated beams and plates. Rosen [3] reviewed the research on static, dynamic, and stability analysis of pretwisted rods and beams. Chidamparam and Leissa [4] reviewed the published literature on the vibrations of curved bars, beams, and rings of arbitrary shape which lie in a plane. Qatu [5] dedicated a book to vibration of composite beams, plates and shells. Hodges [6] made an extensive literature survey of the modern history of beam analysis. Recently, a review is conducted on laminated beams by the authors [7]. Among the conclusions of this review is the lack of a consistent set of equations that treat moderately thick beams with curvature and general lamination sequence.

This paper is concerned with the development of a general approach for static and in-plane free vibration analyses of generally laminated composite deep curved beams. While the vibration part was treated before, the formulation there was limited to simply supported beams with cross-ply laminates [8]. In this paper accurate deflection, moment resultants and natural frequencies of generally laminated deep curved beams are presented and can be used for possible use by researchers and practicing engineers.