A Strength of Materials Formulation for Thin Walled Composite Beams with Torsion

Abstract

A simple methodology for the analysis of thin walled composite beams subjected to bending, torque, shear, and axial forces is developed. Members with open or closed cross section are considered. The cross section is modeled as a collection of flat. arc-circular, and concentrated area segments. Each laminated segment is modeled with the constitutive equations of classical lamination theory accounting for a linear distribution of normal and shear strains through the thickness of the walls, thus allowing for greater accuracy than classical thin walled theory when the walls are moderately thick. The geometric properties used in classical beam theory such as area, first moment of area, center of gravity, etc., are no longer used because of the variability of the materials properties in the cross section. Instead, mechanical properties such as axial stiffness, mechanical first moment of area. mechanical center of gravity, etc., are defined to incorporate both the geometry and the material properties. Warping, restriction to warping, and secondary stresses are considered. Failure predictions are made with customary failure criteria. Comparison with experimental results are presented.

Composite stacking sequence optimization for aeroelastically tailored forward-swept wings

“…[3] presented an approach to analyze the mechanical behavior of thin-walled composite beams. Torsion has been taken into account in the model [37]. [40] used these results to derive a relation between the beam's loads and deformation.…”

Stiffness control in adaptive thin-walled laminate composite beams

“…For the calculation of the stiffnesses of the thin walled beam, the model proposed by Massa and Barbero [17] was used. Because this paper examines the influence of the presence of the adaptive material in the beam response, hygrothermal effects on the composite material are not considered in the model formulation.…”

“…Each had its corre sponding associated stiffness matrices and constitutive equations. If these equations are inverted and the undeformability of the con tour assumption of the classical theory of thin walled beams is applied together with the assumption of no coupling between nor mal and shearing effects [17], a reduced expression results, leading to the reduced constitutive equations of each i th segment in terms of the segment stiffness: The global coordinate system used to define the stiffnesses is centred on the mechanical centre of gravity of the cross section and each laminate has a local coordinate system (s, r) where the s axis defines the width and the r axis defines the thickness of the laminate. The axial stiffness of the box section was determined by adding the contribution of all the segments, b i being the i th segment length.…”

“…Pluzsik and Kollár [16] present a theory that takes into account the transverse shear and the restrained warping when calculating the bending and torsional stiffnesses of the section. Massa and Bar bero [17] developed a theory for the study of thin walled beams made from laminates and the calculation of the stiffnesses of sec tions of any geometry.…”

“…In present work the model proposed by Massa and Barbero [17] was used because it allows a variable stiffness material to be easily incorporated into the calculation of the stiffnesses of the thin walled composite beam. This analytical model is applicable to sec tions of different geometries, both open and closed, and thus offers the possibility of analysing different sections with relatively few modifications in the calculation process.…”