# Design and Analysis of a Laminated Composite Tube

2183 Words Apr 25th, 2013 9 Pages
COMPOSITES COURSEWORK

DESIGN AND ANALYSIS OF A LAMINATED COMPOSITE TUBE

ABSTRACT

This report details the process for the design of a composite laminate tube, the software package 'MathCAD' was used to determine a lamina design with a configuration that avoids mechanical failure under loading conditions. It was also used to obtain twist angles and maximum stresses for specific lamina wind up angles. The report will provide analysis of the methods used to obtain these criteria.

AIM

Use a Mathcad script to determine the procedure used during the manufacture of a wound laminate composite tube and to assess its validity for use in stress and strain analyses.

INTRODUCTION

FIGURE 1 A DEVELOPED VIEW OF A TAPE-WOUND CYLINDRICAL TUBE

The
The Love-Kirchhoff hypothesis generalises the plane section assumption in beam theory; assuming the normal to the laminate remains normal to the deformed laminate and the normal undergoes no extension of shortening. Leading to:

Resultant displacements:

Where:

u0 and v0 are in plane displacements.

w is the deflection.

z=0 as reference surface.

Therefore:

. (3)

Due to the assumptions that it demonstrates a linear distribution for plane strains throughout the laminate thickness and that out of plane strains can therefore be ignored.

{ε0} is the in plane strain and {k} is the curvature of the reference surface.

From equation (1) and appropriate coordinate transformations the following relationship is obtained.

(4)

Though integration and manipulation of the elasticity equations with respect to the "z" the membrane forces can be found as:

(5)

Thus the bending moments are as follows:

(6)

{N} and {M} are the generalised stresses can can be expressed as membrane strains and curvatures by using the laminar stress-strain relationship and Love Kirchhoff hypothesis.

, (7)

As {κ} = 0

Also as there is no bending, this can be assumed to be equal to {ε}.

Where [A], [B] and [D] are integrated over the layer thickness of the laminate, Figure 5: