Stress Analysis of a Pressurized Composite Hemisphere

by

Mr. James Cross

Prof. Mark Tuttle

Overview •  Strains induced along two meridians in a pressurized hemispherical

composite dome were measured using rectangular strain gage rosettes

•  No analytical solution exists for the pressurized composite dome studied

•  A numerical (finite-element) analysis has been attempted, but thus far a valid analysis has not been achieved

•  The following slides summarize –  How the dome was designed, built, instrumented, and tested –  Measured principal strains (normalized to internal pressure) and orientation of the

principal coordinate system relative to the two instrumented meridians –  The inconsistent finite-element results that have been obtained thus far using

ANSYS

Design of the Composite Dome •  Dome wall built up from 8 plies; each ply produced using unidirectional “peels” •  Peel dimensions sized to allow complete coverage of doubly-curved surface •  The structural analyses assumes fibers emanate from two points (called

“poles”) within an individual layer

unidirectional ply Peels cut from a ply A single layer within the dome wall

Design of the Composite Dome •  Plies are described by specifying the (latitude/longitude) of the ply pole. •  The poles of the ply shown here are on the “equator”….at a 0º latitude •  The “prime meridian” was arbitrarily defined as the meridian that passes

through the pole on the equator. Hence, the pole location for this ply is (0º/0º)

unidirectional ply Peels cut from a ply A single layer within the dome wall

Design of the Composite Dome •  This pole is at the “north pole”…since all meridians pass through the north

pole, we designate this pole location as (90º/θ)

unidirectional ply Peels cut from a ply

A single layer within the dome wall

Design of the Composite Dome

•  The dome was produced using eight plies and six pole positions

•  Pole positions varied from ply-to-ply

•  Consequently, the stacking sequence varies from point-to-point…an algorithm (not described here) has been developed to calculate the stacking sequence at any point in the dome

•  here two poles are shown

Dome wall with two poles: (0º, 0º)

and (45º, 45º)

Fabrication Method used to produce the composite dome

can be roughly divided into three major steps: 1.  Produce a male foam plug

2.  Produce female composite tool

3.  Produce composite dome

1. Produce Foam Plug •  Plug was produced using a high density, closed-cell urethane foam •  Film adhesive used to bond 3 blocks together

1. Produce Foam Plug •  CNC mill used to machine plug to near final dimensions

1. Produce Foam Plug •  CNC mill used to machine plug to near final dimensions

1. Produce Foam Plug •  Hand-sanded, primed, and high-temp wax release applied

2. Produce Female Composite Tool •  Epoxy surface coat applied to prepared foam plug: becomes

the inner surface of the female tool, eliminates surface pitting, prevents fiber damage

2. Produce Female Composite Tool

•  Twill weave tooling prepreg was used; conforms well to complex tool geometries

2. Produce Female Composite Tool

•  Assembly vacuum-bagged; cured in autoclave

2. Produce Female Composite Tool

3. Produce Composite Dome •  Prepreg “peels” cut w/ CNC router

3. Produce Composite Dome •  Peels placed in composite tool by hand

3. Produce Composite Dome

•  Poles varied from one ply to the next

3. Produce Composite Dome

•  Poles varied from one ply to the next

3. Produce Composite Dome

•  Entire assembly vacuum bagged, cured in autoclave

•  Finished dome involves eight layers and six pole positions: [(0º,0º)/ (45º,45º)/ (90º,90º)/ (45º,-135º)/ (45º,135º)/ (90º,90º)/ (45º,-45º)/ (0º,0º)]

Test Setup and Instrumentation

Test Setup and Instrumentation

(fitting used to introduce and measure internal pressure not shown)

Test Setup and Instrumentation •  3-element rectangular stacked rosettes (M-M

C2A-06-125WW-350) bonded along 0º and -90º meridians •  A total of 13 rosettes used (39 strain gage elements)

Typical Strain Measurements

•  Pressure increased from 0 to 45 psi

•  No audible cracking or other forms of damage observed

•  All gage readings increased linearly, returned to zero as pressure returned to zero, and were essentially identical after several pressure cycles.

•  Strains recorded by rosette D, bonded at (45º/0º), shown at right to illustrate typical measured strains

Measured Principal Strains (Normalized to Pressure) and Orientations along the 0º Meridian

(i.e., along the Prime Meridian)

Measured Principal Strains (Normalized to Pressure) and Orientations along the -90º

Meridian

FE Modeling Efforts •  An assembly of 4 identical parts was imported from Solidworks via a

STEP file, which can be seen below •  Some inaccuracies occur along bonded contacts and at “material

poles”