isotensoidDomeType

The shape a filament-wound dome takes when every filament carries the same tension. It does not reach the axis: the filaments turn around a polar opening of radius r_p, which is larger than zero, and the dome is closed there by a flat disk of that radius.

The meridian has no closed form. It is the solution of

dr/dx = -tan(phi), dphi/dx = (1/r) (2 - rp^2/(r^2 - rp^2))

integrated from the cylinder towards the pole, where r is the radius, x the distance along the axis, φ the angle between the meridian and the axis, and r_p is the polar opening radius. The integration starts at the junction with the cylinder, at r = R and φ = 0. It ends where r has fallen to the square root of 1.5 times r_p, the radius at which the equation becomes singular and the meridian angle stops turning. From there the meridian carries on along its tangent down to the polar opening, which closes the dome without a kink. The distance from the cylinder to that opening is the dome height h.

This construction, including the straight continuation beyond the singular radius, follows the patent of J. C. Murphy, "Filament-wound isotensoid pressure vessels having geodesic domes", EP 0714753 A2, 1996. The theory of isotensoid domes and their design are treated in depth in V. V. Vasiliev, "Composite Pressure Vessels: Design, Analysis, and Manufacturing", Bull Ridge Publishing, Blacksburg, 2009.

The excerpt is one of the wound cylinders of the example, whose polar opening is 0.05 m wide at a cylinder radius of 0.28 m.

<vessel uID="bellyTank_vessel1">
    ...
    <domeType>
        <isotensoid>
            <polarOpeningRadius>0.05</polarOpeningRadius>
        </isotensoid>
    </domeType>
    ...
</vessel>

Isotensoid dome

Attributes

Name	Type	Use	Description
`@externalDataDirectory`	`xsd:string`	optional	Directory of the external file the element was read from, as URI
`@externalDataNodePath`	`xsd:string`	optional	Path of the parent element in the merged dataset, at which the element was inserted from an external file
`@externalFileName`	`xsd:string`	optional	Name of the external file the element was read from

Child elements

Name	Type	Constraints	OccurrenceHow often the element may appear at this place. The schema writes it as minOccurs and maxOccurs on the declaration.	Default	Description
allThe children below may appear in any order. Each may appear at most once.
`polarOpeningRadius`	`doubleBaseType`		[1..1] required		Radius of the polar opening that closes the dome [m]

isotensoidDomeType

Attributes

Child elements

Used by

In a dataset · 1 path

In the schema · 1 declaration