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, 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.

The singular radius also limits the polar opening: a dome exists only while it is smaller than the cylinder radius, that is for a polar opening radius below R divided by the square root of 1.5, about 0.816 R. Well below that limit the dome height hardly depends on the opening, between 0.60 R for a small opening and 0.63 R at an opening of 0.3 R. Towards the limit it grows without bound: 0.88 R at an opening of 0.7 R, 1.14 R at 0.75 R and 3.09 R at 0.80 R. A vessel whose dome is much taller than its radius is a sign that the opening is too large, not a shape anyone intended.

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 data file
`@externalDataNodePath`	`xsd:string`	optional	Path of the node inside the external data file
`@externalFileName`	`xsd:string`	optional	Name of the external data file

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