Abbott Aerospace – Analysis Method

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Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures

Circular Membranes

Abbott Aerospace – Analysis Method

XL-VIKINGDisplay Your Math in Excel

Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures

Circular Membranes

This section is taken substantially from (AFFDL-TR-69-42, 1986) which has a goodsuccinct summary of relevant analysis methods.A membrane is a plate that has no bending rigidity, all stresses and in the plane of thesurface and a usually tension.

This section uses the following nomenclature:

Where:𝒂 Longitudinal dimension of membrane, in𝑫 Diameter, in𝑬 Material modulus of elasticity, psi𝒇 Calculated stress, psi𝒇𝒎𝒂𝒙 Calculated maximum stress, psi𝒏𝟏 − 𝒏𝟕 Coefficients𝒑 Pressure, psi

𝑹 Outside radius of circular membrane, in𝒕 Thickness of membrane, in𝒙, 𝒚 Rectangular coordinates, in𝜹 Deflection, in𝜹𝒄 Deflection at center of circular membrane, in𝝁 Poisson’s Ratio

Abbott Aerospace – Analysis Method

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Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures

Circular Membranes

The maximum deflection of a circularmembrane with a clamped edge is given by

𝛿𝑐 = 0.662 ∙ 𝑅 ∙3 𝑝 ∙ 𝑅

𝐸 ∙ 𝑡

The deflection of the membrane at a distance,r, from the center of the plate is:

𝛿 = 𝛿𝑐 ∙ 1 − 0.09 ∙𝑟

𝑅

2

− 0.10 ∙𝑟

𝑅

5

Abbott Aerospace – Analysis Method

XL-VIKINGDisplay Your Math in Excel

Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures

Circular Membranes

The stress at the center of the membrane is

𝑓 = 0.423 ∙3 𝐸 ∙ 𝑝2 ∙ 𝑅2

𝑡2

The stress at the edge of the membrane is

𝑓 = 0.328 ∙3 𝐸 ∙ 𝑝2 ∙ 𝑅2

𝑡2

This method is available in a spreadsheet:

AA-SM-013-051 Circular Membranes