Abbott Aerospace – Analysis Method

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

Local Stability – Panel Compression Buckling

Abbott Aerospace – Analysis Method

XL-VIKINGDisplay Your Math in Excel

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

Local Stability – Panel Compression Buckling

Panel compression buckling is common when considering the primary failure model of the upper wing skin panels, horizontal tail skins and vertical tail skins. Compression also contributes to the failure of other parts of the structure in combined failure modes.

Web Compression Buckling Coefficient (NACA-Report-733)

𝐹𝑐𝑟 = 𝜂 ⋅ 𝑘 ⋅𝜋2 ∙ 𝐸

12 ∙ 1 − 𝜈𝑒2

𝑡

𝑏

2

Abbott Aerospace – Analysis Method

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

Local Stability – Panel Compression Buckling

The compression buckling coefficient in the previous slide is derived using the following expression from (NACA-Report-733):

𝑘 =

𝜋𝑏𝜆

2

120 +1

𝜋𝑏𝜆

2 +16 𝜖2 + 1 +

𝜖2

𝑏𝜆+𝜆𝑏

2 12 1 +

𝜖2 −

4𝜖𝜋2

+2𝜖

𝜋𝑏𝜆

2

𝜋2𝜖2

120 +4𝜖𝜋2

1 +𝜖2 +

12 1 +

𝜖2

2

Where:k Panel Compression Buckling Coefficient𝝀 Half wave length of the buckle pattern𝒃 Panel width, in𝝐 Restraint coefficient

𝜖 =4 ∙ 𝑆0 ∙ 𝑏

𝐷

𝑺𝟎 Stiffness per unit length of elastic restraining medium, or moment required to rotate a unit length of elastic medium through one-fourth radian𝑫 Flexural rigidity of Panel per unit length

𝐷 =𝐸 ∙ 𝑡3

12 ∙ 1 − 𝜈𝑒2

𝒃 Width of loaded edge of panel, in𝒕 Panel thickness, in𝑬 Panel material young’s modulus, psi𝝂𝒆 Panel material elastic Poisson’s ratio

Abbott Aerospace – Analysis Method

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

Local Stability – Panel Compression Buckling

The simplest approach to panelcompression buckling and the approachthat is commonly used for initial sizing isto assume that 𝜂 = 1 and the panel issimply supported:

𝐹𝑐𝑟 = 𝑘𝑠𝑠 ⋅𝜋2 ∙ 𝐸

12 ∙ 1 − 𝜈𝑒2

𝑡

𝑏

2

The coefficient for the simply supportededge condition is given by the followingexpression:

𝑘𝑠𝑠 =𝜆

𝑟+𝑟

𝜆

2 Where:r Panel aspect ratio, a/b𝝀 Half wave length of the bucklepattern

Abbott Aerospace – Analysis Method

XL-VIKINGDisplay Your Math in Excel

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

Local Stability – Panel Compression Buckling

The simple and the general Panel compression buckling coefficients are calculated inthis spreadsheet:

AA-SM-007-092 Mathematical Derivation of Compression Buckling Coefficients

The simple approach to panel compression buckling is given in this spreadsheet:Using this simple approach, to account for panel material plasticity if 𝐹𝑐𝑟 exceeds 𝐹𝑐𝑦then limit 𝐹𝑐𝑟 to 𝐹𝑐𝑦.

AA-SM-007-021 Buckling of Flat Isotropic Plates - Compression Buckling - Simple