How does increasing laminate thickness affect bending stiffness and buckling load? Provide the scaling law.

How does increasing laminate thickness affect bending stiffness and buckling load? Provide the scaling law.

• A. Bending stiffness scales with thickness^1; buckling load decreases with thickness.
• B. Bending stiffness scales with thickness^2; buckling load is unaffected.
• C. Bending stiffness scales with thickness^3; buckling load generally increases with thickness (depends on boundary conditions).
• D. Bending stiffness scales with thickness^0; buckling load scales with thickness.

Answer: (C)

Bending stiffness grows with the cube of thickness because bending rigidity is the product of the material’s stiffness and the plate’s resistance to bending, which comes from the second moment of area. For a plate, the second moment scales as t^3, so the flexural rigidity D ∝ E t^3 (with the usual 1−ν^2 factors for a plate). Doubling the thickness increases bending stiffness eightfold. Critical buckling load under in-plane compression is linked to this bending rigidity through the plate’s ability to resist deformation, and the governing buckling relation shows the load is proportional to D times a geometric factor that depends on boundary conditions. Therefore, the buckling load generally increases with thickness as well, though the exact numerical constant changes with how the plate is supported or constrained. So, the bending stiffness scales with thickness cubed, and the buckling load typically increases with thickness (the precise scaling depends on boundary conditions).

Bending stiffness grows with the cube of thickness because bending rigidity is the product of the material’s stiffness and the plate’s resistance to bending, which comes from the second moment of area. For a plate, the second moment scales as t^3, so the flexural rigidity D ∝ E t^3 (with the usual 1−ν^2 factors for a plate). Doubling the thickness increases bending stiffness eightfold.

Critical buckling load under in-plane compression is linked to this bending rigidity through the plate’s ability to resist deformation, and the governing buckling relation shows the load is proportional to D times a geometric factor that depends on boundary conditions. Therefore, the buckling load generally increases with thickness as well, though the exact numerical constant changes with how the plate is supported or constrained.

So, the bending stiffness scales with thickness cubed, and the buckling load typically increases with thickness (the precise scaling depends on boundary conditions).