Which statement correctly describes the A matrix in CLT?

Which statement correctly describes the A matrix in CLT?

• A. A is the extensional stiffness relating in-plane forces to strains.
• B. A is the bending stiffness relating curvatures to moments.
• C. B is the extensional coupling.
• D. D is the shear stiffness.

Answer: (A)

In classical laminate theory, the response of a laminate to in-plane loads and bending is captured by the ABD matrices. The A matrix is the extensional stiffness: it relates in-plane forces to in-plane mid-plane strains. It summates the transformed in-plane stiffness of every ply across the thickness, so when there is no bending (curvature zero), the in-plane force result is N = A ε0. This is why the statement describing A as the extensional stiffness linking in-plane forces to strains is the best fit. The other descriptions point to different parts of the theory. B describes the extensional–bending coupling, not the pure extensional response. D describes bending stiffness, relating curvatures to bending moments. And shear stiffness is not what A represents in the CLT framework.

In classical laminate theory, the response of a laminate to in-plane loads and bending is captured by the ABD matrices. The A matrix is the extensional stiffness: it relates in-plane forces to in-plane mid-plane strains. It summates the transformed in-plane stiffness of every ply across the thickness, so when there is no bending (curvature zero), the in-plane force result is N = A ε0. This is why the statement describing A as the extensional stiffness linking in-plane forces to strains is the best fit.

The other descriptions point to different parts of the theory. B describes the extensional–bending coupling, not the pure extensional response. D describes bending stiffness, relating curvatures to bending moments. And shear stiffness is not what A represents in the CLT framework.