In Classical Laminates Theory, which matrix relates in-plane forces to midplane strains?

In Classical Laminates Theory, which matrix relates in-plane forces to midplane strains?

• A. B is the extensional stiffness relating in-plane forces to strains.
• B. D is the extensional stiffness relating strains to in-plane forces.
• C. A is the extensional stiffness relating in-plane forces to strains.
• D. C matrix is the extensional stiffness.

Answer: (C)

In Classical Laminates Theory, the in-plane force resultants relate to midplane strains through the extensional stiffness matrix, usually denoted A. The governing relation is N = A ε0 + B κ, where N are in-plane forces per unit length, ε0 are midplane strains, and κ are curvatures. If bending is not active (κ = 0), this reduces to N = A ε0, so A is exactly the matrix that maps midplane strains to in-plane forces. The A matrix is obtained by summing the transformed reduced stiffness of each ply across the laminate thickness. The B matrix accounts for coupling between extension and bending, and the D matrix relates curvatures to bending moments. There is no separate C matrix that serves this role in the standard CLT formulation.

In Classical Laminates Theory, the in-plane force resultants relate to midplane strains through the extensional stiffness matrix, usually denoted A. The governing relation is N = A ε0 + B κ, where N are in-plane forces per unit length, ε0 are midplane strains, and κ are curvatures. If bending is not active (κ = 0), this reduces to N = A ε0, so A is exactly the matrix that maps midplane strains to in-plane forces. The A matrix is obtained by summing the transformed reduced stiffness of each ply across the laminate thickness. The B matrix accounts for coupling between extension and bending, and the D matrix relates curvatures to bending moments. There is no separate C matrix that serves this role in the standard CLT formulation.