Which statement about the extensional stiffness matrix A in a laminate is true?

Which statement about the extensional stiffness matrix A in a laminate is true?

• A. It relates in-plane forces to out-of-plane strains.
• B. It relates out-of-plane bending to curvatures.
• C. It relates shear forces to shear strains.
• D. It relates in-plane forces to in-plane strains.

Answer: (D)

In laminated composites, the extensional stiffness matrix describes how the laminate’s mid-plane strains respond to in-plane force resultants. The in-plane forces (N_x, N_y, N_xy) relate to the mid-plane strains (ε_x, ε_y, γ_xy) through N = A · ε^0. This is the part of the theory that governs stretching and in-plane shear of the laminate. It does not describe bending or curvatures—that role is played by the bending stiffness matrix D (linking curvatures to moments) and the coupling matrix B (linking in-plane strains to curvatures). So the statement that the extensional stiffness matrix connects in-plane forces to in-plane strains best captures its purpose.

In laminated composites, the extensional stiffness matrix describes how the laminate’s mid-plane strains respond to in-plane force resultants. The in-plane forces (N_x, N_y, N_xy) relate to the mid-plane strains (ε_x, ε_y, γ_xy) through N = A · ε^0. This is the part of the theory that governs stretching and in-plane shear of the laminate.

It does not describe bending or curvatures—that role is played by the bending stiffness matrix D (linking curvatures to moments) and the coupling matrix B (linking in-plane strains to curvatures). So the statement that the extensional stiffness matrix connects in-plane forces to in-plane strains best captures its purpose.