What does a symmetric laminate imply for B-matrix coupling in laminate theory?

What does a symmetric laminate imply for B-matrix coupling in laminate theory?

• A. It creates always nonzero coupling terms
• B. It maximizes bending-extension coupling
• C. It minimizes or eliminates bending-extension coupling, making B terms zero or near zero
• D. It has no effect on coupling terms

Answer: (C)

In laminate theory, the B-matrix represents coupling between bending (curvature) and extension (mid-plane strain). An exactly symmetric stack has a plane of symmetry through the mid-plane, so every ply above the mid-plane has a mirror ply below with the same thickness and opposite orientation. When you sum the contributions, the coupling terms cancel out, making the B-matrix vanish. Physically, this means in-plane strains do not induce bending moments and curvatures do not generate in-plane forces. So, symmetry minimizes or eliminates bending-extension coupling, yielding B terms that are zero (or effectively zero in real, nearly symmetric laminates). The other statements conflict with this: nonzero coupling would persist only if the symmetry is broken; maximizing coupling is the opposite of what symmetry does; and saying there’s no effect ignores the specific role of symmetry in canceling those terms.

In laminate theory, the B-matrix represents coupling between bending (curvature) and extension (mid-plane strain). An exactly symmetric stack has a plane of symmetry through the mid-plane, so every ply above the mid-plane has a mirror ply below with the same thickness and opposite orientation. When you sum the contributions, the coupling terms cancel out, making the B-matrix vanish. Physically, this means in-plane strains do not induce bending moments and curvatures do not generate in-plane forces.

So, symmetry minimizes or eliminates bending-extension coupling, yielding B terms that are zero (or effectively zero in real, nearly symmetric laminates). The other statements conflict with this: nonzero coupling would persist only if the symmetry is broken; maximizing coupling is the opposite of what symmetry does; and saying there’s no effect ignores the specific role of symmetry in canceling those terms.