How does a symmetric laminate affect the B-matrix and coupling between bending and extensional responses?

How does a symmetric laminate affect the B-matrix and coupling between bending and extensional responses?

• A. Symmetry about mid-plane increases B-matrix coupling.
• B. Symmetry about mid-plane yields B = 0, eliminating extensional–bending coupling.
• C. Symmetry makes A zero.
• D. Symmetry has no effect on B.

Answer: (B)

Mid-plane symmetry in a laminate makes the B-matrix vanish, so there is no coupling between extensional and bending responses. In classical laminate theory, B links in-plane forces to bending moments and also links in-plane strains to curvatures. When the stacking is mirrored about the mid-plane, the contributions from mirrored plies cancel in the B terms, leaving B equal to zero. That leaves the in-plane behavior governed by A (extensional stiffness) and the bending behavior governed by D (bending stiffness) as a clean, decoupled pair. So extensional loads cause in-plane strains without inducing bending, and bending moments cause curvatures without in-plane strains from those moments. If the laminate were not symmetric, those coupling terms would not cancel and extensional and bending responses would influence each other. The other statements contradict this: symmetry does not increase B, does not force A to zero, and itself does affect B by making it zero.

Mid-plane symmetry in a laminate makes the B-matrix vanish, so there is no coupling between extensional and bending responses. In classical laminate theory, B links in-plane forces to bending moments and also links in-plane strains to curvatures. When the stacking is mirrored about the mid-plane, the contributions from mirrored plies cancel in the B terms, leaving B equal to zero. That leaves the in-plane behavior governed by A (extensional stiffness) and the bending behavior governed by D (bending stiffness) as a clean, decoupled pair. So extensional loads cause in-plane strains without inducing bending, and bending moments cause curvatures without in-plane strains from those moments. If the laminate were not symmetric, those coupling terms would not cancel and extensional and bending responses would influence each other. The other statements contradict this: symmetry does not increase B, does not force A to zero, and itself does affect B by making it zero.