How does laminate symmetry influence coupling between bending and extension?

How does laminate symmetry influence coupling between bending and extension?

• A. Symmetry eliminates B-matrix coupling, preventing bending-extension coupling.
• B. Symmetry increases bending-extension coupling.
• C. Symmetry has no effect on coupling between bending and extension.
• D. Symmetry reduces density but not coupling.

Answer: (A)

The key idea is that bending and extension in a laminate are linked through the B-matrix in classical laminate theory. When a laminate is symmetric about its mid-plane, the contributions that could couple bending to in-plane extension cancel out, making the B-matrix zero. With B = 0, the equations decouple: in-plane forces depend only on mid-plane strains, and bending moments depend only on curvatures. That means bending does not induce extension and extension does not induce bending. The other statements miss this point—the symmetry doesn’t increase coupling, it eliminates it; it does affect coupling, and density isn’t the factor in play here.

The key idea is that bending and extension in a laminate are linked through the B-matrix in classical laminate theory. When a laminate is symmetric about its mid-plane, the contributions that could couple bending to in-plane extension cancel out, making the B-matrix zero. With B = 0, the equations decouple: in-plane forces depend only on mid-plane strains, and bending moments depend only on curvatures. That means bending does not induce extension and extension does not induce bending. The other statements miss this point—the symmetry doesn’t increase coupling, it eliminates it; it does affect coupling, and density isn’t the factor in play here.