Home › GATE ME › Mechanical Engineering › platetheory › For a SYMMETRIC laminate, classical lamination t…
For a SYMMETRIC laminate, classical lamination theory simplifies because:
A{'text': 'Material is isotropic', 'label': 'A'}
B{'text': 'The coupling matrix [B] = 0, decoupling in-plane behavior from bending — a 6×6 system splits into two 3×3 systems', 'label': 'B'}
C{'text': 'D = 0', 'label': 'C'}
D{'text': 'Plate is square', 'label': 'D'}
Answer & Solution
Correct answer: B. {'text': 'The coupling matrix [B] = 0, decoupling in-plane behavior from bending — a 6×6 system splits into two 3×3 systems', 'label': 'B'}
Symmetric stacking ⇒ contributions to B (odd powers of z) cancel. The 6-DOF system {N, M} ↔ {ε°, κ} decouples into the in-plane part (A) and the bending part (D), independently. This is why aerospace composites are universally symmetric.
Related questions
The TRANSITION from beam theory to plate theory is required when:For a thin plate, increasing thickness t by 2× changes flexural rigidity D by what factor?In the laminate ABD constitutive equation, the COUPLING matrix B is computed as:The STRESS RESULTANTS used in plate theory are integrals through the thickness. The bendinFor an ANISOTROPIC plate (e.g., laminate), the governing equation involves which sub-matriThe biharmonic equation $\nabla^4 w = D^{-1} q$ in plate theory has the form:The PRESENCE of "concentrated corner forces" at the corners of a simply-supported rectanguAt a FREE edge of a thin plate (x = a), Kirchhoff's theory imposes how many independent bo