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Explicit expressions of the matrices \(\mathbf{H}\), \(\mathbf{L}\) and \(\mathbf{S}\) for the bending of symmetrically laminated anisotropic plates. (English) Zbl 1321.35237

Summary: Derived in this work are the explicit expressions of the three real matrices \(\mathbf{H}\), \(\mathbf{L}\) and \(\mathbf{S}\) in the Stroh-type formalism for the bending deformation of an anisotropic, linearly elastic plate based on the Kirchhoff theory. The plate is homogeneous in the thickness direction or symmetrically laminated about its mid-plane, and thus, the stretching and bending deformations are decoupled. The three real matrices are the counterparts of the Barnett-Lothe tensors in the Stroh formalism for generalized plane strain elasticity. Identities relating \(\mathbf{H}\), \(\mathbf{L}\) and \(\mathbf{S}\) are developed. Several applications are presented to demonstrate the usefulness of the derived expressions of \(\mathbf{H}\), \(\mathbf{L}\) and \(\mathbf{S}\).

MSC:

35Q74 PDEs in connection with mechanics of deformable solids
74B05 Classical linear elasticity
74K20 Plates
30E25 Boundary value problems in the complex plane
35J56 Boundary value problems for first-order elliptic systems
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