Shear constitutive relations of a first-order shear deformation theory for laminated anisotropic shells and plates are formulated following Mindlin’s procedure for homogeneous isotropic plates. Because thickness-shear motions for laminated anisotropic thickness profiles may not be polarized in planes normal to the reference surface, the concept of generalized principal shear planes is needed. These planes are established by least-squares minimization of the out-of-plane motions of infinitely long thickness-shear waves based on an elasticity analysis of the profile. Typical shear rigidities for a variety of laminated composite and sandwich profiles are given. In a companion paper, the efficacy of this form of shear constitutive relations in predicting the response of a class of laminated composite and sandwich cylindrical shells is demonstrated.

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