A refined laminated plate and shell theory with applications

Abstract The present paper is concerned with the development and certain applications of a refined shear deformable theory suitable for the dynamic analysis of laminated anisotropic plates as well as cylindrical shells of either circular or non-circular configuration. The theory accounts for parabolic variation of transverse shear strains and it is capable of satisfying zero shear traction boundary conditions at the external shell or plate surfaces, and makes no use of transverse shear correction factors. It can be considered as a transverse shear deformable analogue of the classical laminate Donnell-type and Love-type shell theories while, through certain new definitions of force and moment resultants, the higher order moment and transverse shear force resultants occurring acquire some pysical substance. Under certain conditions, some dynamical problems studied earlier by the present author are considered as applications of the refined theory developed. As a further application, the present theory is employed for the study of the free vibration problem of antisymmetric angle-ply laminated closed circular cylindrical shells. This problem is solved by two different mathematical techniques; namely, the helical modal pattern approach and an approach based on Galerkin's method. Numerical results based on both solutions obtained are presented and compared and the efficiency of both approaches, with regard to the prediction of the natural frequencies of vibration, is discussed.

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