Fundamental Equations of Laminated Beams, Plates and Shells

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Beams, plates and shells are named according to their size or/and shape features. Shells have all the features of plates except an additional one-curvature (Leissa in Vibration of Plates (NASA SP-160), US Government Printing Office, Washington, DC, pp. 1–353, 1969, Vibration Of Shells (NASA SP-288), US Government Printing Office, Washington, DC, pp. 1–428, 1973). Therefore, the plates, on the other hand, can be viewed as special cases of shells having no curvature. Beams are one-dimensional counterparts of plates (straight beams) or shells (curved beams) with one dimension relatively greater in comparison to the other two dimensions. This chapter introduces the fundamental equations (including kinematic relations, stress-strain relations and stress resultants, energy functions, governing equations and boundary conditions) of laminated shells in the framework of the classical shell theory (CST) and the shear deformation shell theory (SDST) without proofs due to the fact that they have been well established. The corresponding equations of laminated beams and plates are specialized from the shell ones.