Classical and Improved Theories
In this chapter, the theoretical background for two commonly used structural theories for the modelling and analysis of laminates and sandwiches is considered, namely the classical laminate theory and the first-order shear deformation theory. The classical laminate theory (CLT) and the first-order shear deformation theory (FSDT) are the most commonly used theories for analyzing laminated or sandwiched beams, plates and shells in engineering applications. The CLT is an extension of Kirchhoff’s classical plate theory for homogeneous isotropic plates to laminated composite plates with a reasonable high width-to-thickness ratio. For homogeneous isotropic plates the Kirchhoff’s theory is limited to thin plates with ratios of maximum plate deflection w to plate thickness h < 0.2 and plate thickness/ minimum in-plane dimensions < 0.1. Unlike homogeneous isotropic structure elements, laminated plates or sandwich structures have a higher ratio of in-plane Young’s moduli to the interlaminar shear moduli, i.e. such composite structure elements have a lower transverse shear stiffness and often have significant transverse shear deformations at lower thickness-to span ratios < 0.05. Otherwise the maximum deflections can be considerable larger than predicted by CLT. Furthermore, the CLT cannot yield adequate correct through-the-thickness stresses and failure estimations. As a result of these considerations it is appropriate to develop higher-order laminated and sandwich theories which can be applied to moderate thick structure elements, e.g. the FSDT. CLT and FSDT are so-called equivalent single-layer theories (ESLT).
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