Modelling and Analysis of Plates

Abstract

The modelling and analysis of plates constituted of laminate or sandwich material is a problem of more complexity than that of beams, considered in Chap. 7. Generally, plates are two-dimensional thin structure elements with a plane middle surface. The thickness h is small relatively to the two other dimensions a, b (Fig. 8.1). In Chap. 8 all derivatives are as a matter of priority restricted to rectangular plates including the special case of a plate strip, i.e. a rectangular plate element which is very long, for instance in the x ²-direction and has finite dimension in the x ¹ direction. When the transverse plate loading, the plate stiffness, and the boundary conditions for the plate edges x ¹ = const are independent of the coordinate x ², the plate strip modelling can be reduced to a one-dimensional problem. The analysis is nearly the same as in the beam theory. Chapter 8 gives a first introduction to the classical plate theory and the plate theory including transverse shear deformations. The derivations of the principal equations for plates relies upon the basic considerations of Chap. 5.