When examining a structure’s response to loading, it is necessary to express the equilibrium equations in terms of displacements [1]. This can be done by expressing stress resultants in terms of reference surface strains and curvatures, and then by expressing the surface strains and
2
curvatures in terms of surface displacements. The matrix relation between the stress resultants and the reference surface deformations are: (2)
where the laminate stiffness matrix is defined as: ∑ ∑
(3a) (3b) (3c) (4a)
,
∑ and the reference strains and curvatures are defined as: , ,
, ,
,
,
,
(4b) (4c) (4d)
,
,
Boundary conditions are extremely important in the examination of laminated plates. For the governing equations to be effective, boundary conditions must be satisfied along each edge of the plate. This results in four boundary conditions, which are used to simplify the extensive equilibrium equations. Furthermore, the specific class of the laminate can be used to simplify the equations further, resulting in a more manageable calculation. The most common simplifications result from symmetric laminates, symmetric balanced laminates, symmetric cross-ply laminates, and isotropic plates [1]. After expressions for the displacements are generated and simplified, the stresses and strains of the plates can be determined. This can be accomplished via kinematics for classical plates. Kinematics describes how a