Kirchhoff shear force

The boundary conditions for these equilibrium equations are more complicated than for classical lamination theory. However, they are more logical because the Kirchhoff shear force or free-edge condition, in which... 

This set of partial differential equations has two boundary conditions at each edge which are represented by the first two choices in Equations (D.23) and (D.24). When the geometric boundary condition of edge restraint in the z-direction is considered, the Kirchhoff shear force is not active as a boundary condition. 

The simplest physical idealization of the film that incorporates bending resistance is that of an elastic plate which admits extensional and bending deformation but no shear deformation this model is known commonly as a Kirchhoff plate. The boundary value problem is illustrated schematically in Figure 4.4, where the film and the substrate have been separated to show the shear stress distribution q x) and the normal stress distribution p x) together which represent interaction between the film and substrate. Also shown acting on a section of the film at distance x from the edge is an internal extensional force t x), an internal shear force s x) and an internal bending moment m x), all measured per unit thickness in the j/—direction. 

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