A nonlinear, in-plane displacement assumption is proposed, based on an
undetermined variation df/dz of transverse shear strains through the
plate thickness. A second-order ordinary differential equation for f(z
) and two surface conditions, as well as a set of eighth-order partial
differential equations and four associated boundary conditions, are d
erived from the principle of minimum potential energy. Coupling exists
between the partial and ordinary differential equations. In the homog
eneous solutions for the former, in addition to an interior solution c
ontribution, there exist two edge-zone solution contributions, one of
which induces self-equilibrated (in the thickness direction) boundary
stresses. Three examples are calculated using the present theory. The
last gives the stress couple and maximum-stress concentration factors
at the free edge of a circular hole in a large bent plate. Numerical r
esults for the examples are compared with those given by three-dimensi
onal elasticity theory and several two-dimensional theories. It is fou
nd chat the present theory can accurately predict nonlinear variations
of in-plane stresses through the thickness of a plate.