The classical stress analysis relations of the small deformation theory of plates resulting from lateral loading have been discussed in preceding chapters. Attention is now directed to problems where combined lateral and in-plane forces act at a plate section. The in-plane forces are also called membrane forces, which may be applied directly at the plate edges, or they may result from temperature changes. First, the governing differential equations are modified to include the simultaneous action of the combined loading. Then, buckling stresses caused by in-plane compression, pure shear, and biaxial compression are considered.
Discussions include the development of governing equations for the deflection surface and buckling of plates, through the use of equilibrium, energy, and finite difference methods. Also treated are plates with initial curvature and long rectangular plates bent into a cylindrical surface. The problem of plates with small initial curvature under the action of combined forces is analyzed. The chapter concludes by considering a plate bent into a simple surface of practical importance.