Buckling of a plate on a pasternak foundation under uniform in-plane bending loads

In-plane bending loads occur in many thin-walled structures, including web core sandwich panels (foam-filled panels with interior webs) under transverse loading. The design of such structures is limited in part by local buckling of the thin webs and the subsequent impact on stiffness and strength. However, the core material can have a significant impact on web buckling strength and thus must be considered in design. This paper presents solutions for the buckling strength of simply supported plates under in-plane bending loads. The location of the neutral bending axis is allowed to vary and is characterized by a load parameter. A Pasternak model is used to account for the resistance of the foundation to compression and shear. Using the principle of minimum potential energy, buckling solutions are developed for infinitely long plates and representative foundation materials. The solutions match known results for two special cases: Uniform loading with variable foundation, and bending loads with no foundation. An order of magnitude increase in buckling strength is possible, depending on loading and foundation stiffness. The results suggest an important avenue for future development of lightweight structures, including sandwich panels and structures such as plate girders that are not typically associated with the use of foam filling.