Buckling equations of orthotropic thin plates

Abstract

Conventionally, only three components of stress, i.e., the membrane stresses ( 1σ xx, 1σ yy, 1σ xy) in x-y plane along span directions, are considered in deriving the buckling equations of thin plates using energy approaches. Of particular interest in this study is to take all the six components of stress into account in formulating the potential energy for an orthotropic plate. By invoking the conditions of stress equilibrium for the plate and Green's theorem to relate the potential energy to external virtual works, all the instability potential terms associated with the non-conventional stresses ( 1σ xz, 1σ yz, 1σ zz) can either cancel those terms conventionally referred to as higher-order terms or combine with them to yield some new but meaningful terms. For this reason, the present approach contains more physical and compact meaning than conventional ones in the process of derivation. With the present governing differential equations, bending buckling problems of orthotropic rectangular plates will be investigated in this study. Copyright © 2012 The Society of Theoretical and Applied Mechanics, R.O.C.