A three-dimensional boundary element stress and bending analysis of transversely/longitudinally graded plates with circular cutouts under biaxial loading

In the present paper, a full three-dimensional graded boundary element model adequate for elastostatic response investigation of heterogeneous plates fabricated from functionally graded materials (FGMs) with circular cutouts is presented. The local volume fractions of the constituent materials vary continuously in the transverse or longitudinal direction according to an exponential law. In contrast to all of the available works, influence of the bending-extension coupling due to asymmetric transverse distribution of the material properties is considered under a biaxial loading. The available works have used the plane stress assumption. A numerical implementation of Somigliana identity for three-dimensional elasticity of the isotropic heterogeneous plates is represented implicitly. On the basis of the constitutive and governing equations of the FGM plate and the weighted residual technique, an effective computational formulation is developed for the heterogeneous isotropic solid models. Verification is accomplished through comparisons made with results of ANSYS software for homogeneous models. Influence of the location of the cutout, effects of the distance from the boundary, and effects of the load ratio have also been studied and discussed in detail. •A full 3D graded BEM is developed for response analysis of heterogeneous plates.•The exponentially graded plate contains a circular cutout.•Bending-extension coupling is considered under biaxial loadings, for the first time.•A numerical Somigliana identity for 3D elasticity of the FGMs is implemented.•Effects of hole location, hole-edge interaction, and load ratio are also studied.