On the free terms of boundary integral equations for thick plates undergoing large displacements

Abstract

This work presents a theoretical derivation of the convective terms appearing in integral equations for large displacement analysis of the Mindlin and the Reissner plate models. They are necessary to complete the Somigliana identities of the problem, since the non-linear terms in the Green-Lagrange strain tensor require additional derivative, hypersingular integral equations for the gradient of the displacement field. The attainment of these terms is commonly omitted in the literature, in spite of their presence in the integral equations for most nonlinear elasticity problems. With all the free terms identified, a complete set of integral equations for large displacement analysis of moderately thick plate models is obtained, aiming its BEM implementation. Numerical comparisons are made with available solutions showing good agreement.