Author(s)

Y.A. Melnikov

Abstract

Invited paper Green's function approach to some nonlinear problems in applied mechanics Y.A. Melnikov Department of Mathematics and Statistics, Middle Tennessee State University, Murfreesboro, 7W ABSTRACT This presentation briefly introduces two new applications of the Green's function method (GFM) to nonlinear boundary value problems in applied mechanics. In particular, the geometrically nonlinear bending of a system of parallel thin elastic plates is discussed. The method is also applied to the construction of specially modified elasto-potentials which are used to solve two-dimensional external contact problems whose statement assumes that contact zones are initially unknown. The present paper begins with a brief history of the development of the GFM in the former Soviet Union and a review of the author's more recent results. INTRODUCTION The remarkable contributions of Russian-speaking scientists to the boundary element methodology are universally reco

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