A welded stiffened microplate with surface elasticity containing a rigid line at the interface

Abstract

In additive manufacturing, explosive welding, and related processes, rigid inclusions inevitably form at the interface of bimaterial plates. This article investigates the influence of interfacial rigid lines on the bending behavior of a welded microplate structure, with particular emphasis on the interfacial stress fields, through theoretical modeling and numerical analysis. The original problem is transformed into a mixed boundary value problem via the superposition principle. Then, it is reduced to a Cauchy singular integral equation of the first kind using the Fourier transform method. Explicit expressions for the whole fields of internal moments and stresses at any position of the welded microplate are derived analytically. The obtained numerical results reveal that, at the nanoscale, surface effects significantly affect the singularity coefficients at the tips of rigid lines. A singular interfacial shear stress is also induced along the rigid line. When the bi-plate system reduces to a homogeneous plate stiffened by a rigid line, the results agree with previously reported solutions, validating the effectiveness of the present model.