Abstract
In the present work, a Finite Element–Boundary Integral Equation (FE–BIE) coupling method is proposed to investigate the problem of axially loaded thin structures bonded to a homogeneous elastic half-plane. Making use of a mixed variational formulation including the Green function of the substrate, the axial displacement of the bar is interpolated using Lagrange polynomials of first or second order, whereas the interfacial shear stress is approximated by piecewise constant functions. Bars subject to different load conditions are investigated, including the case of a bar partially detached from the substrate. The strength of interfacial stress singularities is investigated in detail.
Highlights
The problem of an axially loaded bar attached to a plate has been widely investigated in mechanical and civil engineering, where it is relevant to stress distribution in stiffened sheet [1]
Interest in the problem has been renewed by composite materials used in structural strengthening of concrete, steel, wood [2], ceramic coatings protecting alloy substrate [3] and electronic devices with metal films bonded to a polymer or silicon substrate [4]
A coupled Finite Element–Boundary Integral Equation (FE–boundary integral equation (BIE)) method has been proposed to evaluate the mechanical behaviour of elastic thin structures bonded to a homogeneous isotropic half-plane under axial forces or thermal loads
Summary
The problem of an axially loaded bar attached to a plate has been widely investigated in mechanical and civil engineering, where it is relevant to stress distribution in stiffened sheet [1]. The problem of a bar of finite length bonded to an elastic half-space and subject to various load conditions was investigated, for example, in [8,9,10] In these references, the governing integro-differential equation is solved by adopting power or Chebyshev polynomials series expansion to approximate the unknown interfacial stress. Similar to the one presented in this paper, was used in [27] to study the frictionless interaction of a Timoshenko beam with the underlying soil In this respect, the present work represents the natural extension of the method to analyse a bar, with zero bending stiffness, perfectly bonded to a substrate. These advantages allow accurate solutions and the strength of the interfacial stress singularity can be correctly assessed
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