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A coupled FE-BIE model for the static analysis of Timoshenko beams bonded to an orthotropic elastic half-plane. (English) Zbl 1403.74240
Summary: Interface displacements, surface tractions and stresses of a flexible beam bonded to an elastic orthotropic half-plane are analysed by means of a Finite Element-Boundary Integral Equation (FE-BIE) method. Numerical results are obtained by using locking-free shear deformable beams and piecewise constant interfacial reactions. Making use of the generalised Green’s function for the half-plane, the mechanical behaviour of fully bonded or detached beams subjected to force, couple or thermal load is investigated. The special cases of a beam in bilateral frictionless contact with the half-plane and a beam having a vanishing bending rigidity (thin film) are considered also. In particular, the maximum bending moment of beams subjected to a vertical point force are compared with some closed-form solutions of the contact problem of a rigid indenter and with the solution of an infinite Euler-Bernoulli beam in bilateral frictionless contact with an isotropic substrate.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74M15 Contact in solid mechanics
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