Stress singularities in BVPs with Robin and Ventcel boundary conditions. Applications in FEM modeling

Abstract: Linear-elastic antiplane-strain problems governed by the 2D Laplace equation are considered in domains with corners and cracks. First, power-logarithmic stress singularities in Neumann-Robin BVPs in infinite corner (polar sector) type domains are studied. Asymptotic solutions given by a double asymptotic series with the main and the associated shadow terms are presented. An application of such an asymptotic series to the numerical solution of the BVP of a crack in a thin adhesive interface layer modeled by the spring interface is shown by implementing a finite element method (FEM) procedure. Second, similar asymptotic analysis of power-logarithmic stress singularities in Dirichlet-Robin BVPs in infinite corners with a power-law variation (with the distance to the corner apex) of the governing coefficient in the Robin boundary condition is presented. An application of such an asymptotic solution to the BVPs of bridged cracks with a power-law variation of the stiffness of linear-elastic spring distribution is presented. Finally, a power-logarithmic stress singularity in a Dirichlet-Ventcel BVP in half domain is studied by a similar asymptotic procedure. An application of this asymptotic solution to the FEM solution of a BVP with a finite and open Gurtin-Murdoch material surface is presented.

MathematicsPhysics

Audience: researchers in the topic

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Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)

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