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A modified plate model for an efficient analytical treatment of stress concentrations at notches
Author(s) -
Felger Julian,
Becker Wilfried
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800133
Subject(s) - plate theory , shear (geology) , bending of plates , shear stress , deformation (meteorology) , mechanics , bending , stress (linguistics) , stress field , transverse shear , mathematical analysis , critical resolved shear stress , bending moment , transverse plane , physics , geometry , materials science , mathematics , structural engineering , shear rate , boundary value problem , finite element method , engineering , composite material , linguistics , philosophy , viscosity
In the present work, a modified plate model is proposed lying in‐between the established Kirchhoff‐Love and first‐order shear deformation plate theories. The resulting system of partial differential equations can be solved using a complex potential approach which allows for tackling complex geometries such as sharp or rounded notches. Using the proposed model, the singular stress field in the vicinity of a sharp notch can be obtained explicitly and the influence of the notch opening‐angle on the singular behaviour is investigated. It is shown that resulting bending moments and transverse shear forces match with asymptotic solutions according to first‐order shear deformation plate theory and are in very good agreement with numerical results.