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A boundary integral equation method for plate flexure with conditions inside the domain
Author(s) -
Bezine G.
Publication year - 1981
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620171106
Subject(s) - mathematics , boundary value problem , discretization , mathematical analysis , integral equation , plate theory , bending of plates , deflection (physics) , invertible matrix , geometry , structural engineering , bending , physics , classical mechanics , engineering , pure mathematics
A method for solving boundary value problems for thin plate flexure as described by Kirchhoff's theory is proposed. An integral formulation leads to a system of boundary integral equations involving values of deflection, slope, bending moment and transverse shear force along the edge. A discretization leading to a matrix formulation is proposed. To solve problems with inner conditions in the plate domain, an elimination of boundary unknowns proves successful. The degenerate case where the boundary is free (which leads to a non‐invertible matrix) is investigated. Three examples illustrate the efficiency of the method.