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Plane elastostatic boundary value problems (II). The role of inversion
Author(s) -
Buchwald V. T.
Publication year - 1963
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300003338
Subject(s) - biharmonic equation , mathematics , inversion (geology) , mathematical analysis , boundary value problem , inverse , transformation (genetics) , plane (geometry) , inverse problem , geometry , structural basin , paleontology , biochemistry , chemistry , gene , biology
Summary It is shown that in a certain sense, inversion transforms biharmonic functions into biharmonic functions. The first boundary value problem of elastostatics is also largely unchanged by this transformation, and known solutions can be used to obtain new results for inverse regions. As an example, the problem of a stress free dumb‐bell shaped hole in an infinite plate is solved.