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Decomposition method in linear elastic problems with eigenstrain
Author(s) -
Nyashin Y.,
Lokhov V.,
Ziegler F.
Publication year - 2005
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200510202
Subject(s) - eigenstrain , decomposition , mathematics , materials science , mathematical analysis , composite material , chemistry , residual stress , organic chemistry
The general theory of linearized elasticity with eigenstrain is considered with applications to continuous, discrete and discretized structures. It is shown that any eigenstrain can be uniquely decomposed into impotent and nilpotent constituents. The proven theorem on decomposition is based on the concepts of functional analysis, in particular, with respect to Hilbert functional spaces. This unique decomposition allows for the individual and independent control of stress, strain and displacement (e.g. shape control). The associated algorithm avoids the cumbersome solution of boundary‐value problems with eigenstrain in connection with these control problems. Decomposition of eigenstrain opens the practically important opportunity to fully separate the control of strain and stress produced by force loading.