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A Linear, First‐order Shell Model for Transverse Isotropic Material under a Uniform Change of Temperature
Author(s) -
Pomp Andreas
Publication year - 1996
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199610)19:15<1177::aid-mma821>3.0.co;2-3
Subject(s) - isotropy , transverse plane , shell (structure) , mathematics , thermal expansion , plane (geometry) , bending , stress (linguistics) , thermal , mathematical analysis , mechanics , geometry , materials science , physics , thermodynamics , composite material , optics , structural engineering , linguistics , philosophy , engineering
Abstract A first‐order shell model is derived for describing the behaviour of a thin, arbitrarily curved structure made from homogeneous, transverse isotropic material under the influence of a uniform change of temperature. Transverse isotorpy means that the elastic behaviour and the thermal expansion is isotropic in in‐plane directions but different in thickness direction. The influence of the different thermal expansion is incorporated by equivalent stress couples and bending moments. Thus, a higher‐order approximation in thickness direction is not necessary. However, the so‐called ‘second approximation of shell theory’ must be used which deals with more accurate constitutive relations than the standard theory. Further the question is investigated in which cases a stress‐free transverse isotropic thermal deformation exists.