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Finite layer analysis of layered elastic materials using a flexibility approach. Part 2—Circular and rectangular loadings
Author(s) -
Small J. C.,
Booker J. R.
Publication year - 1986
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.1620230515
Subject(s) - flexibility method , anisotropy , matrix (chemical analysis) , stiffness , flexibility (engineering) , stiffness matrix , compressibility , finite strip method , direct stiffness method , mathematics , mathematical analysis , layer (electronics) , hankel transform , structural engineering , fourier transform , finite element method , geometry , materials science , engineering , mechanics , composite material , physics , optics , statistics
The finite layer techniques introduced in Part 1 of this paper are extended to allow the analysis of circular or general loadings applied to horizontally layered anisotropic materials. The analysis is considerably simplified through the use of Hankel transforms (circular loadings) and double Fourier transformations (general loadings). Once again an exact flexibility matrix is found for each finite layer, and it is shown that this flexibility matrix has precisely the same form whether the loading is a strip, circular or general loading. The flexibility matrix has the advantage of not becoming singular for incompressible materials as is the case for the stiffness matrices used in a conventional finite strip analysis. Examples are given of the behaviour of circular and general (rectangular) loadings applied to multilayered anisotropic materials. It is also shown by means of an example, that the method is extremely useful for analysis of problems involving incompressible materials.