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Application of the Ritz method to plane elasticity problems for composite sheets with variable fibre spacing
Author(s) -
Martin A. F.,
Leissa A. W.
Publication year - 1989
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.1620280808
Subject(s) - ritz method , elasticity (physics) , variable (mathematics) , composite number , mathematics , mathematical analysis , plane (geometry) , stress (linguistics) , materials science , composite material , geometry , algorithm , linguistics , boundary value problem , philosophy
The plane stress problem of a parallel fibre, rectangular composite sheet with variable fibre content is investigated. The resulting sheets are governed by partial differential equations that have variable coefficients, which are generally unsolvable exactly. A Ritz method is used to approximate the solution and is checked against known problems having exact solutions. The method is found to determine closely both the displacements and the stresses with fewer than 200 degrees of freedom. It is then applied to two interesting problems for which no exact solutions exist, including that of uniform normal stress applied in the direction of the fibres.