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Three dimensional hybrid‐ Trefftz stress finite elements for plates and shells
Author(s) -
Martins P. H. C.,
Bussamra F. L. S.,
Luceeto E.
Publication year - 2017
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.5715
Subject(s) - hexahedron , finite element method , mathematics , stress field , stress (linguistics) , polynomial , displacement field , boundary value problem , mathematical analysis , a priori and a posteriori , displacement (psychology) , constraint (computer aided design) , boundary (topology) , geometry , structural engineering , engineering , psychology , philosophy , linguistics , epistemology , psychotherapist
Summary Three‐dimensional hybrid‐Trefftz stress finite elements for plates and shells are proposed. Two independent fields are approximated: stresses within the element and displacement on their boundary. The required stress field derived from the Papkovitch‐Neuber solution of the Navier equation, which a priori satisfies the Trefftz constraint, is generated using homogeneous harmonic polynomials. Restriction on the polynomial degree in the coordinate measured along the thickness direction is imposed to reduce the number of independent terms. Explicit expressions of the corresponding independent polynomials are listed up to the fifth order. Illustrative applications to evaluate displacements and stresses are conducted by hexahedral hybrid‐Trefftz stress element models. The hierarchical p ‐ and h ‐refinement strategy are exploited in the numerical tests.