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Consistent force resultant distributions in displacement elements with varying sectional properties
Author(s) -
Prathap G.,
Naganarayana B. P.
Publication year - 1990
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.1620290407
Subject(s) - finite element method , displacement (psychology) , displacement field , mathematics , consistency (knowledge bases) , mathematical analysis , elasticity (physics) , field (mathematics) , element (criminal law) , quadratic equation , type (biology) , classical mechanics , geometry , physics , structural engineering , engineering , psychology , ecology , biology , law , pure mathematics , psychotherapist , thermodynamics , political science
Force fields computed directly from strains calculated in a displacement type finite element description of a structural element of varying sectional rigidities show extraneous oscillations. The origin of these oscillations is traced to the fact that the displacement type finite element procedure determines strains derived from the displacement field in a least squares correct sense and that force resultants computed using these strain fields and the actual sectional rigidities result in unwanted oscillations. It is necessary to introduce the concept of redistributed assumed force resultant fields that maintain a ‘consistent’ relationship to the strain fields and also are orthogonal to these strain functions. In this paper, the Hu–Washizu theorem is invoked to justify the introduction of an orthogonally correct reconstituted assumed force resultant field which will then be free of extraneous oscillations. The quadratic isoparametric tapered bar element serves to illustrate the underlying principles. It follows that the extremely general Hu–Washizu principle is the most practical procedure of implementing an assumed force resultant, assumed strain displacement type formulation to introduce consistency and thereby remove problems associated with field‐inconsistency (such as cause locking in constrained media elasticity) and force resultant oscillations due to varying sectional properties.