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A conforming finite element with internal equilibrium for two‐dimensional problems
Author(s) -
Yam Lloyd C. P.
Publication year - 1972
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.1620040307
Subject(s) - compatibility (geochemistry) , finite element method , displacement field , stiffness matrix , mathematics , displacement (psychology) , mathematical analysis , slab , mixed finite element method , convergence (economics) , extended finite element method , stiffness , geometry , structural engineering , engineering , psychology , chemical engineering , economics , psychotherapist , economic growth
A method is presented for the derivation of displacement fields which satisfy compatibility of normal slopes at inter‐element boundaries and the condition of internal equilibrium. The displacement field is obtained by integrating the governing partial differential equation over the element, using the initial value approach. The method is applied to calculate the stiffness matrix of a triangular bending element with nine degrees of freedom. Comparison with published solutions based on various element models shows a high degree of accuracy and convergence of the method. The advantage of internal equilibrium is illustrated by an example involving slab‐column interaction. The solution correlates satisfactorily with existing experimental results.