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A direct vector combination procedure for finite element stiffness matrix formulation
Author(s) -
Mau S. T.
Publication year - 1982
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.1620180605
Subject(s) - stiffness matrix , finite element method , direct stiffness method , mathematics , displacement (psychology) , mathematical analysis , matrix (chemical analysis) , tangent stiffness matrix , structural engineering , engineering , materials science , psychology , composite material , psychotherapist
A direct vector combination procedure is developed for the formulation of finite element stiffness matrices. Only the homogeneous solution modes to governing equations of a problem and a uniquely defined interpolation displacement function along the element boundary are used to generate pairs of nodal displacement and nodal force vectors. The stiffness matrix is obtained by a simple multiplication of the nodal displacement and nodal force vectors. The element formed passes all the higher order patch tests for the order of solution modes included in the formulation. However, the stiffness matrix may become unsymmetrical. Restoring symmetry leads to compromising some of the higher order patch test performances. The present procedure is shown to have direct relations to those of the displacement model and the hybrid stress model. The present procedure presents new possibilities for the improvement of element performance. The procedure itself can also be used to study the limitations of element behaviour.