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Improved quadratic elements
Author(s) -
Chang Anthony T.
Publication year - 1976
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.1620100616
Subject(s) - quadratic equation , mathematics , eigenvalues and eigenvectors , vibration , quadratic programming , quadratic function , node (physics) , bar (unit) , binary quadratic form , finite element method , element (criminal law) , mathematical optimization , geometry , structural engineering , engineering , physics , quantum mechanics , meteorology , political science , law
A general method to formulate improved quadratic elements is presented. Derivation of the method is based on more accurate shape functions that take into account effects of governing differential equations. These new shape functions have the same form as those of the standard eight‐node quadratic element. Therefore, they may be easily adapted into existing programs. The new quadratic element is compared with both standard and standard condensed quadratic elements. To show relative merits of different quadratic elements eigenvalue tests are performed. Several examples ranging from field problems, plane stress and bar vibration are used to demonstrate the applicability of this approach.