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A critical analysis of quadratic beam finite elements
Author(s) -
Rakowski Jerzy
Publication year - 1991
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.1620310509
Subject(s) - discretization , stiffness matrix , finite element method , mathematics , beam (structure) , quadratic equation , timoshenko beam theory , mathematical analysis , bending stiffness , matrix (chemical analysis) , stiffness , direct stiffness method , type (biology) , simple (philosophy) , geometry , structural engineering , engineering , materials science , ecology , philosophy , epistemology , composite material , biology
A new methodology of evaluation of C 0 beam elements is presented. It is shown that, knowing the stiffness matrix of an arbitrary type of element, it is possible to create equivalent equilibrium conditions expressed in the form of one difference equation for a regular beam discretized by these elements. The study of the convergence of one difference equation gives an interpretation of the source of troubles occurring in low‐order bending elements which is more convincing than the usually applied consideration of the conditioning of element stiffness matrices. A careful examination of quadratic Mindlin elements provides a very clear explanation of the shear locking essence in the Timoshenko beam. The presented method enables one to identify errors that appear also in the reduced integrated or constrained elements. For each type of analysed quadratic element an adequate difference equation is derived and compared with the exact one. Based on this comparison a simple method of corrections is proposed that completely eliminates the errors associated with the application of C 0 bending elements.