Premium
Effective hybrid hierarchical element generator for vibration analysis of plates
Author(s) -
Alaylioglu Ayse,
Alaylioglu H.
Publication year - 1987
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.1620240902
Subject(s) - finite element method , vibration , generator (circuit theory) , convergence (economics) , computer science , stiffness , range (aeronautics) , rank (graph theory) , boundary (topology) , structural engineering , algorithm , mathematical optimization , engineering , mathematics , mathematical analysis , acoustics , power (physics) , physics , quantum mechanics , combinatorics , aerospace engineering , economics , economic growth
Cost effective high precision hybrid elements are presented in a hierarchical form for vibration analysis of plates. The elements are constructed by introducing computer installed hierarchical element generator algorithms which take advantage of the exact analytical treatment of the energy integrals automatically. Additional benefits accrue from: (i) the careful selection of assumed stresses and displacements satisfying finite element requirements, and maintaining the correct stiffness rank and invariance; (ii) the ability to reduce computational costs associated with various operations and the independence with respect to element geometries, which serve to build up a methodology to handle the generation of finite elements in any general purpose finite element system efficiently. Extensive numerical studies are made to predict the natural frequencies and harmonic response of plates with different boundary conditions. Accuracy of the solutions is assessed by comparison with the well established results. The noteworthy aspects of the applications are that the proposed elements are faster than those cited previously, and show a more favourable comparison to the analytical solutions for a wider range of vibration modes by maintaining rapid convergence characteristics.