ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
A family of high-order, conforming triangles for the finite element analysis of plate bending problems is developed, using the displacement method of formulation.The development proceeds in two steps. A family of non-conforming triangles, based on polynomial expansions of order 〉4 is first generated, and its performance found to be unacceptable. Nodal variables for the non-conforming family are selected from the set w, wx, wy, wn. The elements are then made to conform, by adding a twist nodal variable wnt at the mid-side nodes. Rational functions define the three additional degrees-of-freedom. Simple and very accurate procedures solve the problems associated with the use of such functions.Numerical results are presented for the conforming triangles of order 4 and 7, following a brief description of the two elements. A listing of the explicit shape functions for the quartic triangle is included.The numerical results are very good. In particular, they are superior per degree-of-freedom to the results predicted by the various non-conforming and conforming, cubic and related elements at present used in computer packages. Together with a similar performance by the quintic member10 of the family, they validate the proposed theoretical solution.
Additional Material:
10 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620190903
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