ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
An explicit expression for the stiffness matrix is worked out for a triangular plate bending element considering the effect of transverse shear deformation. The element has twelve nodes on the sides and four nodes internal to it. The formulation is displacement type and the use of area co-ordinates makes it possible to obtain the shape functions explicitly. Separate polynomials are assumed for transverse displacement and rotations. To obtain the element stiffness matrix no matrix inversion or numerical integration need be carried out and only a few matrix multiplications of low order are necessary. The element, which is initially of thirty five degrees of freedom, can be reduced to a thirty degrees of freedom one by condensation of the internal nodes. An interesting feature of the element developed is that the values of nodal moments computed at a node point, considering different elements surrounding the node, do not vary significantly. Thus the nodal moments can be obtained directly at node points. Also, the element does not give rise to any inconvenience like locking, even for very thin plates. The straightforward approach in formation of the element stiffness will cut down the storage space considerably and will also call for less CPU time, thus making the use of the element well suited to low capacity computers. A number of plate bending problems have been worked out using the present element for different thickness to side ratios and a comparison has been made with the available results. Good accuracy has been observed in all cases, even for a small number of elements.
Additional Material:
5 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620320703
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