ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
A theory is proposed in this paper to explain, in a unified manner, the three rational approaches using the incompatible displacements uλ in the hybrid element formulation. Limited to the plane stress case, the theory suggests that the introduction of uλ is to constrain the total value of the invariant I2(= σxσy - τxy2) of the assumed stresses over the element to zero. In the plane stress case, this is the well-known condition for the stress distributions to be independent of the elastic constants of the material. The theory proposed is also used to explain the closeness of the performances of the four 4-node hybrid stress membrane elements, 5β-I, 5β-II, 5β-A and 5β-C, that have been developed previously. The differences among them are shown to be of the second degree in the distortion measures of the element shape, when they are compared on the basis of the non-vanishing total value of I2 of their respectively adopted assumed stress field. Several numerical examples are used to verify and to illustrate the proposed theory.
Additional Material:
4 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620370306
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