ELASTOSTATICS 149
elements and used two different boundary element discretisations:
one with 9 segments and the other with 18 segments for comparison
(Figure 5.21). By the symmetry of the problem only the area ABCDE
of Figure 5.20 was considered.
For the purposes of the analysis the wires were taken to be perfectly
rigid. The overall imposed strain was 1-667 x
10
"
2
inthexj direction.
The modulus of elasticity was taken to be 20 N mm "
2
and the two
values of Poisson's ratio v = 0-45 and v = 0-5 were considered.
For v = 0-45 the stresses σ
χ
χ
calculated using the two meshes were
virtually indistinguishable (Figure 5.22(a)). The stars represent the
results for the coarse mesh and the solid line shows the values
obtained using the finer, 18 element mesh.
For v = 0-5 (Figure 5.22(b)) this difference was greater, up to 5 of
the maximum stress. However, there is very little difference between
the displacements.
Note. The finite element displacement method is incapable of treating
the case v = 0-5.
REFERENCES
1.
Cruse, T. A. and Wilson, R. B., 'Advanced Applications of Boundary Integral
Equation Methods', Nuclear Engng Design, 46, 223-34 (1978)
2.
Cruse, T. A. and Meyers, G. J., Two dimensional fracture mechanics analysis', J.
Struct. Div, Proc. ASCE, 103, 309-20 (1977)
3.
Brebbia, C. A. and Nakaguma, R., 'Applications of Boundary Elements in the
Analysis of Offshore Structures', Proc. Brazil Offshore/11 Rio de Janeiro, Pentech
Press (1978)
4.
Boissenot, J. M., Lachat, J. C. and Watson, J., "fetude par Equations Integrals
D'une fiprouvette C. T. 15', Rev. Physique Appl, 9, 611, July (1974)
5. Cruse, T. A., 'Two Dimensional BIE Fracture Mechanics Analysis', Proc. 1st Int.
Seminar on Recent Advances in Boundary Element Methods, Southampton
University, July 1978, Pentech Press (1978)
6. Krenk, S., 'Stress Concentration Around Holes in Anisotropie Sheets', Proc. 1st
Int. Seminar on Recent Advances in Boundary Element, Methods, Southampton
University, July 1978, Pentech Press (1978)
7.
Lekhnitskii, S. G., Theory of Elasticity of an Anisotropie Elastic Body, Holden-Day
Inc.,
San Francisco (1963)
8. Lachat, J. C, 'A Further Development of the Boundary Integral Technique for
Elastostatics', Ph.D. Thesis, University of Southampton, Dept of Civil
Engineering, February (1975)
9. Peterson, R. E. Stress Concentration Factors, Wiley, New York (1953)
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