The three-dimensional boundary integral equation (BIE) method is used to solve two elastostatic problems involving complex toroidal geometries. The first problem concerns a thick-walled 180 degree pipe bend connected to tangent pipes, subjected to in-plane bending and internal pressure. Results are presented for stresses and are compared with results from previous numerical and experimental work. The second problem concerns a thick-walled pressurized torus, with cross bores situated in the toroidal plane. Separate solutions are given for cross bores located at the intrados and extrados of the torus. Results are presented for the stress concentration factor, and are compared with numerical work for thick-walled cylindrical pipes.
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References
1.
KorneckiA.‘Stress distribution in a pressurized thick-walled toroidal shell - A three dimensional analysis’, College of Aeronautics, Cranfield, Note 137, 1963.
2.
McgillD. J.RappI. H.‘Axisymmetric stresses and displacements in thick-walled elastic torus’, J. engng Mech. Div., ASCE, 1973, 99, 629–633.
3.
LangH. A.‘Toroidal elastic stress fields for pressurized elbows and pipe bends’, Int. J. Pressure Vessels Piping, 1984, 15, 291–305.
4.
ColleA.Elastostatic analysis of thick-walled tori and pipe bends using the boundary integral equation method, MASc thesis, University of Ottawa, 1986.
5.
CruseT. A.‘Numerical solutions in three dimensional elastostatics’, Int. J. Solid Structures, 1969, 5, 1259–1274.
6.
CruseT. A.‘Application of the boundary integral equation method to three dimensional stress analysis’, Comput. Struct., 1973, 3, 509–527.
7.
CruseT. A.‘An improved boundary integral equation method for three dimensional elastic stress analysis’, Comput. Struct.1974, 4, 741–754.
8.
BoissenotJ. M.LachatJ. C.WatsonJ. O.‘Etude par equation integrale d'une eprouvette C.T. 15’, Revue de Physique Appliquée, (Département D.T.E.-CETIM) 1974, 9, 611–615.
9.
LachatJ. C.A further development of the boundary integral technique for elastostatics, PhD thesis, University of Southampton 1975
10.
LachatJ. C.WatsonJ. O.‘A second generation boundary integral equation problem for three dimensional elastic analysis’, ASME Proc. AMD, 1975, 11.
11.
LachatJ. C.WatsonJ. O.‘Effective numerical treatment of boundary integral equations’, Int. J. numer. Methods Engng, 1976, 10, 991–1005.
12.
LachatJ. C.WatsonJ. O.‘Progress in the use of boundary integral equations, illustrated by examples’, Comp. Meths. appl. mech. Engng, 1977, 10, 273–289.
13.
WatsonJ. O.‘Advanced implementation of the boundary element method for two and three dimensional elastostatics’, in Developments in Boundary Element Methods 1, 1979 (Edited by Banerjee and Butterfield) (Applied Science, London) pp. 31–63.
14.
TanC. L.FennerR. T.‘Three-dimensional stress analysis by the boundary integral equation method’, J. Strain Analysis, 1978, 13, 213–219.
15.
TanC. L.FennerR. T.‘Elastic fracture mechanics analysis by the boundary integral equation method’, Proc. R. Soc. Lond., 1979, A369, 243–260.
16.
ColleA. R.RedekopD.TanC. L.‘Pressure loading and bending of hollow tori’, Int. J. Pressure Vessels Piping, 1987, 27, 137–154.
17.
PardueT. E.VignessI.‘Properties of thin walled curved tube of short-bend radius’, Trans ASME, 1951, 73, 77–87.
18.
JonesN.‘In plane bending of a short curved pipe bend’, J. Engng Ind., 1967, 271–277.
19.
ThailerH. J.ChengD. H.‘In-plane bending of a U-shaped circular tube with end constraints’, Trans ASME, 197092, 792–796.
20.
KalminoA.‘Stress analysis of curved tubes’, 1st Int. Conf. on P.V. Tech., Part I, Delft, 1969, pp. 223–235.
21.
NatarajanR.BlomfieldJ.‘Stress analysis of curved pipes with end restraints’, Comput. Struct.1975, 5, 187–196.
22.
ThompsonJ. J.‘Shell theory analysis of pure in-plane bending of a pipe bend’, Trans. Third Int. Conf. Struct. Mech. Reactor Tech., London F6/1, pp. 1–5.
23.
OhtsuboH.WatanabeO.‘Flexibility and stress factors of pipe bends - An analysis by finite ring method’, ASME J. Pressure Vessel Technol., 1977, 2, 281–290.
24.
WhathamJ. F.‘In-plane bending of flange pipe elbows’, Inst. Eng. Au Civ. Eng. Trans, 1979, 21, 80–85.
25.
BatheK. J.AlmeidaC. A.‘A simple and effective pipe elbow element - linear analysis’, ASME J. Appl. Mech., 1980, 47, 93–100.
26.
TurnerC. E.FordH.‘Examination of the theories for calculating the stresses in pipe bends subjected to in-plane bending’, Proc. Instn mech. Engrs1957, 171, 513–525.
27.
SwansonS. A. V.FordH.‘Stresses in thick-walled plane pipe bends’, J. Mech. Engng, 1959, 103–112.
28.
PattabiramanJ.RamamurtiV.ReddyD. V.‘Statics and dynamics of elastic shells with cutouts - a review’, J. Ship Res., 1974, 18, 113–126.
29.
GuzA. N.‘Investigation in the theory of thin shells with openings (review)’, Sov. Appl. Mech., 1979, 15, 1015–1042.
30.
Van DykeP.‘Stresses about a circular hole in a cylindrical shell’, AIAA J., 1965, 3, 1733–1742.
31.
GavelyaS. P.‘Calculation of the stress-strain state of a toroidal shell with holes’, Sov. Appl. Mech., 1973, 9, 117–124.
32.
MorrisonJ. L. M.CrosslandB.ParryJ. S. C.‘Fatigue strength of cylinders with cross bores’, J. mech. Engng. Sci., 1959, 1, 207–210.
33.
FaupelJ. H.HarrisD. B.‘Stress concentration in heavy-walled cylindrical pressure vessels’, J. Ind. Chem., 1979, 49, 1979–1986.
34.
GerdeenJ. C.Analysis of stress concentrations in thick cylinders with side holes and cross bores’, J. Eng. Ind. Trans. ASME, 1972, 94, 815–824.
35.
GerdeenJ. C.SmithR. E.‘Experimental determination of stress concentration factors in thick-walled cylinders with cross bores and side holes’, Expl. Mech., 1972, 12, 530–536.
36.
TanC. L.FennerR. T.‘Boundary integral equation stress analysis of some problems in high pressure engineering’, Proc. Second Int. Num. Anal. Appl. Eng. Sci., Montréal, 1980, pp. 787–795.
37.
Abdul-MihseinM. J.FennerR. T.‘Some boundary integral equation solutions for three-dimensional stress concentration problem’, J. Strain Analysis, 1983, 18, 207–215.
38.
TanC. L.‘Stress redistribution in thick-walled cylinders due to the introduction of a cross bore after autofrettage’, J. Strain Analysis, 1986, 21, 177–183.
