An effective method is developed for determining the individual stresses from the trace of the stress tensor (isopachics) in a region adjacent to an arbitrarily-shaped traction-free boundary of a loaded component. The approach is facilitated by the fact that the stresses throughout such a region can be described completely in terms of only one complex potential. Equilibrium and compatibility prevail within the region, and the traction-free boundary conditions are satisfied. The concept is expected to be particularly useful for thermoelastic stress analysis.
RyallT. G.WongA. K.‘Determining stress components from thermoelastic data - a theoretical study’, Mech. Mater., 1988, 7, 205–214.
3.
BalasJ.‘Some applications of experimental analysis of models and structures’, Expl Mech., 1967, 7, 127–139.
4.
OliverD. E.‘Stress pattern analysis by thermal emission (SPATE)’, Handbook of experimental mechanics1986 (Edited by KobayashiA. S.) (Prentice-Hall, New York) ch. 14, pp. 610–620.
5.
MuskhelishviliN. I.Some basic problems of the mathematical theory of elasticity, 1963, 4th Edition, (Noordhoff, The Netherlands).
6.
SavinG. N.Stress concentration around holes, 1961 (Pergamon Press, Oxford).
7.
SokolnikoffI. S.Mathematical theory of elasticity, 1956 (McGraw-Hill, New York).
8.
HuangY. M.Determination of individual stresses from thermoelastically measured trace of stress tensor, PhD thesis, University of Wisconsin, 1989.
9.
GerhardtT. D.‘A hybrid finite-element stress analysis of notched anisotropic materials’, J. Appl. Mech., 1984, 15, 804–809.
10.
FreeseC. E.BowieO. L.‘Stress analysis of configurations involving small fillets,’J. Strain Analysis, 1975, 10, 53–58.
ChallisN. V.BurleyD. M.‘A numerical method for conformal mapping’, J. Numer. Analysis, 1982, 2, 169–181.
13.
HuangY. M.RowlandsR. E.LesniakJ. R.‘Thermoelastic determination of the individual stresses in the neighborhood of hole in a tensile plate’, Expl Mech., in press.
14.
ChurchillR. V.BrownJ. W.VerheyR. F.Complex variables and applications, 1974, 3rd Edition (McGraw-Hill, New York).
