Modified complementary variational principles for a boundary-value problem in twisting of ring sectors

Arthurs, A. M.; Duggan, R. C.

doi:10.1090/qam/449131

Authors: A. M. Arthurs and R. C. Duggan
Journal: Quart. Appl. Math. 33 (1975), 304-307
MSC: Primary 73.49
DOI: https://doi.org/10.1090/qam/449131
MathSciNet review: 449131
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Abstract: New dual extremum principles and error bounds for the problem of stress in close-coiled helical springs are presented. An accurate variational solution is obtained in an illustrative calculation.

S. Timoshenko, Theory of elasticity, New York, 1934, pp. 355–361.

N. Anderson and A. M. Arthurs, Complementary variational principles for a boundary-value problem in twisting of ring sectors, Quart. Appl. Math. 33 (1975/76), 87–89. MR 446025, DOI https://doi.org/10.1090/S0033-569X-1975-0446025-0
J. L. Synge, Note on a paper by N. Anderson [Norman Anderson] and A. M. Arthurs: “Complementary variational principles for a boundary-value problem in twisting of ring sectors” (Quart. Appl. Math. 33 (1975), 87–89), Quart. Appl. Math. 33 (1975/76), 91–92. MR 446026, DOI https://doi.org/10.1090/S0033-569X-1975-0446026-3

A. M. Arthurs, Complementary variational principles, Oxford, 1970

A. M. Arthurs, J. Math. Anal. Appl., to appear

A. M. Arthurs, Dual extremum principles and error bounds for a class of boundary value problems, J. Math. Anal. Appl. 41 (1973), 781–795. MR 386299, DOI https://doi.org/10.1016/0022-247X%2873%2990249-7