On stress functions for elastokinetics and the integration of the repeated wave equation
Authors:
E. Sternberg and R. A. Eubanks
Journal:
Quart. Appl. Math. 15 (1957), 149-153
MSC:
Primary 73.2X
DOI:
https://doi.org/10.1090/qam/91657
MathSciNet review:
91657
Full-text PDF Free Access
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B. Galerkin, Contribution à la solution générale du problème de la théorie de l’élasticité dans le cas de trois dimensions, C. R., Acad. Sci. Paris 190, 1047 (1930)
- Maria Iacovache, On an extension of Galerkin’s method to the system of equations of elasticity, Acad. Repub. Pop. Române. Bul. Şti. A. 1 (1949), 593–596 (Romanian, with French and Russian summaries). MR 45554
- Gr. C. Moisil, Sur les systèmes d’équations aux dérivées partielles linéaires et à coefficients constants, Acad. Repub. Pop. Române. Bul. Şti. A. 1 (1949), 341–351 (French, with Romanian and Russian summaries). MR 37442
P. F. Papkovich, Solution générale des équations différentielles fondamentales d’élasticité exprimée par trois fonctions harmoniques, C. R., Acad. Sci. Paris 195, 513 (1932)
Emilio Almansi, Sull’ integrazione dell’ equazione differenziale ${\nabla ^{2n}} = 0$ Ann. di Mat., Ser 3, 2, 1 (1899)
- R. D. Mindlin, Note on the Galerkin and Papkovitch stress functions, Bull. Amer. Math. Soc. 42 (1936), no. 6, 373–376. MR 1563303, DOI https://doi.org/10.1090/S0002-9904-1936-06304-4
- H. M. Westergaard, Theory of elasticity and plasticity, Harvard University Press, Cambridge, Mass.; John Wiley & Sons, Inc., New York, 1952. MR 0051675
H. B. Phillips, Vector analysis, John Wiley & Sons, New York, 1933
H. Neuber, Ein neuer Ansatz zur Lösung räumlicher Probleme der Elastizitätstheorie, Z. angew. Math. Mech. 14, 203 (1934)
- R. D. Mindlin, Force at a point in the interior of a semi-infinite solid, Proceedings of The First Midwestern Conference on Solid Mechanics, April, 1953, The Engineering Experiment Station, University of Illinois, Urbana, Ill., 1954, pp. 56–59. MR 0061547
- R. A. Eubanks and E. Sternberg, On the axisymmetric problem of elasticity theory for a medium with transverse isotropy, J. Rational Mech. Anal. 3 (1954), 89–101. MR 59147, DOI https://doi.org/10.1512/iumj.1954.3.53006
B. Galerkin, Contribution à la solution générale du problème de la théorie de l’élasticité dans le cas de trois dimensions, C. R., Acad. Sci. Paris 190, 1047 (1930)
Maria Iacovache, O extindere a metodei lui Galerkin pentru sistemul ecuaţiilar elasticitaţii, Bul. Stiint., Acad. Repub. Pop. Române A 1, 593 (1949)
Gr. C. Moisil, A supra sistemelor de ecuaţiicu derivate parţiale lineare şi cu coeficienţi constanti, Bul. Stiint., Acad. Repub. Române A 1, 341 (1949)
P. F. Papkovich, Solution générale des équations différentielles fondamentales d’élasticité exprimée par trois fonctions harmoniques, C. R., Acad. Sci. Paris 195, 513 (1932)
Emilio Almansi, Sull’ integrazione dell’ equazione differenziale ${\nabla ^{2n}} = 0$ Ann. di Mat., Ser 3, 2, 1 (1899)
R. D. Mindlin, Note on the Galerkin and Papkovich stress functions, Bull. Amer. Math. Soc. 42, 373 (1936)
H. M. Westergaard, Theory of elasticity and plasticity, Harvard Univ. Press, Cambridge, Mass., 1952
H. B. Phillips, Vector analysis, John Wiley & Sons, New York, 1933
H. Neuber, Ein neuer Ansatz zur Lösung räumlicher Probleme der Elastizitätstheorie, Z. angew. Math. Mech. 14, 203 (1934)
R. D. Mindlin, Force at a point in the interior of a semi-infinite solid, Proc. First Midwestern Conf. Solid Mech., Univ. of Illinois, Urbana, Ill., 1953
R. A. Eubanks and E. Sternberg, On the axisymmetric problem of elasticity theory for a medium with transverse isotropy, J. Ratl. Mech. Anal. 3, 1, 89 (1954)
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Article copyright:
© Copyright 1957
American Mathematical Society
