Recent Developments Concerning Saint-Venant's Principle

Alwar, 1970, Experimental verification of Saint-Venant's principle in a sandwich beam., AIAA J., 8, 160, 10.2514/3.5624 Amick, 1977, Steady solutions of the Navier-Stokes equations in unbounded channels and pipes., Ann. Scuola Norm. Sup. Pisa Cl. Sci., Serie IV, 4, 473 Amick, 1978, Properties of steady Navier-Stokes solutions for certain unbounded channels and pipes., Nonlinear Anal., 2, 689, 10.1016/0362-546X(78)90014-7 Arridge, 1976, Effect of sample geometry on the measurement of mechanical properties of anisotropic materials., Polymer, 17, 495, 10.1016/0032-3861(76)90129-4 Arridge, 1976, The importance of end effects in the measurement of moduli of highly anisotropic materials., J. Materials Sci., 11, 788, 10.1007/BF01209471 Batra, 1978, Saint-Venant's principle for a helical spring., J. Appl. Mech. (Trans. ASME, Ser. E), 45, 297, 10.1115/1.3424291 Berdichevskii, 1973, An energy incquality in the theory of plate bending., Prikl. Mat. 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ASME), 22, 204, 10.1115/1.4011043 Boley, 1958, Some observations on Saint-Venant's principle., 259 Boley, 1960, Upper bounds and Saint-Venant's principle in transient heat conduction., Quart. Appl. Math., 18, 205, 10.1090/qam/112591 Boley, 1960, On a dynamical Saint-Venant principle., J. Appl. Mech. (Trans. ASME), 27, 74, 10.1115/1.3643938 Boussinesq, 1885 Breuer, 1977, Saint-Venant's principle in linear two-dimensional elasticity for non-striplike domains., Arch. Ration. Mech. Anal., 66, 19, 10.1007/BF00250849 Breuer, 1977, On Saint-Venant's principle in three-dimensional nonlinear elasticity., Arch. Ration. Mech. Anal., 63, 191, 10.1007/BF00280605 Breuer, 1980, A bound on the strain energy for the traction problem in finite elasticity with localized nonzero surface data., J. Elasticity, 10, 11, 10.1007/BF00043133 Choi, 1977, Saint-Venant's principle and end effects in anisotropic elasticity., J. Appl. Mech. (Trans. ASME, Ser. 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Edinburgh, 49, 895, 10.1017/S008045680001718X Dougall, 1913, The method of permanent and transitory modes of equilibrium in the theory of thin elastic bodies., 2, 328 Drake, 1965, Upper bounds and Saint-Venant's principle for incompressible potential-flow fields., J. Appl. Mech. (Trans. ASME), 32, 661, 10.1115/1.3627275 Edelstein, 1969, A spatial decay estimate for the heat equation., Z. Angew. Math. Phys., 20, 900, 10.1007/BF01592299 Edelstein, 1970, On Saint-Venant's principle in linear viscoelasticity., Arch. Ration. Mech. Anal., 36, 366, 10.1007/BF00282273 Edelstein, 1971, Further study of spatial decay estimates for semilinear parabolic equations., J. Math. Anal. Appl., 35, 577, 10.1016/0022-247X(71)90205-8 Ericksen, 1977, On the formulation of St. Venant's problem., 1, 158 Ericksen, 1977, Special topics in elastostatics., 17, 189 Ericksen, 1979, On Saint-Venant's problem for thin-walled tubes., Arch. Ration. Mech. Anal., 70, 7, 10.1007/BF00276377 Ericksen, 1980, On the status of Saint-Venant's solutions as minimizers of energy., Int. J. Solids Struct., 16, 195, 10.1016/0020-7683(80)90073-6 Everstine, 1971, Stress channelling in transversely isotropic elastic composites., Z. Angew. Math. Phys., 22, 825, 10.1007/BF01591811 Fadle, 1940, Die Selbstspannungs-Eigenwertfunktionen der quadratischen Scheibe., Ingenieur-Archiv, 11, 125, 10.1007/BF02084699 Fichera, 1977, II principio di Saint-Venant: Intuizione dell'ingegnere e rigore del matematico., Rend, di Mat. Serie VI, 10, 1 Fichera, 1978, Remarks on Saint-Venant's principle., 543 1979, Rend, di Mat. Serie VI, 12, 181 Flavin, 1974, On Knowles' version of Saint-Venant's principle in two-dimensional elastostatics., Arch. Ration. Mech. Anal., 53, 366, 10.1007/BF00281492 Flavin, 1978, Another aspect of Saint-Venant's principle in elasticity., Z. Angew. Math. Phys., 29, 328, 10.1007/BF01601527 Folkes, 1975, The measurement of shear modulus in highly anisotropic materials: The validity of St. Venant's principle., J. Phys. D: Appl. Phys., 8, 1053, 10.1088/0022-3727/8/9/010 Friedrichs, 1947, On the boundary-value problems of the theory of elasticity and Korn's inequality., Ann. Math., 48, 441, 10.2307/1969180 Fung, 1965 Gilbarg, 1977 Grandin, 1974, Dynamic Saint-Venant region in a semi-infinite elastic strip., J. Elasticity, 4, 131, 10.1007/BF00045662 Gregory, 1980, The traction boundary-value problem for the elastostatic semi-infinite strip; existence of solution and completeness of the Papkovich-Fadle eigenfunctions., J. Elasticity, 10, 295, 10.1007/BF00127452 Gurtin, 1972, The linear theory of elasticity., VI a/2, 1 Gurtin, 1981 Gutiérrez, 1976, Acotacion de la energia potencial elastica de un cilindro de seccion cuadrada., Rev. Real Acad. Ci, Exact. Fis. Natur. Madrid, 70, 549 Hardy, 1967 Ho, 1970, Energy inequalities and error estimates for torsion of elastic shells of revolution., Z. Angew. Math. Phys., 21, 352, 10.1007/BF01627942 Hoff, 1945, The applicability of Saint-Venant's principle to airplane structures., J. Aero. Sciences, 12, 455, 10.2514/8.11285 Horgan, 1972, On Saint-Venant's principle in plane anisotropic elasticity., J. Elasticity, 2, 169, 10.1007/BF00125525 Horgan, 1972, Some remarks on Saint-Venant's principle for transversely isotropic composites., J. Elasticity, 2, 335, 10.1007/BF00045717 Horgan, 1973, On the strain energy density in linear elasticity., J. Eng. Math., 7, 231, 10.1007/BF01535284 Horgan, 1974, The axisymmetric end problem for transversely isotropic circular cylinders., Int. J. Solids. Struct., 10, 837, 10.1016/0020-7683(74)90027-4 Horgan, 1975, Inequalities of Korn and Friedrichs in elasticity and potential theory., Z. Angew. Math. Phys., 26, 155, 10.1007/BF01591503 Horgan, 1975, On Korn's inequality for incompressible media., SIAM J. Appl. Math., 28, 419, 10.1137/0128036 Horgan, 1978, Plane entry flows and energy estimates for the Navier-Stokes equations., Arch. Ration. Mech. Anal., 68, 359, 10.1007/BF00250987 Horgan, 1979, Eigenvalue estimates and the trace theorem., J. Math. Anal. Appl., 69, 231, 10.1016/0022-247X(79)90190-2 Horgan, 1982, Saint-Venant's principle in anisotropic elasticity theory., 853 Horgan, 1971, Eigenvalue problems associated with Korn's inequalities., Arch. Ration. Mech. Anal., 40, 384, 10.1007/BF00251798 Horgan, 1981, The effect of nonlinearity on a principle of Saint-Venant type., J. Elasticity, 11, 271, 10.1007/BF00041940 Horgan, 1979, Exponential decay estimates for a class of nonlinear Dirichlet problems., Arch. Ration. Mech. Anal., 71, 221, 10.1007/BF00280597 Horgan, 1975, On maximum principles and spatial decay estimates for heat conduction., 331 Horgan, 1975, A spatial decay estimate for pseudoparabolic equations., Lett. Appl. Eng. Sci., 3, 237 Horgan, 1976, Saint-Venant's principle and the torsion of thin shells of revolution., J. Appl. Mech. (Trans. ASME, Ser. E), 43, 663, 10.1115/1.3423951 Horgan, 1976, Spatial decay estimates for the heat equation via the maximum principle., Z. Angew. Math. Phys., 27, 371, 10.1007/BF01590509 Horgan, 1977, Maximum principles and pointwise error estimates for torsion of shells of revolution., J. Elasticity, 7, 387, 10.1007/BF00041730 Horgan, 1977, Exponential decay estimates for second-order quasilinear elliptic equations., J. Math. Anal. Appl., 59, 267, 10.1016/0022-247X(77)90107-X Horgan, 1978, Spatial decay estimates for the Navier-Stokes equations with application to the problem of entry flow., SIAM J. Appl. Math., 35, 97, 10.1137/0135008 Horvay, 1957, Biharmonic eigenvalue problem of the semi-infinite strip., Q. Appl. Math., 15, 65, 10.1090/qam/85734 Horvay, 1957, Saint-Venant's principle: a biharmonic eigenvalue problem., J. Appl. Mech. (Trans. ASME), 24, 381, 10.1115/1.4011550 Horvay, 1957, Some aspects of Saint-Venant's principle., J. Mech. Phys. Solids, 5, 77, 10.1016/0022-5096(57)90053-4 John, 1975, A priori estimates, geometric effects, and asymptotic behavior., Bull. Am. Math. Soc., 81, 1013, 10.1090/S0002-9904-1975-13887-0 Johnson, 1965, The semi-infinite strip., Quart. Appl. Math., 22, 335, 10.1090/qam/187479 Johnson, 1959, On the foundations of the theory of thin elastic shells., J. Math. and Phys., 37, 371, 10.1002/sapm1958371371 Keller, 1965, Saint-Venant's procedure and Saint-Venant's principle., Q. Appl. Math., 22, 293, 10.1090/qam/189321 Klemm, 1970, The semi-infinite elastic cylinder under self-equilibrated end loading., SIAM J. Appl. Math., 19, 712, 10.1137/0119073 Knowles, 1966, On Saint-Venant's principle in the two-dimensional linear theory of elasticity., Arch. Ration. Mech. Anal., 21, 1, 10.1007/BF00253046 Knowles, 1967, A Saint-Venant principle for a class of second-order elliptic boundary value problems., Z. Angew. Math. Phys., 18, 473, 10.1007/BF01601718 Knowles, 1971, On the spatial decay of solutions of the heat equation., Z. Angew. Math. Phys., 22, 1050, 10.1007/BF01590873 Knowles, 1976, On finite anti-plane shear for incompressible elastic materials., J. Aust. Math. Soc., 19, 400, 10.1017/S0334270000001272 Knowles, 1977, A note on the spatial decay of a minimal surface over a semi-infinite strip., J. Math. Anal. Appl., 59, 29, 10.1016/0022-247X(77)90090-7 Knowles, 1977, The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids., Int. J. 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Appl., 48, 687, 10.1016/0022-247X(74)90143-7 Oleinik, 1979, Energetic estimates analogous to the Saint-Venant principle and their applications., 703, 328 Oleinik, 1979, Applications of the energy estimates analogous to Saint-Venant's principle to problems of elasticity and hydrodynamics., 90, 422 Oleinik, 1976, An analogue of Saint-Venant's principle and the uniqueness of solutions of boundary value problems for parabolic equations in unbounded domains., Uspekhi Mat. Nauk, 31, 142 Oleinik, 1977, Boundary value problems for second order elliptic equations in unbounded domains and Saint-Venant's principle., Ann. Scuola Norm. Sup. Pisa Cl. Sci., Serie IV, 4, 269 Oleinik, 1977, On singularities at the boundary points and uniqueness theorems for solutions of the first boundary value problem of elasticity., Comm. 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Anal., 8, 89, 10.1007/BF00277432 Pipkin, 1979, Stress analysis for fiber-reinforced materials., 19, 1 Protter, 1967 Rao, 1980, Saint-Venant's principle in sandwich strip., Comput. Struct., 12, 185, 10.1016/0045-7949(80)90004-8 Reissner, 1945, The effect of transverse shear deformation on the bending of elastic plates., J. Appl. Mech (Trans. ASME), 12, A69, 10.1115/1.4009435 Robinson, 1966 Roseman, 1966, A pointwise estimate for the stress in a cylinder and its application to Saint-Venant's principle., Arch. Ration. Mech. Anal., 21, 23, 10.1007/BF00253047 Roseman, 1967, The principle of Saint-Venant in linear and nonlinear plane elasticity, Arch. Ration. Mech. Anal., 26, 142, 10.1007/BF00285678 Roseman, 1973, Phragmén-Lindelöf theorems for some nonlinear elliptic partial differential equations., J. Math. Anal. Appl., 43, 587, 10.1016/0022-247X(73)90279-5 Roseman, 1974, The rate of decay of a minimal surface defined over a semi-infinite strip., J. Math. Anal. Appl., 46, 545, 10.1016/0022-247X(74)90261-3 de Saint-Venant, 1856, Mémoire sur la torsion des prismes., Mémoires présentés pars divers Savants a l' Acadèmie des Sciences de l' Institut Impérial de France, 14, 233 de Saint-Venant, 1856, Mémoire sur la flexion des prismes., J. Math. Pures Appl., 1, 89 Shield, 1965, On the stability of linear continuous systems., Z. Angew. Math. Phys., 16, 649, 10.1007/BF01590967 Shield, 1966, Some least work principles for elastic bodies., Z. Angew. Math. Phys., 17, 663, 10.1007/BF01595104 Sigillito, 1970, On the spatial decay of solutions of parabolic equations., Z. Angew. Math. Phys., 21, 1078, 10.1007/BF01594864 Sigillito, 1974, Exponential decay of functionals of solutions of a pseudoparabolic equation., SIAM J. Math. Anal., 5, 581, 10.1137/0505059 Simmonds, 1977, Saint-Venant's principle for semi-infinite shells of revolution., 8, 367 Sokolnikoff, 1956 Spencer, 1972 Stanley, 1972, Generalized torsional waves and the non-axisymmetric end problem in a solid circular cylinder., Int. J. Solids and Structures, 8, 807, 10.1016/0020-7683(72)90044-3 Sternberg, 1954, On Saint-Venant's principle., Q. Appl. Math., 11, 393, 10.1090/qam/58414 Sternberg, 1964, On Green's functions and Saint-Venant's principle in the linear theory of viscoelasticity., Arch. Ration. Mech. Anal., 15, 112, 10.1007/BF00249521 Sternberg, 1966, Minimum energy characterizations of Saint-Venant's solution to the relaxed Saint-Venant problem., Arch. Ration. Mech. Anal., 21, 89, 10.1007/BF00266569 Synge, 1945, The problem of Saint-Venant for a cylinder with free sides., Q. Appl. Math., 2, 307, 10.1090/qam/12037 Timoshenko, 1934 Timoshenko, 1970 Titchmarsh, 1958 Toupin, 1965, Saint-Venant's principle., Arch. Ration. Mech. Anal., 18, 83, 10.1007/BF00282253 Toupin, 1965, Saint-Venant and a matter of principle., Trans. N.Y. Acad. Sci., 28, 221, 10.1111/j.2164-0947.1965.tb02876.x Truesdell, 1959, The rational mechanics of materials—Past, present, future., Appl. Mech. Rev., 12, 75 Truesdell, 1966, The rational mechanics of materials—Past, present, future. Reprinted version of Truesdell 1959 with corrections and additions., 225 Truesdell, 1978, Some challenges offered to analysis by rational thermodynamics., 495 Wan, 1975, An eigenvalue problem for a semi-infinite pretwisted strip., Stud. Appl. Math., 54, 351, 10.1002/sapm1975544351 Warren, 1967, End effect in semi-infinite transversely isotropic cylinders., AIAA J., 5, 1448, 10.2514/3.4218 Weck, 1976, An explicit St. Venant's principle in three-dimensional elasticity., 564, 518 Wheeler, 1976, A two-dimensional Saint-Venant principle for second-order linear elliptic equations., Q. Appl. Math., 34, 257, 10.1090/qam/450770 Wheeler, 1975, A Saint-Venant principle for the gradient in the Neumann problem., Z. Angew. Math. Phys., 26, 141, 10.1007/BF01591502 Wu, 1970, A Saint-Venant principle for the Neumann problem with a non-thin two-dimensional domain., Int. J. Eng. Sci., 8, 389, 10.1016/0020-7225(70)90076-5 Yosifian, 1978, An analog of Saint-Venant's principle and the uniqueness of the solutions of the first boundary value problem for Stokes' system in domains with noncompact boundaries., Dokl. Akad. Nauk. SSSR, 242, 36 Yosifian, 1979, Saint-Venant's principle for the flow of a viscous incompressible liquid., Uspekhi Mat. Nauk, 34, 191 Zanaboni, 1937, Dimostrazione generale del principio del De Saint-Venant., Atti Acad. Naz. dei Lincei, Rendiconti, 25, 117 Zanaboni, 1937, Valutazione dell'errore massimo cui dà luogo l'applicazione del principio del De Saint-Venant in un solido isotropo., Atti Acad. Naz. dei Lincei, Rendiconti, 25, 595 Zanaboni, 1937, Sull'approssimazione dovuta al principio del De Saint-Venant nei solidi prismatici isotropi., Atti Acad. Naz. dei Lincei, Rendiconti, 26, 340