On the linear theory of viscoelasticity
Tóm tắt
Từ khóa
Tài liệu tham khảo
Boltzmann, L.: Zur Theorie der elastischen Nachwirkung. Sitzungsberichte der Mathematisch-Naturwissenschaftlichen Classe der Kaiserlichen Akademie der Wissenschaften 70, 2, 275 (1874).
Volterra, V.: Sulle equazioni integro-differenziali della teoria dell'elasticità. Atti della Reale Accademia dei Lincei 18, 2, 295 (1909).
Gross, B.: Mathematical Structure of the Theories of Viscoelasticity. Paris: Hermann & Co. 1953.
Staverman, A. J., & F. Schwarzl: Linear Deformation Behavior of High Polymers, Chapter 1 in: Die Physik der Hochpolymeren, edited by H. A. Stuart, Vol. 4. Berlin-Göttingen-Heidelberg: Springer 1956.
Freudenthal, A. M., & Hilda Geiringer: The Mathematical Theories of the Inelastic Continuum, in: Encyclopedia of Physics, edited by S. Flügge, Vol. 6. Berlin-Göttingen-Heidelberg: Springer 1958.
Bland, D. R.: The Theory of Linear Viscoelasticity. New York: Pergamon Press 1960.
Love, E. R.: Linear superposition in visco-elasticity and theories of delayed effects. Australian J. of Physics 9, 1, 1 (1956).
König, H., & J. Meixner: Lineare Systeme und lineare Transformationen. Mathematische Nachrichten 19, 256 (1958).
Biot, M. A.: Linear Thermodynamics and the Mechanics of Solids. Proceedings, Third U.S. National Congress of Applied Mechanics, The American Society of Mechanical Engineers, New York, 1958.
Coleman, B. D., & W. Noll: Foundations of linear viscoelasticity. Reviews of Modern Physics 33, 2, 239 (1961).
Alfrey, T.: Non-homogeneous stresses in visco-elastic media. Quarterly of Applied Mathematics 2, 2, 113 (1944).
Read, W. T.: Stress analysis for compressible viscoelastic materials. J. of Applied Physics 21, 7, 671 (1950).
Lee, E. H.: Stress analysis in viscoelastic bodies. Quarterly of Applied Mathematics 13, 2, 183 (1955).
Lee, E. H.: Viscoelastic Stress Analysis. Proceedings, First Symposium on Naval Structural Mechanics. New York; Pergamon Press 1960.
Hu Hai-Chang: On reciprocal theorems in the dynamics of elastic bodies and some applications. Scientia Sinica 7, 2, 137 (1958).
Volterra, V.: Sulle equazioni integro-differenziali. Atti della Reale Accademia dei Lincei 18, 1, 167 (1909).
Mikusinski, J.: Operational Calculus. New York: Pergamon Press 1959.
Apostol, T.: Mathematical Analysis. London: Addison-Wesley Publishing Company 1960.
Smithies, F.: Integral Equations. London: Cambridge University Press 1958.
Riesz, F., & B. Sz.-Nagy: Functional Analysis, translated by Leo F. Boron. New York: Frederick Ungar Publishing Company 1955.
Natanson, I. P.: Theory of Functions of a Real Variable, translated by Leo F. Boron. New York: Frederick Ungar Publishing Company 1955.
Temple, G.: Cartesian Tensors. New York: John Wiley & Sons 1960.
Boley, B. A., & J. H. Weiner: Theory of thermal stresses. New York: John Wiley & Sons 1960.
Corneliussen, A. R., & E. H. Lee: Stress distribution analysis for linear viscoelastic materials, Report No. 2, Contract No. DA-19-020-ORD-4750, Brown University, December 1958. To appear in Proceedings, Symposium on Creep in Structures, International Union of Theoretical and Applied Mechanics. Berlin-Göttingen-Heidelberg: Springer 1962.
Sokolinikoff, I. S.: Mathematical Theory of Elasticity, Second Edition. New York: McGraw-Hill Book Company 1956.
Duffin, R. J.: Analytic continuation in elasticity. J. of Rational Mechanics and Analysis 5, 6, 939 (1956).
Friedrichs, K. O.: On the first boundary value problem of the theory of elasticity and Korn's inequality. Annals of Mathematics 48, 2, 441 (1947).
Frank, Ph., & R. v. Mises: Die Differential-und Integralgleichungen der Mechanik und Physik, Vol. 1 New York: Mary S. Rosenberg 1943.
Gurtin, M. E., & E Sternberg: Theorems in linear elastostatics for exterior domains. Arch. Rational Mech. Anal. 8, 2, 99 (1961).
Breuer, S., & E. T. Onat: On uniqueness in linear viscoelasticity. Quarterly of Applied Mathematics 19, 4, 355 (1962).
Gurtin, M. E., & E. Sternberg: On the first boundary-value problem of linear elastostatics. Arch. Rational Mech. Anal. 6, 3, 177 (1960).
Widder, D. V.: The Laplace Transform. Princeton: Princeton University Press 1941.
Goldberg, R. R.: Fourier Transforms. London: Cambridge University Press 1961.
Loève, M.: Probability Theory, Second Edition. New York: D. van Nostrand Company 1960.
Boa-Teh Chu: Stability criteria for isotropic linear viscoelastic materials. Technical Report No. 26, Contract Nonr-562(20), Brown University, November 1961.
Galerkin, B.: Contribution à la solution général du problème de la théorie de l'élasticité dans le cas de trois dimensions. Comptes Rendus, Académie des Sciences, Paris 190, 17, 1047 (1930).
Papkovich, P. F.: The representation of the general integral of the fundamental equations of elasticity theory in terms of harmonic functions (in Russian).
Izvestiya Akademii Nauk SSSR, Physics-Mathematics Series 10, 1425 (1932).
Neuber, H.: Ein neuer Ansatz zur Lösung räumlicher Probleme der Elastizitätstheorie. Z. für angewandte Mathematik und Mechanik 14, 203 (1934).
Courant, R.: Partial Differential Equations, Vol. 2 of Methods of Mathematical Physics by R. Courant & D. Hilbert. New York: Interscience Publishers 1962.
Sternberg, E., & M. E. Gurtin: On the completeness of certain stress functions in the linear theory of elasticity. Technical Report No. 12, Contract Nonr-562(25), Brown University, July 1961. To appear in the Proceedings of the Fourth U. S. National Congress of Applied Mechanics.
Elder, A. S.: Stress function theory for linearly viscoelastic solids. Memorandum Report No. 1282, Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland, June 1960.