Eigen value approach in micropolar elastic medium with voids

• Autorzy: Singh R. , Singh K.

Identyfikatory

DOI

10.2478/ijame-2013-0031

• Języki publikacji: EN

Abstrakty

EN

The eigen value approach, following the Laplace and Hankel transformation has been employed to find a general solution of the field equations in a micropolar elastic medium with voids for an axisymmetric problem. An infinite space with the mechanical source has been applied to illustrate the utility of the approach. The integral transformations has been inverted by using a numerical inversion technique to get the result in physical domain. The results in the form of normal displacement, volume fraction, normal force stress, tangential force stress and tangential couple stress components have been obtained numerically and illustrated graphically.

Słowa kluczowe

EN

eigenvalue; voids; Laplace transform; Hankel transform; concentrated force; Romberg's integration

PL

próżnia; transformata Laplace'a; transformacja Hankela; integracja Romberga

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2013
• Tom: Vol. 18, no. 2
• Strony: 521--536
• Opis fizyczny: Bibliogr. 27 poz., wykr.

Twórcy

autor

Singh R.

• Department of Mathematics, S.G.A.D. Govt. College Tarn Taran-143401, Punjab, India

autor

Singh K.

• Department of Mathematics, S.G.A.D. Govt. College Tarn Taran-143401, Punjab, India

Bibliografia

• Achenbach J.D. (1973): Wave Propagation in Elastic Solids. - Oxford, p.310.
• Chandrasekharaiah D.S. (1987): Plane waves in a rotating elastic solid with voids. - International Journal of Engineering Sciences, vol.25, pp.591-596.
• Chandrasekharaiah D.S. (1989): Complete solution in the theory of elastic materials with voids-II. - The Quarterly Journal of Mechanics and Applied Mathematics, vol.42, pp.41-54.
• Cosserat E. and Cosserat F. (1909): Theories des Corp Formables. - Paris: Aherrman.
• Cowin S.C. and Nunziato J.W. (1983): Linear elastic materials with voids. - Journal of Elasticity, vol.13, pp.125-147.
• Eringen A.C. (1966): Linear theory of micropolar elasticity. - Journal of Mathematical and Mechanics, vol.15, pp.909-924.
• Eringen A.C. (1968): Theory of micropolar elasticity in fracture. - Vol II, Academic Press, New York, pp.621-729.
• Eringen A.C. (1984): Plane waves in non-local micropolar elasticity. - International Journal of Engineering Sciences, vol.22, pp.1113-1121.
• Eringen A.C. and Suhubi E.S. (1964): Non-linear theory of simple micropolar solids I. - International Journal of Engineering Sciences, vol.2, pp.189-203.
• Goodman M.A. and Cowin S.C. (1971): A continuum theory of granular materials. - Archive for Rational Mechanics and Analysis, vol.44, pp.249-266.
• Honig G. and Hirdes V. (1984): A method for the numerical inversion of the Laplace transforms. - Journal of Computational and Applied Mathematics, vol.10, pp.113-132.
• Iesan D.A. (1985): Shock waves in micropolar elastic materials with voids. - Analele Stiintifice ale Universitatu Al. l. Cuza din lasi Seria Noua Sectiunea la Matematica 31, pp.177-186.
• Iesan D.A. (1986): Theory of thermoelastic materials with voids. - Acta Mechanica, vol.60, pp.67-89.
• Kumar R. and Choudhary S. (2003): Interaction due to mechanical sources in micropolar elastic medium with voids. - Journal of Sound and Vibration, vol.266, pp.889-904.
• Marin M. (1996): On elastostatics of micropolar materials with voids. - Bull. Stiinca Univ. Politech. Ser. Math., vol.41, pp.29-37.
• Marin M. (1996): Generalized solutions in elasticity of micropolar bodies with voids. - Revista dele Academia Canaria de Ciencias, vol.8, pp.101-106.
• Marin M. (1998): A temporally evolutionary equation in elasticity of micropolar bodies with voids. - Politehn. Univ. Bucharest Sci. Bull. Ser. Appl. Math. Phys., vol.60, pp.3-12.
• Mindlin R.D. (1964): Microstructure in linear elasticity. - Archive for Rational Mechanics and Analysis, vol.16, pp.51-78.
• Nunziato J.W. and Cowin S.C. (1979): A non-linear theory of elastic materials with voids. - Archive for Rational Mechanics and Analysis, vol.72, pp.175-201.
• Pouget J. and Maugin G.A. (1983): Nonlinear electroacoutic equations for piezoelectric powders. - Journal of Acoustical Society of America, vol.74, pp.925-940.
• Pouget J. and Maugin G.A. (1983): Continuum approach to electroacoutic echoes in piezoelectric powders. - Journal of Acoustical Society of America, vol.74, pp.941-954.
• Press W.H., Teukolsky S.A., Vellerlig W.T. and Flannery B.P. (1986): Numerical Recipes in FORTRAN, 2nd Edition. - Cambridge: Cambridge University Press.
• Puri P. and Cowin S.C. (1985): Plane waves in linear elastic materials with voids. - Journal of Elasticity, vol.15, pp.167-183.
• Scarpetta E. (1990): On the fundamental solution in micropolar elasticity with voids. - Acta Mechanica, vol.82, pp.151-158.
• Scarpetta E. (1995): Wellposedness theorems for linear elastic materials with voids. - International Journal of Engineering Sciences, vol.33, pp.151-161.
• Sharma J.N. and Chand D. (1992): On the axisymmetric and plane strain problems of generalized thermoelasticity. - Int. J. Engng. Sci., vol.33, pp.223-230.
• Wheeler L.T. and Isaak A.K. (1982): On voids of minimum stress concentration. - International Journal of Solids and Structures, vol.18, pp.85-89.