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Use of the reciprocity theorem for axially symmetric transient problems

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Summary

A fundamental solution, to be used in reciprocal theorem for the solutions of axially symmetric transient problem of elastodynamics, is presented. A cylindrical cavity problem has been solved to check the formulation. The strong singularity of the resulting integral equation for this problem has been reduced to the weak form. The new formulation provides the initial velocity on the surface for a transient loading. Some differences have been introduced for the use of generalized functions.

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References

  1. Achenbach, J.D.: Wave propagation in elastic solids. North-Holland, Amsterdam London, 1973

    MATH  Google Scholar 

  2. Cole, D.M.;Kosloff, D.D.;Minster, J.B.: A numerical boundary integral equation method for elastodynamics. B Seismol Soc Am. 5 (1978) 1331–1357

    Google Scholar 

  3. Kadioglu, N.;Ataoglu, S.: An elastodynamic state for the solutions of axial symmetric problems. In: Nikitin, A.G., Boyko, V.M., Popovych, R.O., Yehorchenko, I.A. (eds) Symmetry in nonlinear mathematical physics. Institute of Mathematics of NAS of Ukraine. Kiev, pp. 1348–1355, 2004

    Google Scholar 

  4. Kadioglu, N.;Ataoglu, S.: Use of elastodynamic reciprocity for the solutions of spherically symmetric problems. Wave Motion 40(2) (2004) 137–142

    Article  MATH  Google Scholar 

  5. Israil, A.S.M.;Banerjee, P.K.: Advanced time-domain formulation of BEM for two-dimensional transient elastodynamics. Int. J Num Method Eng 7 (1990) 1421–1440

    Article  MathSciNet  Google Scholar 

  6. Kromm, V.A.: Zur Ausbreitung von Stoßwellen in Kreislochscheiben. Z angew Math Mech 4 (1948) 104–114

    Article  MathSciNet  Google Scholar 

  7. Kromm, V.A.: Ausbreitung von Stoßwellen in Kreislochscheiben. Z angew Math Mech 10 (1948) 297–303.

    Article  MathSciNet  Google Scholar 

  8. Moon, P.;Spencer, D.E.: Field theory handbook, p. 24, Springer, Berlin, 1961

    MATH  Google Scholar 

  9. Sokolnikoff, I.S.: Mathematical theory of elasticity, p. 270. McGraw-Hill, New York, 1956.

    MATH  Google Scholar 

  10. Srivastava, H.M.;Buschman, R.G.: Theory and applications of convolution integral equations, Kluwer, Dordrecht, 1992.

    MATH  Google Scholar 

  11. Wang, H.C.;Banerjee, P.K.: Axisymmetric transient elastodynamic analysis by boundary element method. Int J solids Structures 4, (1990) 401–415

    Google Scholar 

  12. Wheeler, L.T.;Sternberg, E.: Some theorems in classical elastodynamics. Arch Rational Mech Anal 1, (1968) 51–90

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Division of Mechanics, Department of Civil Engineering. Faculty of Civil Engineering, Istanbul Technical University, Maslak, 34469, Istanbul, Turkey

    N. Kadioglu & S. Ataoglu

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  1. N. Kadioglu
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  2. S. Ataoglu
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Correspondence to N. Kadioglu.

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Kadioglu, N., Ataoglu, S. Use of the reciprocity theorem for axially symmetric transient problems. Arch. Appl. Mech. 74, 325–337 (2005). https://doi.org/10.1007/BF02637034

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  • DOI: https://doi.org/10.1007/BF02637034

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