Numerical solution of the nonlinear evolutional inverse problem related to elastoplastic torsional problem


Tatar S., MURADOĞLU Z.

APPLICABLE ANALYSIS, cilt.93, ss.1187-1200, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 93 Konu: 6
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1080/00036811.2013.823479
  • Dergi Adı: APPLICABLE ANALYSIS
  • Sayfa Sayıları: ss.1187-1200

Özet

This paper is devoted to the determination of an unknown function that describes elastoplastic properties of a bar under torsion. The mathematical (evolution) model leads to an inverse problem that consists of determining the unknown coefficient g = g(xi(2)), xi(2) = vertical bar del u vertical bar(2), in the nonlinear parabolic equation u(t) - del, (g(vertical bar del u vertical bar(2))del u) = 2t, (x,y,t) epsilon del(t)* := del x(0,t*], del subset of R-2 using measured output data given in the integral form. Existence of a quasi-solution of the considered inverse problem is obtained in the appropriate class of admissible coefficients. The direct problem is solved using a semi-implicit finite difference scheme. The inverse problem is solved using the semi-analytic inversion method (also known the fast algorithm). Finally, some examples are presented related to direct and inverse problems.