Simultaneous determination of the strain hardening exponent, the shear modulus and the elastic stress limit in an inverse problem
| Autor: | Ramazan Tınaztepe, Zahir Muradoğlu, Salih Tatar |
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| Rok vydání: | 2016 |
| Předmět: |
Discretization
Applied Mathematics Numerical analysis 010102 general mathematics Mathematical analysis Strain hardening exponent Inverse problem 01 natural sciences 010101 applied mathematics Shear modulus Tikhonov regularization Nonlinear system Modeling and Simulation Method of steepest descent 0101 mathematics Mathematics |
| Zdroj: | Applied Mathematical Modelling. 40:6956-6968 |
| ISSN: | 0307-904X |
| Popis: | This paper is devoted to simultaneous determination of the strain hardening exponent, the shear modulus and the elastic stress limit in an inverse problem. The inverse problem consists of determining the unknown coefficient f = f ( T 2 ) , T 2 : = | ∇ u | 2 in the nonlinear equation u t − ∇ . ( f ( T 2 ) ∇ u ) = 2 t , ( x , y , t ) ∈ Ω T : = Ω × ( 0 , T ) , Ω ⊂ R 2 , by measured output data (or additional data) given in the integral form. After we solve direct problem using a semi-implicit finite difference scheme, a numerical method based on discretization of the minimization problem, steepest descent method and least squares method is proposed for the solution of the inverse problem. We use Tikhonov regularization to overcome the ill-posedness of the inverse problem. Numerical examples with noise free and noisy data illustrate applicability and accuracy of the proposed method to some extent. |
| Databáze: | OpenAIRE |
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