Commenced in January 2007
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Edition: International
Paper Count: 2

preconditioning Related Publications

2 Preconditioned Jacobi Method for Fuzzy Linear Systems

Authors: Lina Yan, Shiheng Wang, Ke Wang

Abstract:

A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

Keywords: preconditioning, M-matrix, Jacobi method, fuzzy linear system (FLS)

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1 Limiting Fiber Extensibility as Parameter for Damage in Venous Wall

Authors: Lukas Horny, Rudolf Zitny, Hynek Chlup, Tomas Adamek, Michal Sara

Abstract:

An inflation–extension test with human vena cava inferior was performed with the aim to fit a material model. The vein was modeled as a thick–walled tube loaded by internal pressure and axial force. The material was assumed to be an incompressible hyperelastic fiber reinforced continuum. Fibers are supposed to be arranged in two families of anti–symmetric helices. Considered anisotropy corresponds to local orthotropy. Used strain energy density function was based on a concept of limiting strain extensibility. The pressurization was comprised by four pre–cycles under physiological venous loading (0 – 4kPa) and four cycles under nonphysiological loading (0 – 21kPa). Each overloading cycle was performed with different value of axial weight. Overloading data were used in regression analysis to fit material model. Considered model did not fit experimental data so good. Especially predictions of axial force failed. It was hypothesized that due to nonphysiological values of loading pressure and different values of axial weight the material was not preconditioned enough and some damage occurred inside the wall. A limiting fiber extensibility parameter Jm was assumed to be in relation to supposed damage. Each of overloading cycles was fitted separately with different values of Jm. Other parameters were held the same. This approach turned out to be successful. Variable value of Jm can describe changes in the axial force – axial stretch response and satisfy pressure – radius dependence simultaneously.

Keywords: Damage, constitutive model, preconditioning, fiber reinforcedcomposite, limiting fiber extensibility, vena cavainferior

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