379945.algorithm_LU-decomposition-plate_bending_final11.doc

# 379945.algorithm_LU-decomposition-plate_bending_final11.doc...

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J. Sertić D. Kozak R. Scitovski ISSN 1333-1124 LU-DECOMPOSITION FOR SOLVING SPARSE BAND MATRIX SYSTEMS AND ITS APPLICATION IN THIN PLATE BENDING UDK 620.174.517.9 Original scientific paper Izvorni znanstveni rad Summary In this paper algorithm for solving sparse band system matrices is proposed. Algorithm is based on LU-decomposition, therefore has good numerical properties. Proposed algorithm is applied within the finite difference method (FDM) on solving thin plates bend problem. In order to compare the solution accuracy obtained by proposed algorithm, the same example has been solved by finite element method. Key words: LU-decomposition, sparse band matrix, thin plate bending, finite difference method LU-DEKOMPOZICIJA ZA RJEŠAVANJE VRPČASTIH RIJETKO POPUNJENIH MATRIČNIH SUSTAVA I PRIMJENA NA SAVIJANJE TANKIH PLOČA Sažetak U ovom se radu predlaže algoritam za rješavanje rijetko popunjenih vrpčastih matričnih sustava. Algoritam se temelji na LU-dekompoziciji, te stoga ima dobra numerička svojstva. Predloženi algoritam primijenjen je uz metodu konačnih diferencija (FDM) na rješavanje problema čvrstoće tankih ploča. Radi usporedbe točnosti rješenja dobivenih pomoću predloženog algoritma, isti primjer riješen je i uz pomoć metode konačnih elemenata. Ključne riječi: LU-dekompozicija, rijetko popunjene matrice, savijanje tankih ploča, metoda konačnih diferencija

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J. Sertić, D. Kozak, R. Scitovski LU-Decomposition for Solving Sparse Band Matrix Systems and Its Application in Thin Plate Bending 1. Introduction Application of numerical methods in solving practical physical boundary problems includes solving a huge system of linear equations. The best known method for solving boundary problems is Finite Difference Method (FDM) [1]. By using this method, the derivatives of function of one or more variables can be approximated by divided differences. In this way a difference equations system is acquired and it must be solved by a numerical method [1]. One of the very used methods which have good numerical properties is the LU decomposition [1], [2], [3]. This paper deals with LU-decomposition for band matrices and its use in FDM. The application of the specified method is presented on a simple example of solving a biharmonic differential equation of the thin quadratic plate bending with constant thickness and uniform load with constant pressure [6]. FDM is often used in researches related to plate theory. In the paper [4] it is possible to see FDM application in calculation of rectangular plates with non-uniform wall thickness under the influence of arbitrary load. The application of the specified method can be also seen in the paper [5], which gives a contribution in the research of orthotropic plate deformation.
• Spring '17
• Dr. S. Fazal Wahid

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