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چكيده انگليسي :

Solution of Solid Mechanics Problems Using Equilibrated Basis Functions and Mesh free Methods Nima Noormohammadi nima noormohammadi@cv iut ac ir Date of Submission February 7 2016 Department of Civil Engineering Isfahan University of Technology Isfahan 84156 83111 IranBijan Boroomand Prof boromand@cc iut ac ir Mohammad Navid Moghim Assist Prof AbstractIn this thesis a new boundary point method and its variants are presented for the solution ofpartial differential equations PDEs arising in some fields of mechanics Regarding the mainshortcoming of the methods of using basis functions as the approximation series for thehomogeneous solution of the equation which is their need to a series of basis functions exactlysatisfying the governing PDE the present method tries to eliminate such a dependency byapproximately satisfying the PDE in a weighted integration procedure Motivated by the methodscategorized as the fictitious domain methods the so called integral will be evaluated over arectangular area of much simpler shape than the main domain leading to a possibility ofdecomposing the main two dimensional integrals into a combination of one variable ones in aspecific order The varying coefficients of the PDEs are another challenge that will be treated bythe use of an incomplete set of monomials selected from the well known Pascal triangle toapproximately replace the so called coefficients Second and forth order PDEs are of interest inthis research and an extended patch test will be employed to investigate the selection scheme ofdifferent parameters of the method Coming up with the most important shortcoming of spectral methods which is the problem of ill conditioning for large scaled problems in real state physics the method defined above will becomposed by two various techniques in which the solution procedure will be extended over localsubdomains that can be overlapping or non overlapping The second case will be focused in theextension of a domain discretization technique and the first one is used in a mesh less localmethod In the domain discretization technique the main domain will be decomposed into anumber of subdomains having some interfaces along which the continuity conditions are appliedup to one order less than the order of differentiation in the PDE In the mesh less local methodthe main domain will be discretized by a finite number of nodes on each the degrees of freedomare defined Corresponding to each node is a local region in adjacency of the node that containssome other nodes by which the central node is connected called a cloud The method will be Department of Civil Engineering Isfahan University of Technology Supervisor Department graduate program coordinator

نورمحمدي، نيما

حل مسايل مكانيك جامدات با استفاده از توابع پايه متعادل شده و روش هاي بدون شبكه