14410

1339 دكتري

كارشناسي ارشد

سازه

اصفهان : دانشگاه صنعتي اصفهان

1397

دوازده، [232]ص.: مصور، جدول، نمودار

بيژن برومند

مجتبي ازهري

سهيل محمدي، محمد مهدي سعادت پور، بشير موحديان

1397/12/08

كتابنامه

عمران

مهندسي برق و كامپيوتر

1397/12/14

ID1339 دكتري

Solution of Linear and Nonlinear Partial Differential Equations in Continuum Mechanics through a Local Meshfree Style Ehsan Soleimanifar ehsan soleimanifar@cv iut ac ir Date of submission January 20 2019 Department of civil engineering Isfahan University of Technology Isfahan 84156 83111 IranBijan Boroomand Prof boromand@cc iut ac ir Mojtaba Azhari Prof Mohammad Navid Moghim Assist Prof AbstractIn this dissertation a new local meshfree method is developed for the solution of linear andnonlinear partial differential equations PDEs The method is first introduced in a local weightedresidual style to meet the linear PDEs with constant coefficients In this method the field variablein each local cloud of nodes is approximated as series of exponential basis functions satisfying thePDE The compatibility of the solutions of neighboring clouds is then taken into account in apointwise weighted residual expression defined on a set of intermediate points The definition ofthe residual expression for the boundary intermediate points is correspondingly set to capture theboundary conditions The final system of equations is then constructed through the minimization ofthe accumulative total weighted residual In spite of multiple salient features the mentionedmethod encounters some limitations mainly due to its structure which is dependent on the basisfunctions satisfying the PDE In order to overcome such deficiencies a new approximationtechnique has been devised to handle a wider range of applications including PDEs with variablecoefficients In this technique the PDE is divided into average and remainder parts and the solutionfunction is divided accordingly Average and remainder parts of the solution are approximated bylinear combinations of exponential and radial basis functions respectively and the relation betweenthese two parts are defined so that to satisfy the PDE Using this recent approximation technique adirect formulation is also derived from the compatibility boundary weighted residuals to develop anovel meshfree method named as the local extended direct method Capabilities of this method arefurther enhanced by introducing a compatible iterative linearization algorithm to deal with non linear problems 2D elastoplastic problems are among the most important applicable non linearproblems that have been addressed in this thesis The method is finally applied to some linear andnonlinear initial value problems In this regard a time marching algorithm has been formulatedbased on the Taylor series expansion of the dependent field variable with respect to time Capabilities of the proposed method have been examined in each section of this dissertation byseveral numerical examples Key WordsPartial Differential Equations PDE Mesh Free Methods Boundary Value Problems BVP Initial Value Problems IVP Non Linear Problems Elastoplastic Problems Exponential BasisFunctions EBFs Radial Basis Functions RBFs Department of Civil Engineering Isfahan University of Technology Supervisor Department of Civil Engineering Isfahan University of Technology Advisor Department Graduate Program Coordinator

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مجتبي ازهري

سهيل محمدي، محمد مهدي سعادت پور، بشير موحديان