7780

7245

كارشناسي ارشد

سازه

اصفهان: دانشگاه صنعتي اصفهان، دانشكده عمران

1391

ده،148ص.: مصور،جدول،نمودار

ص.ع.به فارسي و انگليسي

بيژن برومند

مجتبي ازهري

20/3/92

محمد مهدي سعادتپور، امير مهدي حلبيان

مهندسي عمران

ID7245

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

The Use of Exponential Basis Functions in Solution of Nonlocal Elasticity Differential Equations Reza Abdollahi r abdollahi@cv iut ac ir 20 January 2013 Department of Civil Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Prof Bijan Boroomand boromand@cc iut ac ir Abstract In this dissertation the solution of boundary value problems for materials with nonlocal behavior has been studied Eringen s model of nonlocal integral elasticity is considered that it di ers from the classical local one only for the stress strain constitutive relation Two different methods have been developed for these problems semi analytical solution and the use of exponential basis functions EBFs In the first method a Fourier series or a set of Chebyshev polynomials are used as the basis functions for the main unknown fields This method offers a low residual approximate solution but the procedure is very time consuming The second method that is the main theme of the thesis employs the EBFs for the solution of nonlocal differential equation In this method the displacement field is approximated as a linear combination of bas es which satisfy the differential equation of equilibrium in a central zone The coefficients of these bases are calculated using a weight integral on the boundary zones In the presented method the solution is split into two parts i e homogeneous and particular parts Introduction of the EBFs into the homogeneous governing differential equations leads to a characteristic equation through which the exponents of the EBFs are defined This combination of the bases satisfies the differential equation of equilibrium in a central zone For many cases the characteristic equation possesses some multiple roots In such situations polynomial functions are added to EBFs After selection of the EBFs as the bases for the approximation the unknown coefficients of the series are determined by the satisfaction of the boundary conditions and the equilibrium equations on boundary zone in an element based manner through a weight integral technique The particular part of the solution is constructed by a rather similar approach In this thesis EBFs are evaluated for 1D and 2D problems The capabilities of the method have been shown by defining some norms of residuals and comparing the results with semi analytical solutions Key Words Exponential basis functions Eringen s nonlocal elasticity Fourier series Chebyshev polynomials weight integral

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مجتبي ازهري

محمد مهدي سعادتپور، امير مهدي حلبيان