3653

3452

كارشناسي ارشد

سازه

اصفهان: دانشگاه صنعتي اصفهان، دانشكده عمران

1386

نه، 175، [II]ص. :مصور، جدول، نمودار

ص. ع. به فارسي و انگليسي

بيژن برومند

محمد مهدي سعادت پور

13/5/86

مجتبي ازهري ، حميد هاشم الحسيني

1396/02/24

كتابنامه

عمران

مهندسي عمران

ID3452

به فارسي و انگليسي :قابل رويت به صورت نسخه ديجيتال

AbstractIn this dissertation a new method based on the method of fundamental solutions has beenproposed for solution of partial differential equations PDEs with constant coefficients Thefirst set of the results has been presented for the Helmholtz equation In this method theapproximate solution of the homogeneous equation is expressed as a series using exponentialfunctions as the fundamental solutions Constant coefficients of this series are evaluatedthrough an especial discrete transformation However the results accuracy is highly dependenton the number amplitude and fluctuations of the implemented fundamental solutions Hence finding a suitable pattern for choosing the associated parameters of the fundamental solutionsplays an important role in reducing the computational error and reaching appropriate accuracyin final results Two different methods are also proposed for approximating the particular solution of theHelmholtz equation i e the Fourier series solution and a new method called Exponentialseries based on the discrete transformation Comparison of these two methods revealssignificant supremacy of the latter over the former in almost all problems regarding thecomputational costs After developing an appropriate algorithm for solving the Helmholtz equation this algorithmhas been extended to other important PDEs in solid mechanics including the equations ofelasticity elastic wave static thin thick plates and forced transverse vibration of plates Thesolution of advection diffusion absorption problems has also been addressed Severalbenchmark examples have been solved in each category of problems It has been concludedthat this method is capable of solving miscellaneous problems with excellent precision andaccuracy on complicated domain shapes with various types of boundary conditions The method has also been employed in an element based manner Element implementation indiscretizing the domain obviates some limitations of the method of fundamental solutions andresults in a considerable increase in accuracy in certain cases

بيژن برومند

محمد مهدي سعادت پور

مجتبي ازهري ، حميد هاشم الحسيني