پديد آورنده :
ديباجيان، حسين
عنوان :
درنظرگرفتن عدم قطعيت در روش هاي عددي و كاربرد آن در مسائل مكانيك جامدات
گرايش تحصيلي :
طراحي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده منابع طبيعي
صفحه شمار :
سيزده،82ص.: مصور،جدو،نمودار
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
محمود فرزين، حميد هاشم الحسيني
استاد مشاور :
احمدرضا پيشه ور
تاريخ نمايه سازي :
94/2/6
استاد داور :
بيژن برومند، رضا مختاري، سهيل محمدي، محمدمشايخي
دانشكده :
مهندسي منابع طبيعي
كد ايرانداك :
ID742 دكتري
چكيده انگليسي :
Consideration of uncertainties in numerical methods and their applications in solid mechanics problems Saied houssain dibajian dibajian@me iut ac ir Date of Submission 2014 august 12 Department of mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree Ph D Language Farsi Supervisor Mahmoud Farzin Hamid Hashemalhossaini Abstract In this thesis for the first time uncertainty in numerical methods also called error estimation will be investigated from the viewpoint of probability theory Interpolation differentiation and integration processes are the main concepts in the numerical solutions of partial differential equations Thus a detail study of these issues from the viewpoint of probability theory will create a suitable mathematical structure for numerical methods In summary the following issues will be addressed in this thesis 1 A probabilistic error indicator is presented which is based on Keriging error interpolation 5 and s used i for mesh smoothing purpose This error indicator is used for adaptive mesh smoothing purposes especially in the uncoupled ALE approaches Robustness and accuracy of the ethod are shown through several m examples on different fields with irregular boundaries or brupt changes a 2 Assessment of reliability of the results of numerical integration is studied by using probability theory and a new error indicator is presented Error in the presented approach is indicated as a function of the position of integration oints the integration weights and the variation of ntegrand which are mportant parameters p i i in ordinary numerical integration By minimization of the presented error indicator weights of integration and locations of integration points are obtained This method can be applied to any desired domain in 1D 2D and 3D space Therefore this method can also be applied for mesh less methods with any desired domain geometry Robustness and consistency of the method is examined through several examples 3 Assessment of reliability of the derivative of field is studied by using probability theory A new error indicator for derivatives of field is introduced Using this indicator optimal precision gradient points or Superconvergent points can be identified in various interpolation methods The capability and generality of the present method is shown for finite elements and also mesh less methods In finite element applications this indicator is examined for Lagrange interpolation shape functions for 1 D elements 2 D quadrilateral and triangular elements and 2 D quadratic Serendipity element The indicator is also verified for mesh less methods where MLS approximation is used The presented error indicator using probability theory and application of the presented approach to mesh less method are among the new aspects and main achievements of this thesis Keywords Integration method Superconvergent point mesh smoothing error indicator probabilistic approach meshless method finite element method
استاد راهنما :
محمود فرزين، حميد هاشم الحسيني
استاد مشاور :
احمدرضا پيشه ور
استاد داور :
بيژن برومند، رضا مختاري، سهيل محمدي، محمدمشايخي
