Analysis of Deflection of Nonlocal Nanobeam by Using Spline Collocation Method
Date Issued
2011
Date
2011
Author(s)
Tu, Kuo-Hao
Abstract
SCM(Spline Collocation Method) is a numerical analysis method originating from Spline function which is derived from Forward Difference, and also joining the idea of knot-collocating together. By means of developing B Spline Value Table from differential Spline function in various orders, the calculating process can be simplified greatly by simply looking up to the table. Furthermore, it can be used in computer programming in a systematic way. Therefore it becomes much more rapid and convenient when analyzing by using SCM.
The purpose of this thesis is to apply MSCM(Modified Spline Collocation Method) which is extended from SCM (Spline Collocation Method) to solve the compatibility of the nonlocal nanobeam, analysis of maximum deflection value and the difference between nonlocal nanobeam and Timoshenko beam . Also, Into a variety of different combinations of boundary conditions, all kinds of loading and Winkler elastic foundation, and take the increase in the number of nodes. We can see the convenience of the solution process. And can not be limited to any form of loading or boundary conditions, only need the structure of the control equation, that is able to obtain satisfactory approximate solution
.At last, results from each example analyzed by SCM will be utilized to compare with theoretical solution . Thus it can be verified that the error conducted by SCM is within the standard range of engineering field. It is demonstrated that SCM has its superiority as being one kind of accurate, fast, convenient and applicable numerical method; hence it is indeed worth doing further research.
Subjects
SCM
nonlocal nanobeam
maximum deflection
compatibility
Winkler elastic foundation
Type
thesis
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