A semi-analytical solution of statically indeterminate bar problem by using domain decomposition method

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• 作者：Sushanta Ghuku ; Kashi Nath Saha ; ^{kashinathsaha@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Statically indeterminate ; Variational principle ; Three point conditions ; Domain decomposition method
• 刊名：Perspectives in Science
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：8
• 期：Complete
• 页码：661-663
• 全文大小：650 K

文摘

The paper presents a semi analytical method for solution of a statically indeterminate non-uniform bar problem. The solution of such statically indeterminate bar problem becomes more complicated due to the presence of singularity points in domain. Some examples of such one dimensional problems include, (i) stress and deformation analysis of a clamped–clamped (C–C) bar subjected to a concentrated load within domain, (ii) thermal stress analysis of a ‘C–C’ bar with a point heat source within domain, (iii) three point bending analysis of a roller supported curved beam under a concentrated transverse load, etc.

In the present bar problem, only one such singularity point arising from the application of a concentrated axial load, is considered. Governing equation of the problem is derived from equilibrium condition and expressed in variational form with assumed displacement field by using direct variational principle. The computational domain is divided into two sub-domains based on the location of singularity point within the domain. An approximate solution of the governing equation is obtained assuming a series expression of the unknown variable by using Galerkin's principle. This approximation is carried out by a linear combination of sets of orthogonal co-ordinate functions which satisfy prescribed conditions at three points. The three conditions comprises of two boundary conditions and another condition at the point of application of concentrated load. The solution algorithm is implemented with the help of MATLAB^® computational simulation software. The problem is also studied by using energy functional based variational method and an identical solution is observed. The present analysis highlights the generalized application of domain decomposition method based on variational principle in solving structural problems having singularities in domain.