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Abstract: In this communication exact analytical solution of the well known Saeman''s model equation, which is used to find the bed depth profile of the granular material flowing in a rotary kiln, has been obtained. Mathematically this model equation is characterized by a first order nonlinear ordinary differential equation and the exact analytical solution has been obtained in terms of an implicit form of elementary transcendental function by following the methods of separation of variables and partial fraction decomposition. To the best of the authors'' knowledge, this is perhaps the first attempt towards obtaining the exact analytical solution for the above model equation. The results obtained by using the exact analytical solution have been successfully verified against those obtained by using the numerical method and are found to be superior to those obtained by using the existing approximate analytical solutions. Besides, the exact analytical solution has also been fruitfully employed to simulate various experimental results available in literature. Furthermore, the effects of various parameters on the bed depth profile have also been briefly analyzed. [Copyright &y& Elsevier]

Abstract: Offshore pipelines installed by reeling method are subjected to large plastic strains. When the steel pipes are joined by girth welding, both surface and embedded cracks are inevitably initiated in welding zone. The pipe lines should have adequate resistance against both crack extension by tearing and unstable fracture during installation as well as during operation. However, common flaw assessment procedures, e.g. BS 7910:2005 , are not explicitly developed for such situations with large plastic strains. The main objective of the current paper is to find a way to assess fracture capability of a practical pipeline subject to large plastic deformation. In our study, the evolution of crack tip opening displacement (CTOD) of the pipeline with semi-eliptical surface crack in weld girth is investigated under biaxial loading conditions (uniaxial tensile and internal pressure) using three dimensional elastic–plastic finite element analysis. The effects of crack depth, ratio of semi-major axis to semi-minor axis and internal pressure are examined. The results show that at moderate levels of global strain, the variation of CTOD with global strain can be well approximated by a simple linear relationship under tensile loading as well as biaxial loading conditions. Comparing the fracture assessment for the welded pipe made by BS 7910:2005 with that made by our current study, it is found that the assessment from BS7910:2005 is over conservative. A CTOD-estimation method for strain -based fracture is suggested for the pipelines when the global strain is 3%. [Copyright &y& Elsevier]