Papyrus PressNew Approaches in Civil Engineering2588-71223420200220Solution of Harmonic Engineering Problems Using Equilibrated Basis Functions in a Weak Weighted Residual Approach in Polar CoordinatesSolution of Harmonic Engineering Problems Using Equilibrated Basis Functions in a Weak Weighted Residual Approach in Polar Coordinates243510933010.30469/jnace.2020.109330FAOmid BateniparvarM.Sc. student, Department of Civil Engineering, Faculty of Civil Engineering, Isfahan University of Technology, Isfahan, IranNima NoormohammadiAssistant Professor, Department of Civil Engineering, Faculty of Civil Engineering, Isfahan University of Technology, Isfahan, IranBijan BoroomandProfessor, Department of Civil Engineering, Faculty of Civil Engineering, Isfahan University of Technology, Isfahan, IranJournal Article20200104In solution of many engineering problems, including problems related to flow modeling in civil engineering, the use of mesh-less methods is common due to the provision of the potential field along with continuous and accurate velocity. Methods using basis functions are among the mesh-less techniques that use a set of basic functions that necessarily satisfy the homogeneous form of the equation, which is a major limitation. The equilibrated basis functions are capable of dissolving that defect by approximately satisfying the homogeneous equation in the form of a weighted residual integration, while still providing the continuity of the solution function and its derivatives throughout the domain. In the present study the weak weighted residual form, in which lower derivation orders appear than the strong form, will be implemented. The relations are expanded in a polar coordinate system. To demonstrate the efficiency of the method in engineering problems, the potential flow around a cylindrical barrier will be examined.In solution of many engineering problems, including problems related to flow modeling in civil engineering, the use of mesh-less methods is common due to the provision of the potential field along with continuous and accurate velocity. Methods using basis functions are among the mesh-less techniques that use a set of basic functions that necessarily satisfy the homogeneous form of the equation, which is a major limitation. The equilibrated basis functions are capable of dissolving that defect by approximately satisfying the homogeneous equation in the form of a weighted residual integration, while still providing the continuity of the solution function and its derivatives throughout the domain. In the present study the weak weighted residual form, in which lower derivation orders appear than the strong form, will be implemented. The relations are expanded in a polar coordinate system. To demonstrate the efficiency of the method in engineering problems, the potential flow around a cylindrical barrier will be examined.https://www.jnace.ir/article_109330_a1c340b346af2407c98f1a54e7657af9.pdf