Elasto-Plastic Analysis of Structural Problems Using Atomic Basis Functions
V. Kozuli\'c; B. Gotovac

doi:10.3970/cmes.2011.080.251
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 80, No. 4, pp. 251-274, 2011
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Keywords torsion problem of prismatic bars, plastic failure, atomic basis functions, universality, collocation method, multilevel base.
Abstract The numerical model for the elasto-plastic analysis of prismatic bars subjected to torsion is developed. The functions implemented in this model are Fup basis functions which belong to the class of atomic functions. The collocation method is used to form a system of equations in which the differential equation of the problem is satisfied in collocation points of closed domain, while boundary conditions are satisfied exactly at the domain boundary. The propagation of plastic zones in the cross-section is monitored by applying the incremental-iterative procedure until failure. An approximate solution of arbitrary accuracy is attained by hierarchically increasing the number of basis functions during non-linear calculation (multilevel approach) in places where plastic yielding occurs. The results obtained by the proposed method are compared with the existing exact solutions and numerical solutions obtained by the Finite Element Method. It can be concluded that the presented numerical model efficiently simulates the real non-linear behavior of the structure and provides excellent results for the elaborated problems.
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