WIT Press

Modeling Strain Localisation In A Segmented Bar By A C2-continuous Two-node Integrated-RBF Element Formulation


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D.-A. An-Vo, N. Mai-Duy, C.-D. Tran & T. Tran-Cong


We propose a local C2-continuous 2-node integrated-RBF element (IRBFE) method for the numerical modeling of strain localisation due to material discontinuity in a segmented elastic bar. The proposed local 2-node IRBFE method can be based on structured or unstructured point collocation procedureswhere both accuracy and efficiency are achieved. We introduce an effective way to exactly handle the material discontinuity by means of integration constants. Numerical results obtained for a bimaterial bar are compared with those from the analytic and finite element methods, demonstrating the advantage of the present approach. It will be shown that the solution is C2-continuous except at the bimaterial interface where the actual physical discontinuity is captured. Keywords: integrated-radial-basis-function elements, meshless method, local approximation, segmented bar. 1 Introduction Recently, considerable research effort in computational mechanics has been devoted to the development of meshlessmethods such as the element-freeGalerkin [1], hp-clouds [2], the reproducing kernel particle [3], the smoothed particle hydrodynamics [4], the diffuse element [5], the partition of unity finite element [6], the natural element [7], meshless Galerkin using radial basis functions [8], the meshless local Petrov-Galerkin (MLPG) [9], the modified smoothed particle hydrodynamics (MSPH) [10], and the collocation method using radial basis functions (RBF) [11]. Among these methods, the MLPG and the RBF collocation


integrated-radial-basis-function elements, meshless method, local approximation, segmented bar.