Abstract
The study develops the displacement error recovery method in a mesh free environment for the finite element solution employing the radial point interpolation (RPI) technique. The RPI technique uses the radial basis functions (RBF), along with polynomials basis functions to interpolate the displacement fields in a node patch and recovers the error in displacement field. The global and local errors are quantified in both energy and L2 norms from the post-processed displacement field. The RPI technique considers multi-quadrics/gaussian/thin plate splint RBF in combination with linear basis function for displacement error recovery analysis. The elastic plate examples are analyzed to demonstrate the error convergence and effectivity of the RPI displacement recovery procedures employing mesh free and mesh dependent patches. The performance of a RPI-based error estimators is also compared with the mesh dependent least square based error estimator. The triangular and quadrilateral elements are used for the discretization of plates domains. It is verified that RBF with their shape parameters, choice of elements, and errors norms influence considerably on the RPI-based displacement error recovery of finite element solution. The numerical results show that the mesh free RPI-based displacement recovery technique is more effective and achieve target accuracy in adaptive analysis with the smaller number of elements as compared to mesh dependent RPI and mesh dependent least square. It is also concluded that proposed mesh free recovery technique may prove to be most suitable for error recovery and adaptive analysis of problems dealing with large domain changes and domain discontinuities.
Highlights
The finite element method (FEM) has become a widely accepted method for the solution of solid mechanics problems
The numerical results show that the mesh free radial point interpolation (RPI)-based displacement recovery technique is more effective and achieves target accuracy in adaptive analysis with a smaller number of elements as compared to mesh dependent RPI and mesh dependent least square
It is concluded that the proposed mesh free recovery technique may prove to be most suitable for error recovery and adaptive analysis of problems dealing with large domain changes and domain discontinuities
Summary
The finite element method (FEM) has become a widely accepted method for the solution of solid mechanics problems. The mesh free methods are recently introduced for recovery of FEM solutions errors through various mesh free support domains based interpolating techniques. The mesh free recovery method using support domains, i.e., zone of influence of a node, was recently introduced by Ahmed et al [18] to recover the FEM solution errors. A two-dimensional finite element model employing mesh free nodes interface model based radial point interpolation method to simulate the interaction between soil and structure is proposed by Gong et al [20]. It is evident that most of the techniques proposed to recover the discretization error introduced in the finite element solution are mesh-based, i.e., dependent on element mesh connectivity, and the mesh free recovery technique in finite element method is a recent interest. The effect of radial basis functions with their shape parameters and shape of node zones is assessed on the quality of the error estimation obtained from the RPI-based error recovery techniques
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