scholarly journals Mesh Free Radial Point Interpolation Based Displacement Recovery Techniques for Elastic Finite Element Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1900
Author(s):  
Mohd. Ahmed ◽  
Devinder Singh ◽  
Saeed AlQadhi ◽  
Majed A. Alrefae

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.

Author(s):  
N. A. Nascimento ◽  
J. Belinha ◽  
R. M. Natal Jorge ◽  
D. E. S. Rodrigues

Cellular solid materials are progressively becoming more predominant in lightweight structural applications as more technologies realize these materials can be improved in terms of performance, quality control, repeatability and production costs, when allied with fast developing manufacturing technologies such as Additive Manufacturing. In parallel, the rapid advances in computational power and the use of new numerical methods, such as Meshless Methods, in addition to the Finite Element Method (FEM) are highly beneficial and allow for more accurate studies of a wide range of topologies associated with the architecture of cellular solid materials. Since these materials are commonly used as the cores of sandwich panels, in this work, two different topologies were designed — conventional honeycombs and re-entrant honeycombs — for 7 different values of relative density, and tested on the linear-elastic domain, in both in-plane directions, using the Natural Neighbor Radial Point Interpolation Method (NNRPIM), a newly developed meshless method, and the Finite Element Method (FEM) for comparison purposes.


1976 ◽  
Vol 4 (3-4) ◽  
pp. 143-147 ◽  
Author(s):  
K. Kanaka Raju ◽  
N. Muthiyalu ◽  
G. Venkateswara Rao

2019 ◽  
Vol 17 (07) ◽  
pp. 1950023 ◽  
Author(s):  
Elyas Shivanian

This paper develops pseudospectral meshless radial point Hermit interpolation (PSMRPHI) and pseudospectral meshless radial point interpolation (PSMRPI) in order to apply to the elliptic partial differential equations (PDEs) held on irregular domains subject to impedance (convective) boundary conditions. Elliptic PDEs in simplest form, i.e., Laplace equation or Poisson equation, play key role in almost all kinds of PDEs. On the other hand, impedance boundary conditions, from their application in electromagnetic problems, or convective boundary conditions, from their application in heat transfer problems, are nearly more complicated forms of the boundary conditions in boundary value problems (BVPs). Based on this problem, we aim also to compare PSMRPHI and PSMRPI which belong to more influence type of meshless methods. PSMRPI method is based on a combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which act as basis functions in the frame of PSMRPI and PSMRPHI methods. While the latter one has been rarely used in applications, we observe that is more accurate and reliable than PSMRPI method.


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