A computational study of solitary wave solutions of Kawahara-type equations by meshless spectral interpolation method

2019 ◽  
Vol 30 (12) ◽  
pp. 1950102 ◽  
Author(s):  
Manzoor Hussain ◽  
Sirajul Haq
Keyword(s):  
Numerical Solutions ◽  
Computational Study ◽  
Interpolation Method ◽  
Evolutionary Equations ◽  
Spectral Interpolation ◽  
Radial Point Interpolation ◽  
Point Interpolation ◽  
Waves Propagation ◽  
Quality Of Approximation

In this paper, a meshless spectral radial point interpolation (MSRPI) method using weighted [Formula: see text]-scheme is formulated for the numerical solutions of a class of nonlinear Kawahara-type evolutionary equations. The formulated method is applied for simulation of single and double solitary waves motion, wave generation and oscillatory shock waves propagation. Quality of approximation is measured via discrete [Formula: see text], [Formula: see text] and [Formula: see text] error norms. Three invariant quantities corresponding to mass, momentum and energy are also computed for the method validation. Stability analysis of the proposed method is briefly discussed and verified computationally. Comparison of the obtained results are made with other existing results in the literature revealing the method superiority.

Simulation of the viscoplastic extrusion process using the radial point interpolation meshless method

2021 ◽  
pp. 146442072098858
Author(s):  
ROSS Costa ◽  
J Belinha ◽  
RM Natal Jorge ◽  
DES Rodrigues
Keyword(s):  
Meshless Method ◽  
Fused Deposition Modeling ◽  
Interpolation Method ◽  
Extrusion Process ◽  
Fused Deposition ◽  
Radial Point Interpolation ◽  
Large Growth ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Deposition Modeling

Additive manufacturing is an emergent technology, which witnessed a large growth demanded by the consumer market. Despite this growth, the technology needs scientific regulation and guidelines to be reliable and consistent to the point that is feasible to be used as a source of manufactured end-products. One of the processes that has seen the most significant development is the fused deposition modeling, more commonly known as 3D printing. The motivation to better understand this process makes the study of extrusion of materials important. In this work, the radial point interpolation method, a meshless method, is applied to the study of extrusion of viscoplastic materials, using the formulation originally intended for the finite element method, the flow formulation. This formulation is based on the reasoning that solid materials under those conditions behave like non-Newtonian fluids. The time stepped analysis follows the Lagrangian approach taking advantage of the easy remeshing inherent to meshless methods. To validate the newly developed numerical tool, tests are conducted with numerical examples obtained from the literature for the extrusion of aluminum, which is a more common problem. Thus, after the performed validation, the algorithm can easily be adapted to simulate the extrusion of polymers in fused deposition modeling processes.

The natural neighbor radial point interpolation method in the Elasto-Static analysis of Honeycomb-Shaped foams

2021 ◽  
pp. 2150014
Author(s):  
N. A. Nascimento ◽  
J. Belinha ◽  
R. M. Natal Jorge ◽  
D. E. S. Rodrigues
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interpolation Method ◽  
The Finite Element Method ◽  
Solid Materials ◽  
Cellular Solid ◽  
Natural Neighbor ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation

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.

Sign in / Sign up

Export Citation Format

Share Document