Implementation of PEC boundary condition for Laguerre-RPIM meshless method with novel uniform nodal distribution

2017 ◽  
Vol 27 (4) ◽  
pp. e21084 ◽  
Author(s):  
Kang Luo ◽  
Yan Tao Duan ◽  
Yun Yi ◽  
Qin Yin ◽  
Bin Chen
Keyword(s):  
Boundary Condition ◽  
Meshless Method ◽  
Nodal Distribution

Solving Mid-Frequency Acoustic Problem by the Meshless Method

2013 ◽  
Vol 444-445 ◽  
pp. 1471-1476
Author(s):  
Shuang Wang ◽  
Qi Bai Huang ◽  
Shan De Li
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Radial Basis Function ◽  
Efficient Method ◽  
Basis Function ◽  
Meshless Method ◽  
Medium Frequency ◽  
Pollution Effect ◽  
Acoustic Problem ◽  
Engineering Problems

It is well known that traditional finite element (FEM) is an efficient method in solving engineering problems. However, when solving the acoustic problems in medium frequency, FEM suffers from the so-called pollution effect, which is directly related to the dispersion. In this paper, meshless method based on radial basis function (RBF) is introduced to solve the acoustic problem, which shows that the dispersion can be greatly reduced, thus it is very suitable for the solution of mid-frequency acoustic problem. In addition, an algorithm is presented to treat the boundary condition, which improves the performance of the meshless method.

scholarly journals RBF-Based Meshless Method for Large Deflection of Elastic Thin Rectangular Plates with Boundary Conditions Involving Free Edges

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammed M. Hussein Al-Tholaia ◽  
Husain Jubran Al-Gahtani
Keyword(s):  
Boundary Condition ◽  
Basis Function ◽  
Meshless Method ◽  
Iterative Procedure ◽  
Large Deflection ◽  
Free Edge ◽  
Thin Plates ◽  
Rectangular Plates ◽  
Numerical Examples ◽  
Complex Boundary

An RBF-based meshless method is presented for the analysis of thin plates undergoing large deflection. The method is based on collocation with the multiquadric radial basis function (MQ-RBF). In the proposed method, the resulting coupled nonlinear equations are solved using an incremental-iterative procedure. The accuracy and efficiency of the method are verified through several numerical examples. The inclusion of the free edge boundary condition proves that this method is accurate and efficient in handling such complex boundary value problems.

scholarly journals Vibration Analysis of Permanent Magnet Synchronous Motor using Coupled Finite Element Analysis and Optimized Meshless Method

2021 ◽  
Author(s):  
Wei Xu ◽  
Size Li
Keyword(s):  
Boundary Condition ◽  
Meshless Method ◽  
Vibration Analysis ◽  
Permanent Magnet Synchronous Motor ◽  
Rotating Machinery ◽  
Basis Functions ◽  
Element Analysis ◽  
Harmonic Response ◽  
Electromagnetic Vibration ◽  
Coupling Calculation

Abstract Conventional finite element analysis (FEA) performed in electromagnetic-vibration coupling calculation of motor suffers from several significant drawbacks, such as large memory space, high computational cost and heavy reliance on mesh quality for accurate solution. With the traditional meshless method, special attention needs to be paid to correctly impose the boundary condition like FEA. Besides, the matrix is easily​​prone to be ill-conditioned due to introducing large amount of higher order basis functions. We propose a novel multiphyscial coupling method combining FEA and optimized meshless method. The proposed methodology is further evaluated on the vibration analysis of a 12-slot 10-pole permanent magnet synchronous motor (PMSM). Firstly, 2D stator electromagnetic force is simulated and derived based on the local Jacobian derivative method through FEA. The electromagnetic force spectrum is calculated using FFT analysis and further imported into commercial meshless structural simulation software Simsolid for stator harmonic response analysis. Correct force boundary condition and data mapping between meshless and FEA simulation interface is key to the accuracy of the proposed combined multiphysical modeling methodology. This is achieved by introducing a new high dimensional ramp function in the transition region between FEA and meshless domains, which are defined with the shape functions composed of the FEA and meshless method. This function satisfies the continuity and consistency of the displacement function, ensures the convergence of coupled FEA-meshless method. Subsequently, construction of basis function is key to the establishment of convention meshless discrete equation for the elastic problem of rotating machinery. This is designed using moving least square theory in cylindrical coordinate system. The harmonic response with meshless method is analyzed using a mode superposition method to obtain detailed mode shape data, acceleration and displacement distribution of stator. Finally, the tangential continuity and robustness are not well considered in the traditional simulation with FEA coupled meshless method. To mitigate this problem, we propose an optimized meshless method based on modified local basis functions to recalculate the harmonic response motion. Then the coupling electromagnetic-vibration simulation results of traditional coupled FEA-meshelss method, optimized coupled FEA-meshless method and complete FEA coupled method are compared. It is worth noting that optimized method significantly improves accuracy, robustness and computational speed at the same time. In short, the proposed electromagnetic-structure coupling calculation method provides a novel alternative for the multiphysical coupling calculation of rotating machinery combining FEA and meshless simulation methods.

An RBF Interpolated Generalized Finite Difference Meshless Method for Compressible Turbulent Flows

2009 ◽  
Author(s):  
Kevin J. Erhart ◽  
Salvadore A. Gerace ◽  
Eduardo A. Divo ◽  
Alain J. Kassab
Keyword(s):  
Turbulent Flows ◽  
Meshless Method ◽  
High Speed ◽  
Turbulence Models ◽  
Grid Generation ◽  
Complex Flow ◽  
Solution Algorithms ◽  
Aerospace Applications ◽  
Novel Approach ◽  
Nodal Distribution

Computational Fluid Dynamics (CFD) is a topic that has been researched heavily over the past 50 years, especially since the accessibility to sufficient computational resources has greatly increased. However, it is precisely this increase in technology that has led to a lack of efficiency in many CFD developments, especially when it comes to the process of grid generation. While many researchers are currently focused on solutions to the grid generation problems of traditional CFD techniques, the majority of these approaches still suffer serious numerical difficulties due to the underlying CFD solution algorithms that are used. Therefore, the focus of this work is to demonstrate a novel approach to true CFD automation which is based on traditional Cartesian grid generation coupled with a Meshless flow solution algorithm. As Meshless method solutions require only an underlying nodal distribution, this approach works well even for complex flow geometries. And with the addition of a so-called shadow layer of body-fitted nodes, the stair-casing issues of typical Cartesian solvers are eliminated. This paper will describe the approach taken to automatically generate the Meshless nodal distribution, along with the details of an automatic local refinement process. Also, as the primary interest of automated CFD is for aerospace applications, this work includes the development of standard two-equation turbulence models for use in this Meshless based solver. Finally, results will be shown for the application of high-speed, compressible turbulent flows.

One-Dimensional Fin-Tip Boundary Condition Correction II

2001 ◽  
Vol 22 (5) ◽  
pp. 35-40 ◽  
Author(s):  
D. C. Look Jr ◽  
Arvind Krishnan
Keyword(s):  
Boundary Condition ◽  
One Dimensional

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

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