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.

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.

A Meshless Method for Solving the Mathematical Model Associated the Leakage Problem in Gas Pipeline

2014 ◽  
Vol 986-987 ◽  
pp. 1418-1421
Author(s):  
Jun Shan Li
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Basis Function ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Gas Pipeline ◽  
The Mathematical Model

In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.

Nondestructive Measurement of In-Plane Residual Stress in Silicon Strips

1999 ◽  
Vol 591 ◽  
Author(s):  
Tieyu Zheng ◽  
Steven Danyluk
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Large Deflection ◽  
Thin Plates ◽  
Nondestructive Measurement ◽  
Three Point Bending ◽  
Phase Stepping ◽  
Bending Load ◽  
Bending Loads ◽  
Processing Techniques

ABSTRACTThis paper reports the development of a shadow moiré technique to measure the in-plane residual stresses of thin, flat strips. This is an extension of prior work on the measurement of in-plane residual stresses in silicon plates and wafers. Phase stepping shadow moir6 and digital image processing techniques are employed to measure the deflections of the silicon plate specimens subjected to three-point-bending at several different loads. The measured deflections over the area of the silicon plates are fitted with an equation represented by a 2-D polynomial. With the theory of thin plates with large deflection, the fitting coefficients are used to extract the in-plane stresses at the different bending load. The residual stress is resolved by linear regression of the in-plane stresses versus bending loads.

Large Deflection of Thin Plates in Convex or Concave Cylindrical Bending

2012 ◽  
Vol 138 (2) ◽  
pp. 230-234 ◽  
Author(s):  
Vivek A. Jairazbhoy ◽  
Pavel Petukhov ◽  
Jianmin Qu
Keyword(s):  
Large Deflection ◽  
Thin Plates ◽  
Cylindrical Bending
Sign in / Sign up

Export Citation Format

Share Document