scholarly journals Stabilizing Radial Basis Function Methods for Conservation Laws Using Weakly Enforced Boundary Conditions

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Jan Glaubitz ◽  
Anne Gelb
Keyword(s):  
Boundary Conditions ◽  
Conservation Laws ◽  
Radial Basis Function ◽  
Basis Function ◽  
Radial Basis

scholarly journals Free Vibration Study of Anti-Symmetric Angle-Ply Laminated Plates under Clamped Boundary Conditions

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
K.K. Viswanathan ◽  
K. Karthik ◽  
Y.V.S.S. Sanyasiraju ◽  
Z.A. Aziz
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Radial Basis Function ◽  
Basis Function ◽  
Equations Of Motion ◽  
Spline Approximation ◽  
Numerical Approach ◽  
Laminated Plates ◽  
Radial Basis ◽  
Plane Displacement

AbstractTwo type of numerical approach namely, Radial Basis Function and Spline approximation, used to analyse the free vibration of anti-symmetric angle-ply laminated plates under clamped boundary conditions. The equations of motion are derived using YNS theory under first order shear deformation. By assuming the solution in separable form, coupled differential equations obtained in term of mid-plane displacement and rotational functions. The coupled differential is then approximated using Spline function and radial basis function to obtain the generalize eigenvalue problem and parametric studies are made to investigate the effect of aspect ratio, length-to-thickness ratio, number of layers, fibre orientation and material properties with respect to the frequency parameter. Some results are compared with the existing literature and other new results are given in tables and graphs.

scholarly journals Solving Parabolic and Hyperbolic Equations with Variable Coefficients Using Space-Time Localized Radial Basis Function Collocation Method

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Mohammed Hamaidi ◽  
Ahmed Naji ◽  
Ahmed Taik
Keyword(s):  
Boundary Conditions ◽  
Radial Basis Function ◽  
Collocation Method ◽  
Basis Function ◽  
Hyperbolic Equations ◽  
Dimensional Space ◽  
Variable Coefficients ◽  
Space Time ◽  
Dimensional Problem ◽  
Radial Basis

In this paper, we investigate the numerical approximation solution of parabolic and hyperbolic equations with variable coefficients and different boundary conditions using the space-time localized collocation method based on the radial basis function. The method is based on transforming the original d -dimensional problem in space into d + 1 -dimensional one in the space-time domain by combining the d -dimensional vector space variable and 1 -dimensional time variable in one d + 1 -dimensional variable vector. The advantages of such formulation are (i) time discretization as implicit, explicit, θ -method, method-of-line approach, and others are not applied; (ii) the time stability analysis is not discussed; and (iii) recomputation of the resulting matrix at each time level as done for other methods for solving partial differential equations (PDEs) with variable coefficients is avoided and the matrix is computed once. Two different formulations of the d -dimensional problem as a d + 1 -dimensional space-time one are discussed based on the type of PDEs considered. The localized radial basis function meshless method is applied to seek for the numerical solution. Different examples in two and three-dimensional space are solved to show the accuracy of such method. Different types of boundary conditions, Neumann and Dirichlet, are also considered for parabolic and hyperbolic equations to show the sensibility of the method in respect to boundary conditions. A comparison to the fourth-order Runge-Kutta method is also investigated.

Nonlinear Bending Analysis of Hyperelastic Plates Using FSDT and Meshless Collocation Method Based on Radial Basis Function

2021 ◽  
Vol 13 (01) ◽  
pp. 2150007
Author(s):  
Shahram Hosseini ◽  
Gholamhossein Rahimi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Radial Basis Function ◽  
Collocation Method ◽  
Basis Function ◽  
The Finite Element Method ◽  
Radial Basis ◽  
Meshless Collocation ◽  
Element Method

This paper investigates the nonlinear bending analysis of a hyperelastic plate via neo-Hookean strain energy function. The first-order shear deformation plate theory (FSDPT) is used for the formulation of the field variables. Also, the nonlinear Lagrangian strains are considered via the right Cauchy–Green tensor. The governing equations and nonlinear boundary conditions are derived using Euler–Lagrange relations. The meshless collocation method based on radial basis function is used to discretize the governing equations of the hyperelastic plate. Square and circular plates are studied to evaluate the accuracy of the meshless collocation method based on thin-plate spline (TPS) and multiquadric (MQ) and logarithmic thin-plate spline (LTPS) radial basis function. Also, the results of the meshless method are compared to those of the finite element method. In some cases, the meshless method is more efficient than the finite element method due to no meshing. The linear and nonlinear natural boundary conditions are directly imposed on the stiffness matrix and are compared to each other. The maximum differences between linear and nonlinear natural boundary conditions are 1.43%. The von-Mises stress using meshless collocation method based on TPS basis function is compared to those of the finite element method.

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