An approximate solution with high accuracy of transverse bending of thin rectangular plates under arbitrarily distributed loads

1993 ◽  
Vol 14 (3) ◽  
pp. 241-246 ◽  
Author(s):  
Zhou Ding
Keyword(s):  
Approximate Solution ◽  
High Accuracy ◽  
Rectangular Plates ◽  
Transverse Bending

A New Numerical Method for Solving Nonlinear Fractional Fokker–Planck Differential Equations

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
BeiBei Guo ◽  
Wei Jiang ◽  
ChiPing Zhang
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Reproducing Kernel ◽  
Numerical Solutions ◽  
Simple Algorithm ◽  
High Accuracy ◽  
Computational Work ◽  
Reproducing Kernel Theory ◽  
Transport Problems ◽  
Fokker Planck

The nonlinear fractional-order Fokker–Planck differential equations have been used in many physical transport problems which take place under the influence of an external force filed. Therefore, high-accuracy numerical solutions are always needed. In this article, reproducing kernel theory is used to solve a class of nonlinear fractional Fokker–Planck differential equations. The main characteristic of this approach is that it induces a simple algorithm to get the approximate solution of the equation. At the same time, an effective method for obtaining the approximate solution is established. In addition, some numerical examples are given to demonstrate that our method has lesser computational work and higher precision.

A Hybrid Analytical and Finite Element Method for Mid-Frequency Vibration Analysis of Plate Structures with Discontinuities

2017 ◽  
Vol 17 (04) ◽  
pp. 1750052 ◽  
Author(s):  
Yongbin Ma ◽  
Yahui Zhang ◽  
Bo Ping Wang
Keyword(s):  
Finite Element ◽  
Vibration Analysis ◽  
Present Method ◽  
High Efficiency ◽  
Main Idea ◽  
High Accuracy ◽  
Symplectic Method ◽  
Rectangular Plates ◽  
Fe Method ◽  
Plate Structures

A hybrid analytical and numerical method is presented for the mid-frequency vibration analysis of a class of plate structures with discontinuities based on the concept of structural partitioning. The type of structures considered includes rectangular plates with internal property discontinuity, homogeneous but non-rectangular plates, or built-up structures composed of rectangular homogenous plates with complex joints. Compared with the conventional finite element (FE) method, the present method has the advantage of high accuracy and high efficiency in the analysis of mid-frequency vibration of the structures of concern. The main idea of the proposed approach is to divide the whole structure into uniform rectangular plate regions and other non-rectangular regions. The vibration behavior of the rectangular regions is accurately and efficiently described by analytical wave solutions so that the FE modeling for these regions is not necessary. The other non-rectangular regions are modeled by the conventional FE method. The analytical waves used to describe the rectangular regions are obtained by the symplectic method, thereby avoiding the limitation of the conventional analytical method in dealing with plates having two opposite edges simply supported. By enforcing the displacement continuity and force equilibrium at the connection interfaces, the dynamic coupling is established between the rectangular regions described in terms of the analytical waves and the regions modeled by FEs. Furthermore, the hybrid solution formulation for the mid-frequency vibration of the entire structure is proposed. The high accuracy and efficiency of the present method are demonstrated by several numerical examples, with the effect of element size of the FE regions investigated. Finally, the applicability of the proposed method is analyzed.

scholarly journals Application of Rational Second Kind Chebyshev Functions for System of Integrodifferential Equations on Semi-Infinite Intervals

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
M. Tavassoli Kajani ◽  
S. Vahdati ◽  
Zulkifly Abbas ◽  
Mohammad Maleki
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Galerkin Method ◽  
High Accuracy ◽  
Integrodifferential Equations ◽  
Expansion Test ◽  
Infinite Intervals ◽  
System Of Integrodifferential Equations ◽  
Rational Chebyshev ◽  
Chebyshev Functions

Rational Chebyshev bases and Galerkin method are used to obtain the approximate solution of a system of high-order integro-differential equations on the interval [0,∞). This method is based on replacement of the unknown functions by their truncated series of rational Chebyshev expansion. Test examples are considered to show the high accuracy, simplicity, and efficiency of this method.

scholarly journals The Laplace-Adomian-Pade Technique for the ENSO Model

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Yi Zeng
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Initial Conditions ◽  
Approximate Solutions ◽  
Decomposition Methods ◽  
High Accuracy ◽  
Padé Method

The Laplace-Adomian-Pade method is used to find approximate solutions of differential equations with initial conditions. The oscillation model of the ENSO is an important nonlinear differential equation which is solved analytically in this study. Compared with the exact solution from other decomposition methods, the approximate solution shows the method’s high accuracy with symbolic computation.

Transverse bending of ribbed rectangular plates

1991 ◽  
Vol 27 (12) ◽  
pp. 1182-1185
Author(s):  
G. I. Pshenichnov ◽  
A. Yazdurdyev
Keyword(s):  
Rectangular Plates ◽  
Transverse Bending

scholarly journals Approximate Solution of the Thomas–Fermi Equation for Free Positive Ions

Atoms ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 87
Author(s):  
Aleksey A. Mavrin ◽  
Alexander V. Demura
Keyword(s):  
Approximate Solution ◽  
Asymptotic Representation ◽  
High Accuracy ◽  
Universal Functions ◽  
Ionization Degree ◽  
Thomas Fermi ◽  
Positive Ions ◽  
Ion Size

The approximate solution of the nonlinear Thomas–Fermi (TF) equation for ions is found by the Fermi method. The solution is based on the new asymptotic representation of the TF ion size valid for any ionization degree. The two universal functions and their derivatives, introduced by Fermi, are calculated by recent effective algorithms for the Emden–Fowler type equations with the accuracy sufficient for majority of applications. The comparison of our results with those obtained previously shows high accuracy and validity for arbitrary values of ionization degree. This study could potentially be of interest for the statistical TF method applications in physics and chemistry.

scholarly journals The New Approach to Analysis of Thin Isotropic Symmetrical Plates

2020 ◽  
Vol 10 (17) ◽  
pp. 5931
Author(s):  
Mykhaylo Delyavskyy ◽  
Krystian Rosiński
Keyword(s):  
Present Method ◽  
Automatic Differentiation ◽  
Linear Equations ◽  
High Accuracy ◽  
Rectangular Plates ◽  
System Of Linear Equations ◽  
New Approach ◽  
Summation Convention ◽  
Analytical Formulae ◽  
Einstein Summation Convention

A new approach to solve plate constructions using combined analytical and numerical methods has been developed in this paper. It is based on an exact solution of an equilibrium equation. The proposed mathematical model is implemented as a computer program in which known analytical formulae are rewritten as wrapper functions of two arguments. Partial derivatives are calculated using automatic differentiation. A solution of a system of linear equations is substituted to these functions and evaluated using the Einstein summation convention. The calculated results are presented and compared to other analytical and numerical ones. The boundary conditions are satisfied with high accuracy. The effectiveness of the present method is illustrated by examples of rectangular plates. The model can be extended with the ability to solve plates of any shape.

scholarly journals On the solutions of electrohydrodynamic flow with fractional differential equations by reproducing kernel method

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 685-689 ◽  
Author(s):  
Ali Akgül ◽  
Dumitru Baleanu ◽  
Mustafa Inc ◽  
Fairouz Tchier
Keyword(s):  
Approximate Solution ◽  
Fractional Differential Equations ◽  
Numerical Experiments ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
High Accuracy ◽  
Reproducing Kernel Method ◽  
Fractional Differential ◽  
Kernel Model ◽  
Theoretical Results

AbstractIn this manuscript we investigate electrodynamic flow. For several values of the intimate parameters we proved that the approximate solution depends on a reproducing kernel model. Obtained results prove that the reproducing kernel method (RKM) is very effective. We obtain good results without any transformation or discretization. Numerical experiments on test examples show that our proposed schemes are of high accuracy and strongly support the theoretical results.

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