A New Approach for Exact Bending Solutions of Moderately Thick Rectangular Plates with Completely Clamped Support

2013 ◽  
Vol 378 ◽  
pp. 109-114
Author(s):  
Bo Hu ◽  
Qian Huang ◽  
Xi Yang Zi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Thick Plate ◽  
Integral Transform ◽  
Linear Equations ◽  
High Order ◽  
Rectangular Plates ◽  
Partial Differential ◽  
Transform Method ◽  
Finite Integral

First presents a set of high order partial differential equations for elastic rectangular thick plate base on Mindlin theory. The high order partial differential equations were transformed to linear equations by the double finite integral transform method, and then arrives at the theoretical solution of elastic rectangular thick plate with four edges completely clamped support. Only the basic elasticity equations of the thick plate were used and it was not needed to first select the deformation function arbitrarily. Therefore, the solution in the paper is more reasonable. In order to proof the correction of formulations, the numerical results are also presented to comparing with that of the other references.

scholarly journals Solution of One-dimensional Partial Differential Equation with Higher-Order Derivative by Double Laplace Transform Method

2021 ◽  
Vol 4 (3) ◽  
pp. 1-11
Author(s):  
Anongo D.O. ◽  
Awari Y.S.
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Integral Transform ◽  
Higher Order ◽  
Laplace Transform Method ◽  
Partial Differential ◽  
Transform Method ◽  
Double Laplace Transform ◽  
Engineering Sciences

Many problems in natural and engineering sciences such as heat transfer, elasticity, quantum mechanics, water flow, and others are modelled mathematically by partial differential equations. Some of these problems may be linear, nonlinear, homogeneous, non-homogeneous, and order greater or equal one. Finding the theoretical solution to these problems with less cumbersome techniques is an active area of research in the aforementioned field. In this research paper, we have developed a new application of the double Laplace transform method to solve homogeneous and non-homogeneous linear partial differential equations (pdes) with higher-order derivatives (i.e order n where n≥2) in science and engineering. We discussed a brief theory of double Laplace transforms that helped in its application. The main advantage of our method is the reduction of computational effort in finding solution to pdes. Another major benefit of our method is solving problems in the form of (21) directly by transforming to an algebraic equation where the inverse double Laplace transform is implemented for analytical solution, unlike other integral transform methods that would first transform to a system of ODEs before they are solved, is it also very effective in solving linear high-order partial differential equations and yield fast convergence. We present a well-simplified solution for easier comprehension by upcoming researchers.

scholarly journals A fuzzy solution of nonlinear partial differential equations

2021 ◽  
Vol 5 (1) ◽  
pp. 51-63
Author(s):  
Mawia Osman ◽  
◽  
Zengtai Gong ◽  
Altyeb Mohammed Mustafa ◽  
◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Infinite Series ◽  
Nonlinear Partial Differential Equations ◽  
Differential Transform Method ◽  
Series Expansions ◽  
Partial Differential ◽  
Transform Method ◽  
Differential Transform ◽  
Fuzzy Solution

In this paper, the reduced differential transform method (RDTM) is applied to solve fuzzy nonlinear partial differential equations (PDEs). The solutions are considered as infinite series expansions which converge rapidly to the solutions. Some examples are solved to illustrate the proposed method.

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