scholarly journals EXACT SOLUTIONS FOR AXIAL STATIC ANALYSIS OF NANORODS USING WEIGHTED RESIDUALS

2021 ◽  
Vol 9 (2) ◽  
pp. 588-598
Author(s):  
Mustafa Özgür YAYLI ◽  
Uğur KAFKAS ◽  
Büşra UZUN
Keyword(s):  
Exact Solutions ◽  
Static Analysis ◽  
Weighted Residuals

An Analytical Method for Static Analysis of Double Layer Grids

1989 ◽  
Vol 4 (2) ◽  
pp. 107-116 ◽  
Author(s):  
H.C. Chan ◽  
C.W. Cai ◽  
Y.K. Cheung
Keyword(s):  
Exact Solutions ◽  
Static Analysis ◽  
Double Layer ◽  
Analytical Method ◽  
Transformation Technique ◽  
Simply Supported ◽  
Axial Forces ◽  
Nodal Displacements

An analytical method for the static analysis of double layer grids consisting of diagonals and top and bottom layers which are plane orthogonal grids is presented. It is assumed that the double layer grid is simply supported at all nodes located at the boundary of the top layer. By using the double U-transformation technique, exact solutions for the nodal displacements and axial forces of the bars in the double layer grid can be derived. The validity of the method is demonstrated with a simple example.

Benchmark exact solutions for the static analysis of multilayered piezoelectric composite plates using PVDF

2014 ◽  
Vol 107 ◽  
pp. 389-395 ◽  
Author(s):  
F. Moleiro ◽  
C.M. Mota Soares ◽  
C.A. Mota Soares ◽  
J.N. Reddy
Keyword(s):  
Exact Solutions ◽  
Static Analysis ◽  
Composite Plates ◽  
Piezoelectric Composite

Exact solutions for static analysis of intelligent structures

AIAA Journal ◽  
1993 ◽  
Vol 31 (9) ◽  
pp. 1684-1691 ◽  
Author(s):  
M. C. Ray ◽  
R. Bhattacharya ◽  
B. Samanta
Keyword(s):  
Exact Solutions ◽  
Static Analysis ◽  
Intelligent Structures

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

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