Analysis and Design of Thin Struts With Large Elastic Displacements: Part 1—Analysis of the Properties of the Solutions of the Nonlinear Differential Equations and the Behavior of the Strut

1974 ◽  
Vol 96 (3) ◽  
pp. 917-922 ◽  
Author(s):  
T. Y. Na ◽  
G. M. Kurajian ◽  
D. L. Holbert
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Elastic Behavior ◽  
Large Deflections ◽  
Transformation Technique ◽  
Analysis And Design ◽  
Engineering Aspect ◽  
Practical Engineering

Employing a transformation technique, an analysis is made of the properties of the solution of the differential equations resulting from the analysis of the elastic behavior of an eccentrically loaded thin strut. The thin strut is made to experience large deflections and the end supports are simultaneously pinned and restrained by torsional bar springs. The paper is divided into two parts. Part 1 deals primarily with the properties of the solution of the equations; and Part 2 deals with the practical engineering aspect where, employing Part 1, realistic values and ranges of parameters are assigned. The resulting design curves and tables, useful to the design engineer, are presented.

Large Deflections and Buckling Loads of Cantilever Columns with Constant Volume

2017 ◽  
Vol 17 (08) ◽  
pp. 1750091 ◽  
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Large Deflection ◽  
Nonlinear Differential Equations ◽  
Constant Volume ◽  
Large Deflections ◽  
Buckling Loads ◽  
Geometrical Nonlinear ◽  
Deflection Theory ◽  
Large Deflection Theory

This paper deals with the large deflections and buckling loads of tapered cantilever columns with a constant volume. The column member has a solid regular polygonal cross-section. The depth of this cross-section is functionally varied along the column axis. Geometrical nonlinear differential equations, which govern the buckled shape of the column, are derived using the large deflection theory, considering the effect of shear deformation. The buckling load of the column is approximately equivalent to the load under which a very small tip deflection occurs. In regard to the numerical results, both the elastica and buckling loads with varying column parameters are discussed. The configurations of the strongest column are also presented.

scholarly journals Developing a MATLAB® Toolbox for MWM Buck-boost Converter Analysis and Design

2017 ◽  
Vol 1 (3) ◽  
Author(s):  
Farzin Asadi
Keyword(s):  
Differential Equations ◽  
Transfer Functions ◽  
Nonlinear Differential Equations ◽  
Boost Converter ◽  
Matlab Toolbox ◽  
Analysis And Design ◽  
Component Selection

This paper introduces a MATLAB toolbox for analysis and design of a novel buck-boost topology suggested by Miao, Wang and Ma (MWM). The developed toolbox solves the converter’s nonlinear differential equations and draws the circuit’s different waveforms. So, component selection can be done by using the obtained waveform’s maximum, average, etc. Developed software also calculates the small signaltransfer functions. Obtained transfer functions aretransferred to MATLAB’s workspace so the controllerdesign can be done easily using MATLAB’s controlsystem toolbox. Contact the corresponding author toreceive the software.

A New Approach to the Analysis of the Deflection of Thin Cantilevers

1961 ◽  
Vol 28 (1) ◽  
pp. 87-90 ◽  
Author(s):  
R. Frisch-Fay
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
New Method ◽  
Large Deflections ◽  
New Approach

The paper proposes a new method for the calculation of large deflections. Slender bars under point loads are traced back to the strut problem, thus bypassing the solution of nonlinear differential equations.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

scholarly journals New oscillation criteria for second-order neutral differential equations with distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Osama Moaaz ◽  
Choonkil Park ◽  
Elmetwally M. Elabbasy ◽  
Waed Muhsin
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
The Other ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Continuous Delay ◽  
New Criteria

AbstractIn this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and comparison principles. Furthermore, we obtain iterative criteria that can be applied even when the other criteria fail. The results obtained in this paper improve and extend the relevant previous results as illustrated by examples.

scholarly journals Solving nonlinear differential equations with differentiable quantum circuits

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Oleksandr Kyriienko ◽  
Annie E. Paine ◽  
Vincent E. Elfving
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Quantum Circuits

scholarly journals Nonlinear Differential Equations Modeling the Antarctic Circumpolar Current

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Jifeng Chu ◽  
Kateryna Marynets
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Topological Degree ◽  
Antarctic Circumpolar Current ◽  
Fixed Point Theorems ◽  
Nonlinear Differential Equations ◽  
Existence Results ◽  
Circumpolar Current ◽  
The Antarctic

AbstractThe aim of this paper is to study one class of nonlinear differential equations, which model the Antarctic circumpolar current. We prove the existence results for such equations related to the geophysical relevant boundary conditions. First, based on the weighted eigenvalues and the theory of topological degree, we study the semilinear case. Secondly, the existence results for the sublinear and superlinear cases are proved by fixed point theorems.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

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