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.

scholarly journals A New Approach to Approximate Solutions for Nonlinear Differential Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Safia Meftah
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Small Parameter ◽  
Perturbation Method ◽  
Periodic Solutions ◽  
Asymptotic Expansions ◽  
Nonlinear Differential Equations ◽  
Approximate Solutions ◽  
Approximation Methods ◽  
New Approach

The question discussed in this study concerns one of the most helpful approximation methods, namely, the expansion of a solution of a differential equation in a series in powers of a small parameter. We used the Lindstedt-Poincaré perturbation method to construct a solution closer to uniformly valid asymptotic expansions for periodic solutions of second-order nonlinear differential equations.

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 A PARALLEL MULTIRATE ALGORITHM FOR THE NUMERICAL INTEGRATION OF SYSTEM OF NONLINEAR DIFFERENTIAL EQUATIONS

2014 ◽  
pp. 34-41
Author(s):  
Petro Stakhiv ◽  
Serhiy Rendzinyak
Keyword(s):  
Differential Equations ◽  
Numerical Integration ◽  
Dynamic Behavior ◽  
Large Scale ◽  
Nonlinear Differential Equations ◽  
New Approach ◽  
Large Scale Systems ◽  
Computing Process ◽  
Parallelization Efficiency

The new approach to calculate dynamic behavior of large-scale systems, separated on subsystems is presented. Parallelization efficiency of computing process is described.

scholarly journals An approximation solvability method for nonlocal differential problems in Hilbert spaces

2017 ◽  
Vol 19 (02) ◽  
pp. 1650002 ◽  
Author(s):  
Irene Benedetti ◽  
Nguyen Van Loi ◽  
Luisa Malaguti ◽  
Valeri Obukhovskii
Keyword(s):  
Differential Equations ◽  
Hilbert Spaces ◽  
Nonlinear Differential Equations ◽  
Degree Theory ◽  
Nonlocal Problems ◽  
Abstract Result ◽  
New Approach

A new approach is developed for the solvability of nonlocal problems in Hilbert spaces associated to nonlinear differential equations. It is based on a joint combination of the degree theory with the approximation solvability method and the bounding functions technique. No compactness or condensivity condition on the nonlinearities is assumed. Some applications of the abstract result to the study of nonlocal problems for integro-differential equations and systems of integro-differential equations are then showed. A generalization of the result by using nonsmooth bounding functions is given.

scholarly journals Discrete Temimi-Ansari method for solving a class of stochastic nonlinear differential equations

2021 ◽  
Vol 7 (4) ◽  
pp. 5093-5105
Author(s):  
Mourad S. Semary ◽  
◽  
M. T. M. Elbarawy ◽  
Aisha F. Fareed ◽  
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Landau Equation ◽  
Nonlinear Differential Equations ◽  
New Method ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation

<abstract> <p>In this paper, a numerical method to solve a class of stochastic nonlinear differential equations is introduced. The proposed method is based on the Temimi-Ansari method. The special states of the four systems are studied to show that the proposed method is efficient and applicable. These systems are stochastic Langevin's equation, Ginzburg-Landau equation, Davis-Skodje, and Brusselator systems. The results clarify the accuracy and efficacy of the presented new method with no need for any restrictive assumptions for nonlinear terms.</p> </abstract>

Robust Adaptive Neural Estimation of Restoring Forces in Nonlinear Structures

2001 ◽  
Vol 68 (6) ◽  
pp. 880-893 ◽  
Author(s):  
E. B. Kosmatopoulos ◽  
A. W. Smyth ◽  
S. F. Masri ◽  
A. G. Chassiakos
Keyword(s):  
Nonlinear Dynamics ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Adaptive Methods ◽  
Reinforced Concrete Structure ◽  
Response Measurement ◽  
New Approach ◽  
Model Based ◽  
Restoring Forces ◽  
On Line

The availability of methods for on-line estimation and identification of structures is crucial for the monitoring and active control of time-varying nonlinear structural systems. Adaptive estimation approaches that have recently appeared in the literature for on-line estimation and identification of hysteretic systems under arbitrary dynamic environments are in general model based. In these approaches, it is assumed that the unknown restoring forces are modeled by nonlinear differential equations (which can represent general nonlinear characteristics, including hysteretic phenomena). The adaptive methods estimate the parameters of the nonlinear differential equations on line. Adaptation of the parameters is done by comparing the prediction of the assumed model to the response measurement, and using the prediction error to change the system parameters. In this paper, a new methodology is presented which is not model based. The new approach solves the problem of estimating/identifying the restoring forces without assuming any model of the restoring forces dynamics, and without postulating any structure on the form of the underlying nonlinear dynamics. The new approach uses the Volterra/Wiener neural networks (VWNN) which are capable of learning input/output nonlinear dynamics, in combination with adaptive filtering and estimation techniques. Simulations and experimental results from a steel structure and from a reinforced-concrete structure illustrate the power and efficiency of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document