A Numerical Approach for Simulating a Self-Contacted Elastic Rod

2014 ◽  
Vol 941-944 ◽  
pp. 2336-2340
Author(s):  
Gong Xi Wang ◽  
Wei Jia Zhao
Keyword(s):  
Topological Structure ◽  
Lagrange Equation ◽  
Numerical Approach ◽  
Simplified Model ◽  
State Variables ◽  
Challenging Problem ◽  
Elastic Rod ◽  
Euler Parameters ◽  
Numerical Examples ◽  
Cosserat Rod

A challenging problem in the numerical simulation of a self-contacted elastic rod is the change of topological structure during the contacting process. In this article, a numerical approach is introduced to simulate a self-contacted Cosserat rod. By introducing the angular velocity and Euler parameters as the state variables, an improved Lagrange equation is introduced. A finite element method is built to deal with the simplified model, and numerical examples are given.

Stress Concentration of Periodic Collinear Square Holes in an Infinite Plate in Tension

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Changqing Miao ◽  
Yintao Wei ◽  
Xiangqiao Yan
Keyword(s):  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Infinite Plate ◽  
Numerical Approach ◽  
Numerical Examples ◽  
Calculated Stress ◽  
Bueckner’S Principle

A numerical approach for the stress concentration of periodic collinear holes in an infinite plate in tension is presented. It involves the fictitious stress method and a generalization of Bueckner's principle. Numerical examples are concluded to show that the numerical approach is very efficient and accurate for analyzing the stress concentration of periodic collinear holes in an infinite plate in tension. The stress concentration of periodic collinear square holes in an infinite plate in tension is studied in detail by using the numerical approach. The calculated stress concentration factor is proven to be accurate.

Vibrations of a Helicopter Rotor-Fuselage System Induced by the Main Rotor Blades in Flight

1955 ◽  
Vol 22 (3) ◽  
pp. 355-360
Author(s):  
M. Morduchow ◽  
S. W. Yuan ◽  
H. Reissner
Keyword(s):  
Theoretical Analysis ◽  
Natural Frequencies ◽  
Rotor Blades ◽  
Helicopter Rotor ◽  
Simplified Model ◽  
Main Rotor ◽  
Numerical Examples ◽  
The Masses

Abstract Based on a simplified model of the hub-fuselage structure, a theoretical analysis is made of the response of the hub and fuselage of a helicopter in flight to harmonic forces transmitted by the rotor blades to the hub both in, and normal to, the plane of rotation. The assumed structure is in the form of a plane framework with masses concentrated at the joints. Simple expressions are derived for the vibration amplitudes of the mass points as functions of the masses and natural frequencies of the hub and the fuselage. The pertinent nondimensional parameters are determined, and simple explicit conditions of resonance are derived. Numerical examples are given to illustrate the results.

scholarly journals Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Berna Bülbül ◽  
Mehmet Sezer
Keyword(s):  
Matrix Method ◽  
Numerical Approach ◽  
Duffing Equation ◽  
Matrix Equations ◽  
Algebraic Equations ◽  
Solution Function ◽  
Numerical Examples ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
The Matrix

We have suggested a numerical approach, which is based on an improved Taylor matrix method, for solving Duffing differential equations. The method is based on the approximation by the truncated Taylor series about center zero. Duffing equation and conditions are transformed into the matrix equations, which corresponds to a system of nonlinear algebraic equations with the unknown coefficients, via collocation points. Combining these matrix equations and then solving the system yield the unknown coefficients of the solution function. Numerical examples are included to demonstrate the validity and the applicability of the technique. The results show the efficiency and the accuracy of the present work. Also, the method can be easily applied to engineering and science problems.

scholarly journals Dynamics of Periodic Impulsive Collision in Escapement Mechanism

2013 ◽  
Vol 20 (5) ◽  
pp. 1001-1010
Author(s):  
Jian Mao ◽  
Yu Fu ◽  
Peichao Li
Keyword(s):  
Dynamic Systems ◽  
Impulsive Differential Equation ◽  
Forced Oscillation ◽  
Simplified Model ◽  
Oscillation System ◽  
Dynamical Study ◽  
Numerical Examples ◽  
The Stability ◽  
The Impact ◽  
Escapement Mechanism

Among various non-smooth dynamic systems, the periodically forced oscillation system with impact is perhaps the most common in engineering applications. The dynamical study becomes complicated due to the impact. This paper presents a systematic study on the periodically forced oscillation system with impact. A simplified model of the escapement mechanism is introduced. Impulsive differential equation and Poincare map are applied to describe the model and study the stability of the system. Numerical examples are given and the results show that the model is highly accurate in describing/predicting their dynamics.

scholarly journals Distributed Control for Multiagent Consensus Motions with Nonuniform Time Delays

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Mengji Shi ◽  
Kaiyu Qin
Keyword(s):  
Distributed Control ◽  
Time Delays ◽  
Original System ◽  
Complex Numbers ◽  
Control Problems ◽  
Rectilinear Motion ◽  
State Variables ◽  
Real Numbers ◽  
Numerical Examples ◽  
Delay Margin

This paper solves control problems of agents achieving consensus motions in presence of nonuniform time delays by obtaining the maximal tolerable delay value. Two types of consensus motions are considered: the rectilinear motion and the rotational motion. Unlike former results, this paper has remarkably reduced conservativeness of the consensus conditions provided in such form: for each system, if all the nonuniform time delays are bounded by the maximal tolerable delay value which is referred to as “delay margin,” the system will achieve consensus motion; otherwise, if all the delays exceed the delay margin, the system will be unstable. When discussing the system which is intended to achieve rotational consensus motion, an expanded system whose state variables are real numbers (those of the original system are complex numbers) is introduced, and corresponding consensus condition is given also in the form of delay margin. Numerical examples are provided to illustrate the results.

Multirate Constrained Predictive Control: Algorithm and Experimental Results

2007 ◽  
Vol 2 (3) ◽  
Author(s):  
Qiuping Hu ◽  
Sohrab Rohani
Keyword(s):  
Control System ◽  
Predictive Control ◽  
Control Algorithm ◽  
Design Method ◽  
Pi Control ◽  
State Variables ◽  
Challenging Problem ◽  
State Estimator ◽  
Performance Specifications ◽  
Tank System

Control of multirate systems is a challenging problem due to several reasons such as increased complexity in the design with tighter performance specifications. In this work, an algorithm for multirate constrained predictive control (MCPC) is presented. The multirate predictive control system includes a multirate state estimator, which provides inter-sample estimates of state variables of the process from infrequent and slow measurements. Constraints are addressed rigorously in this framework. The proposed design method is verified via simulation as well as experimentation. The results of the multirate predictive control for temperature control of a stirred tank system are shown and compared with those of a proportional integral (PI) control system.

Numerical approach to the Caputo derivative of the unknown function

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Fanhai Zeng ◽  
Changpin Li
Keyword(s):  
Differential Equation ◽  
Numerical Method ◽  
Differential System ◽  
Numerical Algorithm ◽  
Unknown Function ◽  
Caputo Derivative ◽  
Order Differential Equation ◽  
Numerical Approach ◽  
Numerical Examples ◽  
Integer Order

AbstractIf a function can be explicitly expressed, then one can easily compute its Caputo derivative by the known methods. If a function cannot be explicitly expressed but it satisfies a differential equation, how to seek Caputo derivative of such a function has not yet been investigated. In this paper, we propose a numerical algorithm for computing the Caputo derivative of a function defined by a classical (integer-order) differential equation. By the properties of Caputo derivative derived in this paper, we can change the original typical differential system into an equivalent Caputo-type differential system. Numerical examples are given to support the derived numerical method.

APPLICATION OF AN EFFECTIVE METHOD ON THE SYSTEM OF NONLINEAR FUZZY INTEGRO-DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 21 (2) ◽  
pp. 407-422
Author(s):  
ANGBEEN IQBAL ◽  
JAMSHAD AHMAD ◽  
QAZI MAHMOOD UL HASSAN
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Graphical Representation ◽  
Numerical Approach ◽  
Fuzzy Arithmetic ◽  
Transform Method ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
Sumudu Transform ◽  
Fuzzy Parameter

In real world physical applications purpose, it is complicated to acquire an exact solution of fuzzy differential equations due to complexities in fuzzy arithmetic and therefore creating the need for the use of reliable and efficient techniques in the solution of fuzzy differential equations. The purpose of this research paper is to utilize the reliable analytic approach of homotopy perturbation Sumudu transform method for better understanding of systems of non-linear fuzzy integro-differential equations, while using the concept of fuzzy parameter in certain dynamical problems to remove the hurdles faced in numerical approach. These mathematical models are of great interest in engineering and physics. Some numerical examples are also given to demonstrate the efficiency and superiority of the method, followed by graphical representation of the comparison of exact and approximated solution by using Maple 2017

Elastoplasticity 2D Problems: Numerical Applications of the Tikhonov Regularization Method

2015 ◽  
Vol 751 ◽  
pp. 109-117
Author(s):  
Thales Augusto Barbosa Pinto Silva ◽  
Hilbeth Parente Azikri de Deus ◽  
Claudio Roberto Ávila da Silva
Keyword(s):  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Numerical Approach ◽  
Theoretical Development ◽  
Tikhonov Regularization Method ◽  
Equilibrium Curve ◽  
Numerical Examples ◽  
Elastoplastic Materials ◽  
Ill Conditioning

The numerical simulation is widely used, in now days, to verify the viability and to optimize structural mechanic designs. The numerical approach of elastoplastic materials can found some problems related to ill-conditioning of matrices (from FEM systems), associated to the critical points from the snap through or snap back shape of the equilibrium curve. Aiming to overcome this misfortune it is proposed a strategy via Tikhonov regularization method in association with L-curve technique to determine the regularization parameter. This strategy can be used in many numerical applications for structural analysis. The theoretical development about these Some numerical examples are presented to attest the efficiency of this proposed approach.

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