FORCES, MOMENTS, ROTATIONS, AND DISPLACEMENTS OF POLYNOMIAL-SHAPED CURVED BEAMS

2010 ◽  
Vol 10 (01) ◽  
pp. 77-89 ◽  
Author(s):  
LAZARO GIMENA ◽  
PEDRO GONZAGA ◽  
FAUSTINO GIMENA
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Mechanical Behavior ◽  
Ordinary Differential Equations ◽  
Numerical Method ◽  
The Other ◽  
Curved Beams ◽  
Fourth Degree ◽  
Linear Ordinary Differential Equations ◽  
Parabolic Shape

This paper deals with curved beams with polynomial free geometry. The problem is approached analytically and the differential equations that govern the mechanical behavior of curved beams are presented. A system of twelve linear ordinary differential equations is solved using either an analytical or a customized numerical method with boundary conditions. Results of the different components of forces, moments, rotations, and displacements are given and plotted in the examples for different polynomial-shaped beams of the fourth degree. It is concluded from the present analyses that the parabolic shape has better response to distributed loads than the other polynomial-shaped beams considered.

Radiative Unsteady Rarefied Gaseous Flow Over a Stretching Sheet with Velocity Slip and Temperature Jump Effects

2020 ◽  
Vol 87 (3-4) ◽  
pp. 261
Author(s):  
Ram Prakash Sharma ◽  
N. Indumathi ◽  
S. Saranya ◽  
B. Ganga ◽  
A. K. Abdul Hakeem
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Gaseous Flow ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study a mathematical analysis has been carried out to scrutinize the unsteady boundary layer flow of an incompressible, rarefied gaseous flow over a vertical stretching sheet with velocity slip and thermal jump boundary conditions in the presence of thermal radiation. Using boundary layer approach and suitable similarity transformations, the governing partial differential equations with the boundary conditions are reduced to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved with the help of fourth order Runge-Kutta method with shooting technique. The results obtained for the velocity profile, temperature profile, skin friction coefficient and the reduced Nusselt number are described through graphs. It is predicted that the velocity and temperature profiles are lower for unsteady flow and has an opposite effect for steady flow.

scholarly journals A New Method for Numerical Integration of Higher-Order Ordinary Differential Equations Without Losing the Periodic Responses

2021 ◽  
Vol 7 ◽  
Author(s):  
John T. Katsikadelis
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Method ◽  
Variable Coefficients ◽  
Space Representation ◽  
Parabolic Differential Equations ◽  
Linear Ordinary Differential Equations ◽  
First Order ◽  
Symmetrical Matrices ◽  
The Stability

A new numerical method is presented for the solution of initial value problems described by systems of N linear ordinary differential equations (ODEs). Using the state-space representation, a differential equation of order n > 1 is transformed into a system of L = n×N first-order equations, thus the numerical method developed recently by Katsikadelis for first-order parabolic differential equations can be applied. The stability condition of the numerical scheme is derived and is investigated using several well-corroborated examples, which demonstrate also its convergence and accuracy. The method is simply implemented. It is accurate and has no numerical damping. The stability does not require symmetrical and positive definite coefficient matrices. This advantage is important because the scheme can find the solution of differential equations resulting from methods in which the space discretization does not result in symmetrical matrices, for example, the boundary element method. It captures the periodic behavior of the solution, where many of the standard numerical methods may fail or are highly inaccurate. The present method also solves equations having variable coefficients as well as non-linear ones. It performs well when motions of long duration are considered, and it can be employed for the integration of stiff differential equations as well as equations exhibiting softening where widely used methods may not be effective. The presented examples demonstrate the efficiency and accuracy of the method.

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