Assessing the influence of side friction and intermediate end-boundary conditions on the critical buckling load in piles using the differential transform method

2021 ◽  
Vol 239 ◽  
pp. 112269
Author(s):  
Aaron P. Gallant ◽  
Carlos A. Vega-Posada ◽  
Mauricio Areiza-Hurtado
Keyword(s):  
Boundary Conditions ◽  
Differential Transform Method ◽  
Buckling Load ◽  
Transform Method ◽  
Critical Buckling Load ◽  
Differential Transform ◽  
Side Friction

Solution of Free Vibration Equations of Euler-Bernoulli Cracked Beams by Using Differential Transform Method

2011 ◽  
Vol 110-116 ◽  
pp. 4532-4536 ◽  
Author(s):  
K. Torabi ◽  
J. Nafar Dastgerdi ◽  
S. Marzban
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Differential Transform Method ◽  
Beam Model ◽  
Cracked Beam ◽  
Transform Method ◽  
Simple Method ◽  
Differential Transform

In this paper, free vibration differential equations of cracked beam are solved by using differential transform method (DTM) that is one of the numerical methods for ordinary and partial differential equations. The Euler–Bernoulli beam model is proposed to study the frequency factors for bending vibration of cracked beam with ant symmetric boundary conditions (as one end is clamped and the other is simply supported). The beam is modeled as two segments connected by a rotational spring located at the cracked section. This model promotes discontinuities in both vertical displacement and rotational due to bending. The differential equations for the free bending vibrations are established and then solved individually for each segment with the corresponding boundary conditions and the appropriated compatibility conditions at the cracked section by using DTM and analytical solution. The results show that DTM provides simple method for solving equations and the results obtained by DTM converge to the analytical solution with much more accurate for both shallow and deep cracks. This study demonstrates that the differential transform is a feasible tool for obtaining the analytical form solution of free vibration differential equation of cracked beam with simple expression.

Free vibration analysis of Euler–Bernoulli nanobeam using differential transform method

2018 ◽  
Vol 07 (03) ◽  
pp. 1850020 ◽  
Author(s):  
Subrat Kumar Jena ◽  
S. Chakraverty
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Numerical Technique ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Differential Transform Method ◽  
Inverse Transformation ◽  
Algebraic Equations ◽  
Transform Method ◽  
Differential Transform

In this paper, a semi analytical-numerical technique called differential transform method (DTM) is applied to investigate free vibration of nanobeams based on non-local Euler–Bernoulli beam theory. The essential steps of the DTM application include transforming the governing equations of motion into algebraic equations, solving the transformed equations and then applying a process of inverse transformation to obtain accurate mode frequency. All the steps of the DTM are very straightforward, and the application of the DTM to both the equations of motion and the boundary conditions seems to be very involved computationally. Besides all these, the analysis of the convergence of the results shows that DTM solutions converge fast. In this paper, a detailed investigation has been reported and MATLAB code has been developed to analyze the numerical results for different scaling parameters as well as for four types of boundary conditions. Present results are compared with other available results and are found to be in good agreement.

scholarly journals Effect of viscous dissipation on mixed convection flow in a vertical double passage channel using Robin boundary conditions

1970 ◽  
Vol 8 (3) ◽  
pp. 27-47
Author(s):  
J. Prathap Kumar ◽  
J.C. Umavathi ◽  
M. Karuna Prasad
Keyword(s):  
Boundary Conditions ◽  
Mixed Convection ◽  
Perturbation Method ◽  
Viscous Dissipation ◽  
Perturbation Parameter ◽  
Differential Transform Method ◽  
Robin Boundary Conditions ◽  
Transform Method ◽  
Differential Transform ◽  
Robin Boundary

The laminar fully developed flow in a vertical double passage channel filled with clear fluid has been discussed using Robin boundary conditions. The thin perfectly conductive baffle is inserted in the channel. The governing equations of the fluid which are coupled and nonlinear are solved analytically by the perturbation method and semi analytically using differential transform method (DTM). The reference temperature of the external fluid is considered to be equal and different. The perturbation method which is valid for small values of perturbation parameter is used to find the combined effects of buoyancy forces and viscous dissipation. The limitation imposed on the perturbation parameter is relaxed by solving the basic equations using differential transform method. The influence of mixed convection parameter, Biot number for symmetric and asymmetric wall temperatures on the velocity, temperature and the Nusselt number is explored at different positions of the baffle. The solutions obtained by differential transform method are justified by comparing with the solutions obtained by perturbation method and the solutions agree very well for small values of the perturbation parameter.Keywords: Baffle, Differential Transform Method, Perturbation Method, Viscous dissipation, Robin Boundary Conditions, Double passage channel.

Solution of time fractional Black-Scholes European option pricing equation arising in financial market

2016 ◽  
Vol 5 (4) ◽  
Author(s):  
A.S.V. Ravi Kanth ◽  
K. Aruna
Keyword(s):  
Boundary Conditions ◽  
Option Pricing ◽  
Financial Market ◽  
Differential Transform Method ◽  
European Option ◽  
Transform Method ◽  
European Option Pricing ◽  
Black Scholes ◽  
Differential Transform ◽  
Fractional Differential

AbstractIn this paper, we present fractional differential transform method (FDTM) and modified fractional differential transform method (MFDTM) for the solution of time fractional Black-Scholes European option pricing equation. The method finds the solution without any discretization, transformation, or restrictive assumptions with the use of appropriate initial or boundary conditions. The efficiency and exactitude of the proposed methods are tested by means of three examples.

scholarly journals A multi-step differential transform method and application to non-chaotic or chaotic systems

2010 ◽  
Vol 59 (4) ◽  
pp. 1462-1472 ◽  
Author(s):  
Zaid M. Odibat ◽  
Cyrille Bertelle ◽  
M.A. Aziz-Alaoui ◽  
Gérard H.E. Duchamp
Keyword(s):  
Chaotic Systems ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform
Sign in / Sign up

Export Citation Format

Share Document