Lateral-Torsional Buckling of Nonuniformly Loaded Beam Using Differential Transformation Method

2016 ◽  
Vol 16 (07) ◽  
pp. 1550034 ◽  
Author(s):  
Ryszard Hołubowski ◽  
Kamila Jarczewska
Keyword(s):  
Critical Loads ◽  
Transformation Method ◽  
Variable Coefficients ◽  
Differential Transformation Method ◽  
Lateral Torsional Buckling ◽  
Torsional Buckling ◽  
Differential Transformation ◽  
Distributed Load ◽  
The Difference ◽  
The Stability

The paper presents the application of the differential transformation method (DTM) to the stability analysis of nonuniformly loaded beams under bending. The main advantage of the method is the possibility to obtain the semi-analytical solution for the critical loads of the beam undergoing lateral-torsional buckling. To determine the critical load, the system of two coupled ordinary differential equations with variable coefficients and parameters have to be solved. Numerical analyses were carried out for three different types of load functions: (i) Uniformly distributed load, (ii) linearly varying load and (iii) sinusoidally distributed load. The results were compared with the solutions computed by the finite element method (FEM) and those obtained by the authors using the variational iterative method (VIM). In each case, it was found that the difference with reference to the existing one does not exceed 3%, which testifies the effectiveness of the DTM used. Nevertheless, it should be emphasized that the number of terms of the approximation series used is fairly large and therefore the calculation of higher critical loads can be very time-consuming.

scholarly journals Mixed of Elzaki Transform and Projected Differential Transform Method for a Nonlinear Wave-Like Equations with Variable Coefficients

2018 ◽  
Author(s):  
Ali Khalouta ◽  
Abdelouahab Kadem
Keyword(s):  
Nonlinear Wave ◽  
Transformation Method ◽  
Variable Coefficients ◽  
Differential Transform Method ◽  
Differential Transformation Method ◽  
Transform Method ◽  
Differential Transformation ◽  
Differential Transform

In this work, a mixture of Elzaki transform and projected differential transform method is applied to solve a nonlinear wave-like equations with variable coefficients. Nonlinear terms can be easily manipulated by using the projected differential transformation method. The method gives the results show that the proposed method is very efficient, simple and can be applied to other applications.

AN APPLICATION OF DIFFERENTIAL TRANSFORMATION TO STABILITY ANALYSIS OF HEAVY COLUMNS

2006 ◽  
Vol 06 (03) ◽  
pp. 317-332 ◽  
Author(s):  
Y. H. CHAI ◽  
C. M. WANG
Keyword(s):  
Differential Equation ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Recursive Equation ◽  
Transformation Technique ◽  
Critical Buckling Load ◽  
Differential Transformation ◽  
Governing Differential Equation ◽  
Support Conditions ◽  
The Stability

This paper uses a recently developed technique, known as the differential transformation, to determine the critical buckling load of axially compressed heavy columns of various support conditions. In solving the problem, it is shown that the differential transformation technique converts the governing differential equation into an algebraic recursive equation, which must be solved together with the differential transformation of the boundary conditions. Although a fairly large number of terms are required for convergence of the solution, the differential transformation method is nonetheless efficient and fairly easy to implement. The method is also shown to be very accurate when compared with a known analytical solution. The stability of heavy columns is further examined using approximate formulae currently available in the literature. In this case, the differential transformation method offers a reference for assessing the accuracy of the approximate buckling formulae.

Differential transformation method for circular membrane vibrations

2020 ◽  
Vol 61(12) (2) ◽  
pp. 333-350
Author(s):  
Jaipong Kasemsuwan ◽  
◽  
Sorin Vasile Sabau ◽  
Uraiwan Somboon ◽  
◽  
...  
Keyword(s):  
Transformation Method ◽  
Differential Transformation Method ◽  
Circular Membrane ◽  
Differential Transformation ◽  
Membrane Vibrations

scholarly journals STRAIN-STRESS EXPERIMENTAL BEHAVIOUR OF TAPERED COLUMNS IN SINGLE-SPAN FRAMES/TRAPECINIŲ KOLONŲ VIENANAVIUOSE RĖMUOSE DEFORMACIJŲ-ĮTEMPIŲ BŪVIS

2000 ◽  
Vol 6 (2) ◽  
pp. 82-86 ◽  
Author(s):  
Vaidotas Šapalas
Keyword(s):  
Local Buckling ◽  
Longitudinal Axis ◽  
Lateral Torsional Buckling ◽  
Torsional Buckling ◽  
Perpendicular Plane ◽  
Strain Stress ◽  
Tapered Columns ◽  
The Stability ◽  
Experimental Behaviour ◽  
Tapered Column

Two single-span frame tests were carried out. The width of frame is 6m, column's height 4.17m. Frame supports are pinned. Connection between column and beam is rigid. Beam of the frame was loaded with two vertical and one horizontal loads. The stability of tappered columns was analysed in frame plane and in perpendicular plane, according to [1] and [2] methods. All deflections were calculated taking into account support movements. During the first frame test R1-1 the tapered column collapsed at the load 2V=400kN and H=200 kN (vertical and horizontal loads). During the second test R1-2 the tapered column collapsed at the load 2V=390 kN and H=175 kN. In both tests columns collapsed in lateral-torsional buckling way. Because the column's web is very thin at the load 2V=300 kN and H=150 kN the column's web achieved local buckling. But the column was still carrying the load. During both tests at the load 2V=300 kN and H=150 kN the column began to twist in the middle of its height about the longitudinal axis and to bend about the weak axis. In test R1-1, the vertical experimental deflection (in point 6, see Fig 1 a) is about 17.5% smaller than the theoretical one. The horizontal experimental deflection (in point, see Fig 1 a) is about 11.6% smaller than the theoretical one. In test R1-2, vertical experimental deflection (in point 6, see Fig 1 a) is about 21.1% bigger than the theoretical one. The horizontal experimental deflection (in point, see Fig 1 a) is about 29.6% smaller than the theoretical one. In test R1-1, an experimental compression stresses in section A-A (see Fig 2) are about 11.2% smaller than the theoretical one. Experimental tension stresses in section A-A are about 8.65% smaller than the theoretical one. In test R1-2, an experimental compression stresses in section A-A is about 0.43% bigger than the theoretical one. An experimental tension strain in section A-A is about 1.73% smaller than the theoretical one.

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