Iterative differential quadrature solutions for Bratu problem

Ragb, Ola; Seddek, Laila F.; Matbuly, M. S.

doi:10.1016/j.camwa.2017.03.033

Cited by 22 publications

(13 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To ensure the validity of proposed scheme, the obtained results are compared with previous ones for cracked and un-cracked Euler-Bernoulli and Timoshenko problems. A quadrature numerical scheme is designed to solve cracked Euler-Bernoulli beam problems, equations (22)(23)(24)(25)(26)(27)(28)(29). For each sub-beam, N is to be varied from 5-50 to determine N leading to accurate convergent results.…”

Section: Numerical Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Vibrations Analysis of Cracked Nanobeams Using Quadrature Technique

Elkhalek¹,

Osman²,

Matbuly³

2019

ENGMATH

View full text Add to dashboard Cite

This work concerns with free vibration analysis of cracked nanobeam problems. Based on Eringen's nonlocal elasticity theory, the governing equation of Euler-Bernoulli and Timoshenko nanobeams, are derived. It is assumed that strain at a certain point is a function of the strains at all points within the influence domain. The cracked beam is modeled as multisegments connected by a rotational spring located at the cracked sections. This model promotes discontinuities in rotational displacement due to bending which is proportional to bending moment transmitted by the cracked section. Polynomial based differential quadrature method is employed to solve the problem. Derivatives of the field quantities are approximated as a weighted linear sum of the nodal values. For different supporting cases, the boundary conditions are directly substituted in the equation of motion, such that the problem is reduced to that of linear homogeneous algebraic system. This suggested numerical scheme accurately determined angular frequencies of the problem. A comparative study is tabulated to compare the obtained results with the previous ones. Further, a parametric study is introduced to investigate the influence of crack locations, crack severity and the nonlocal scale parameter on the obtained results. The obtained results recorded that frequency values decrease with the increasing of both of crack severity and the nonlocal scale parameter. The results of the proposed scheme may be applied for structural health monitoring.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

“…Recently, differential quadrature method is introduced as promising numerical technique. This method leads to very accurate results by using small number of nodal points [23][24][25][26]. Rotational spring model is employed to simulate the crack existence.…”

Section: Introductionmentioning

confidence: 99%

Vibrations Analysis of Cracked Nanobeams Using Quadrature Technique

Elkhalek¹,

Osman²,

Matbuly³

2019

ENGMATH

View full text Add to dashboard Cite

show abstract

“…Then, using the iterative quadrature technique (Ragb et al, 2017) to obtain linear an Eigen-value problem as: 1-Firstly, solving the eqs. (35-38) as linear system ( )…”

Section: Discrete Singular Convolution Differential Quadrature Methodmentioning

confidence: 99%

Vibration Analysis of Magneto-Electro-Thermo NanoBeam Resting on Nonlinear Elastic Foundation Using Sinc and Discrete Singular Convolution Differential Quadrature Method

Ragb¹,

Mohamed²,

Matbuly³

2019

MAS

Self Cite

View full text Add to dashboard Cite

Magneto-Electro-Thermo nanobeam resting on a nonlinear elastic foundation is presented. This beam is subjected to the external electric voltage and magnetic potential, mechanical potential and temperature change. Also, we added the new material PTZ-5H-COFe2O4. The governing equations and boundary conditions are derived using Hamilton principle. These equations are discretized by using three differential quadrature methods and iterative quadrature technique to determine the natural frequencies and mode shapes. Numerical analysis is introduced to explain the influence of computational characteristics of the proposed schemes on convergence, accuracy and efficiency of the obtained results. The obtained results agreed with the previous analytical and numerical ones. A detailed parametric study is conducted to investigate the influences of different boundary conditions, various composite materials, nonlinear elastic foundation, nonlocal parameter, the length-to-thickness ratio, external electric and magnetic potentials, axial forces, temperature and their effects on the vibration characteristics of Magneto-Electro-Thermo-Elastic nanobeam.

show abstract

“…In this segment, we exhibit the computational technique employed to solve the nonlinear system of PDEs (14)- (15) with boundary conditions (16). Newton's linearization method (NLM) was utilized to linearize the non-linear system (14)- (16), which was subsequently solved using the differential quadrature method (DQM) [27][28][29][30][31][32][33][34][35][36][37][38][39] and two-point backward finite difference method. Applying NLM on (14)- (16) gives:…”

Section: Hybrid Linearization-differential Quadrature Methods (Hldqm)mentioning

confidence: 99%

The Impact of Sinusoidal Surface Temperature on the Natural Convective Flow of a Ferrofluid along a Vertical Plate

2019

View full text Add to dashboard Cite

The spotlight of this investigation is primarily the effectiveness of the magnetic field on the natural convective for a Fe 3 O 4 ferrofluid flow over a vertical radiate plate using streamwise sinusoidal variation in surface temperature. The energy equation is reduplicated by interpolating the non-linear radiation effectiveness. The original equations describing the ferrofluid motion and energy are converted into non-dimensional equations and solved numerically using a new hybrid linearization-differential quadrature method (HLDQM). HLDQM is a high order semi-analytical numerical method that results in analytical solutions in η-direction, and so the solutions are valid overall in the η domain, not only at grid points. The dimensionless velocity and temperature curves are elaborated. Furthermore, the engineering curiosity of the drag coefficient and local Nusselt number are debated and sketched in view of various emerging parameters. The analyzed numerical results display that applying the magnetic field to the ferroliquid generates a dragging force that diminishes the ferrofluid velocity, whereas it is found to boost the temperature curves. Furthermore, the drag coefficient sufficiently minifies, while an evolution in the heat transfer rate occurs as nanoparticle volume fraction builds. Additionally, the augmentation in temperature ratio parameter signifies a considerable growth in the drag coefficient and Nusselt number. The current theoretical investigation may be beneficial in manufacturing processes, development of transport of energy, and heat resources. Mathematics 2019, 7, 1014 2 of 12 naturalistic kind of boundary condition which considers the effectiveness of thermophoresis Brownian movement. Khan and Pop [4] utilized the idea in [3] to contemplate the principal deal with nanofluid flow over an extending sheet. Bachok et al. [5] implemented an investigation of nanofluid flow past a semi-infinite plate. Rashad et al. [6] inspected the enhancement of heat transfer in a Darcy nanofluid convective flow past a porous cone. Rashad et al. [7] also probed the non-Darcy problem of a thermally stratified nanofluid flow over a vertical cylinder. They explored how heat transfer rate declined as the Brownian motion parameter boosted. However, abundant fundamental investigations are performed in this field, as can be seen in [8-13].Magnetic nanofluids (or ferrofluids) are the colloidal suspension of magneto-nanoparticles in a regular fluid (water, kerosene, mineral oil). Ferrofluids are magnetically controllable nanofluids, which contain magnetic nanoparticles, such as iron, cobalt, nickel, magnetite, ferrite, spinel-type. Since ferrofluids can be easily manipulated by means of an external magnetic force, the use of these fluids is promoted in numerous significant industrial applications, such as in vacuum seals, vibration-dampers, loudspeakers, shock absorbers, transformers coolant, and stepper motors [14][15][16][17][18][19]. Hayat et al. [20,21] probed the magneto-flow of Newtonian and viscoelastic nanofluids over ...

show abstract

Iterative differential quadrature solutions for Bratu problem

Cited by 22 publications

References 31 publications

Vibrations Analysis of Cracked Nanobeams Using Quadrature Technique

Vibrations Analysis of Cracked Nanobeams Using Quadrature Technique

Vibration Analysis of Magneto-Electro-Thermo NanoBeam Resting on Nonlinear Elastic Foundation Using Sinc and Discrete Singular Convolution Differential Quadrature Method

The Impact of Sinusoidal Surface Temperature on the Natural Convective Flow of a Ferrofluid along a Vertical Plate

Contact Info

Product

Resources

About