Abstract In this work, three different integration techniques, which are the numerical, semi-analytical and exact integration techniques are briefly reviewed. Numerical integrations are carried out using three different Quadrature rules, which are the Classical Gauss Quadrature, Gauss Legendre and Generalized Gaussian Quadrature. Line integral method is used to perform semi-analytical integrati...

in this article we have considered a non-standard finite difference method for the solution of second order  fredholm integro differential equation type initial value problems. the non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the fredholm integro-differential equation into a system of equations. we have also developed a numerical met...

The symmetry group method is applied to a generalized Korteweg-de Vries equation and several classes of group invariant solutions for it are obtained by means of this technique. Polynomial, trigonometric, and elliptic function solutions can be calculated. It is shown that this generalized equation can be reduced to a first-order equation under a particular second-order differential constraint w...

This study investigates the free vibration of the Two-Dimensional Functionally Graded Annular Plates (2D-FGAP). The theoretical formulations are based on the three-dimensional elasticity theory with small strain assumption. The Two-Dimensional Generalized Differential Quadrature Method (2D-GDQM) as an efficient and accurate semi-analytical approach is used to discretize the equations of motion ...

In this paper, vibration analysis of rotary tapered axially functionally graded (AFG) Timoshenko nanobeam is investigated in a thermal environment based on nonlocal theory. The governing equations of motion and the related boundary conditions are derived by means of Hamilton’s principle based on the first order shear deformation theory of beams. The solution method is considered using generaliz...

This study investigates how to obtain the natural frequency of functionally graded porous beams simply supported on an elastic substrate in thermal surroundings by theory third-order shear deformation. Temperature constantly changes beam thickness direction and step with distribution volume fraction power law ingredient has been affected material attributes. The uniform porosity at pass phase i...

Abstract In this paper we consider a numerical scheme for the treatment of an integro-differential equation. The latter represents formulation nonlocal diffusion type discretization procedure relies on application line method. However, quadrature formulae are needed evaluation integral operator. They based generalized Bernstein polynomials. Numerical evidence shows that proposed method is suita...

The study of magnetostrictive material in laminated plate under thermal vibration is calculated by using the generalized differential quadrature (GDQ) method. The YNS shear deformation effect is included in the time dependent of displacement field. In the thermoelastic stress-strain relations that containing the linear temperature rise and the magnetostrictive coupling terms with velocity feedb...