Another form of the discrete mKdV hierarchy with self-consistent sources is given in the paper. The self-consistent sources is presented only by the eigenfunctions corresponding to the reduction of the Ablowitz-Ladik spectral problem. The exact soliton solutions are also derived by the inverse scattering transform.

An computationally efficient damage identification technique for the planar and space truss structures is presented based on the force method and the micro genetic algorithm. For this purpose, the general equilibrium equations and the kinematic relations in which the reaction forces and the displacements at nodes are take into account, respectively, are formulated. The compatibility equations in terms of forces are explicitly presented using the singular value decomposition (SVD) technique. Then governing equations with unknown reaction forces and initial elongations are derived. Next, the micro genetic algorithm (MGA) is used to properly identify the site and extent of multiple damage cases in truss structures. In order to verify the accuracy and the superiority of the proposed damage detection technique, the numerical solutions are presented for the planar and space truss models. The numerical results indicate that the combination of the force method and the MGA can provide a reliable tool to accurately and efficiently identify the multiple damages of the truss structures.

A new mathematical model of magnetohydrodynamic (MHD) theory has been constructed in the context of a new consideration of heat conduction with a time-fractional derivative of order 0 < α ≤ 1 and a time-fractional integral of order 0 < γ ≤ 2. This model is applied to one-dimensional problems for a thermoelectric viscoelastic fluid flow in the absence or presence of heat sources. Laplace transforms and state-space techniques will be used to obtain the general solution for any set of boundary conditions. According to the numerical results and its graphs, conclusion about the new theory has been constructed. Some comparisons have been shown in figures to estimate the effects of the fractional order parameters on all the studied fields.

In this paper, the Chebyshev-Galerkin spectral approximations are employed to investigate Poisson equations and the fourth order equations in one dimension. Meanwhile, p-version finite element methods with Chebyshev polynomials are utilized to solve Poisson equations. The efficient and reliable a posteriori error estimators are given for different models. Furthermore, the a priori error estimators are derived independently. Some numerical experiments are performed to verify the theoretical analysis for the a posteriori error indicators and a priori error estimations.

In this paper, the nonlinear boundary value problem (BVP) for the Jeffery-Hamel flow equations taking into consideration the magnetohydrodynamics (MHD) effects is solved by using the modified Adomian decomposition method. We first transform the original two-dimensional MHD Jeffery-Hamel problem into an equivalent third-order BVP, then solve by the modified Adomian decomposition method for analytical approximations. Ultimately, the effects of Reynolds number and Hartmann number are discussed.

The analysis of thermoelastic deformations of a simply supported functionally graded material (FGM) sandwich plates subjected to a time harmonic sinusoidal temperature field on the top surface and varying through-the-thickness is illustrated in this paper. The FGM sandwich plates are assumed to be made of three layers and resting on Pasternak’s elastic foundations. The volume fractions of the constituents of the upper and lower layers and, hence, the effective material properties of them are assumed to vary in the thickness direction only whereas the core layer is still homogeneous. When in-plane sinusoidal variations of the displacements and the temperature that identically satisfy the boundary conditions at the edges, the governing equations of motion are solved analytically by using various shear deformation theories as well as the classical one. The influences of the time parameter, power law index, temperature exponent, top-to-bottom surface temperature ratio, side-to-thickness ratio and the foundation parameters on the dynamic bending are investigated.