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V-notch for a bi-material
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The electroelastic behavior of a piezoelectric multi-material with a V-notch is investigated in this study, via a Hamiltonian approach. At first, we consider the piezoelectric field of the structure, by extending ZHONG's formalism [1] to linear piezoelectricity, through the Two Extreme Point's problem. Following a unified description of ZHONG and B...
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Citations
... Some equations are solved by numerical solutions; some are solved using different analytical methods. Methods that can be introduced to examine the non-linear problems such as the Differential Transform Method (DTM) [1][2], Least Square Method (LSM) [3][4], Akbari-Ganji's Method (AGM) [5][6][7][8], Hamiltonian Approach [9], Variational Iteration Method (VIM) [10], and Adomian's Decomposition Method (ADM) [11], many methods are not considered in this study because of brevity. One of the semi-analytical methods which does not need small parameters is the Homotopy Perturbation Method (HPM). ...
In this research, free convection of a non-Newtonian silver-water nanofluid between two infinite parallel perpendicular flat plates is investigated. The Maxwell Garnetts (MG) nanofluid model is used in this work. The basic partial differential equations are reduced to the ordinary differential equations which are solved analytically using Homotopy Perturbation Method (HPM). The impact of various physical parameters such as nanoparticle volume fraction (φ), dimensionless non-Newtonian viscosity ( ) and Eckert number (Ec) on the velocity and dimensionless temperature profiles is studied. The comparison of the results of HPM, Akbari-Ganji’s Method (AGM), Collocation Method (CM), the fourth-order Runge-Kutta numerical Method (NUM) and FlexPDE software
results shows excellent complying in solving this problem. Also, this research shows that AGM and HPM are powerful methods to solve non-linear differential equations, such as the problem raised in this research.
... Analytical methods have significant advantages over numerical methods in providing analytic, verifiable, rapidly convergent approximations. Therefore, many methods have been used to deal with highly nonlinear problems such as homotopy perturbation transform method [34][35], Differential transform method [36][37][38][39], Optimal homotopy analysis method [40][41], Least square method [42][43], Hamiltonian approach [44][45][46], Homotopy Analysis Method [47][48], variational iteration method [49][50][51], and Decomposition method [52][53][54][55]. One of the semi-exact methods is the homotopy perturbation method (HPM) [56][57][58][59][60]. ...
In this paper we consider steady two dimensional flow of micro polar fluid on a flat plate. The flow under discussion is modified Hiemenz flow for a micro polar fluid which occurs in the hjkns + skms boundary layer near an orthogonal stagnation point. The full governing equation reduced to modified Hiemenz flow. The solution to the boundary value problem is governed by two non dimensional parameters, the material parameterK and the ratio of the micro rotation to skin friction parametern. the obtained nonlinear coupled ordinary differential equations are solved by using Homotopy perturbation method. Comparison between numerical and analytical solution of the problem are shown in tables form for different values of the governing parameters K and n. The effects of the material parameter K on the velocity profile and microrotation profile for different cases of n are discussed by graphically as well as numerically. Velocity profile decreases as material parameterKincreases and microrotation profile increases as material parameter K increases for different cases of n is investigated.
