A Bäcklund transformation(BT) and a recurrence formula are derived by the homogeneous balance(HB) method. A initial problem of Burgers equations is reduced to a initial problem of heat equation by the BT, the initial problem of heat equation is resolved by the Fourier transformation method, substituting various solutions of the initial problem of the heat equation will yield solutions of the in...

This paper studies dynamic stability of homogeneous beams with piezoelectric layers subjected to periodic axial compressive load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Bernoulli-Euler beam theory. Applying the Hamilton's principle, the governing dynamic equation is established. The influences of applied v...

In mechanical engineering, the finite element method is well-known in simulation of homogeneous materials without microstructures. But, particular, microstructures can improve with respect to their applicability engineering. Examples are 2D- and 3D-fiber-reinforced materials, which manufactured microscale or mesoscale, respectively. An efficient these provides an anisotropic continuum formulati...

in this study prediction of the steady-state flow of branched polymer melts in pipe geometry with finite volume method is presented. our analysis in this study revealed that;for normal-stress tqq , the xpp model can predict this tensor unlike the other viscoelastic models such as ptt or gieskus which can not predict tqq for viscoelastic fluid in two dimensional pipe flows. the fluid is modelled...

a new approach is proposed to model a crack in orthotropic composite media using the extended finite element method (xfem). the xfem uses the concept of partition of unity in addition to meshless basic idea of approximating a field variable by its values at a set of surrounding nodes. as a result, higher order approximations can be designed with the same total number of degrees of freedom. in t...

A method is presented, with standard examples, based on an elementary complex integral expression, for developing, in particular, series solutions for second-order linear homogeneous ordinary differential equations. Straightforward to apply, the method reduces the task of finding a series solution to the solution, instead, of a system of simple equations in a single variable. The method elimina...