International Journal of Non-linear Mechanics
About: International Journal of Non-linear Mechanics is an academic journal. The journal publishes majorly in the area(s): Nonlinear system & Boundary value problem. It has an ISSN identifier of 0020-7462. Over the lifetime, 4715 publications have been published receiving 99862 citations.
Topics: Nonlinear system, Boundary value problem, Vibration, Equations of motion, Finite element method
Papers published on a yearly basis
TL;DR: In this paper, a variational iteration method for non-linear problems is proposed, where the problems are initially approximated with possible unknowns and a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory.
Abstract: In this paper, a new kind of analytical technique for a non-linear problem called the variational iteration method is described and used to give approximate solutions for some well-known non-linear problems. In this method, the problems are initially approximated with possible unknowns. Then a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory. Being different from the other non-linear analytical methods, such as perturbation methods, this method does not depend on small parameters, such that it can find wide application in non-linear problems without linearization or small perturbations. Comparison with Adomian’s decomposition method reveals that the approximate solutions obtained by the proposed method converge to its exact solution faster than those of Adomian’s method.
TL;DR: In this article, a coupling method of a homotopy technique and a perturbation technique is proposed to solve non-linear problems, which does not require a small parameter in the equation.
Abstract: In this paper, a coupling method of a homotopy technique and a perturbation technique is proposed to solve non-linear problems. In contrast to the traditional perturbation methods, the proposed method does not require a small parameter in the equation. In this method, according to the homotopy technique, a homotopy with an imbedding parameter p∈[0, 1] is constructed, and the imbedding parameter is considered as a “small parameter”. So the proposed method can take full advantage of the traditional perturbation methods. Some examples are given. The results reveal that the new method is very effective and simple.
TL;DR: In this paper, a simple non-linear equation is used to describe a kind of analytical technique for nonlinear problems, which is based on both homotopy in topology and the Maclaurin series.
Abstract: One simple, typical non-linear equation is used in this paper to describe a kind of analytical technique for non-linear problems. This technique is based on both homotopy in topology and the Maclaurin series. In contrast to perturbation techniques, the proposed method does not require small or large parameters. The example shows that the proposed method can give much better approximations than those given by perturbation techniques. In addition the proposed method can be used to obtain formulae uniformly valid for both small and large parameters in non-linear problems.
TL;DR: In this article, the homotopy analysis method (HAM) was used to obtain an analytic solution of the 2D laminar viscous flow over a semi-infinite flat plate.
Abstract: By means of using an operator A to denote non-linear differential equations in general, we first give a systematic description of a new kind of analytic technique for non-linear problems, namely the homotopy analysis method (HAM). Secondly, we generally discuss the convergence of the related approximate solution sequences and show that, as long as the approximate solution sequence given by the HAM is convergent, it must converge to one solution of the non-linear problem under consideration. Besides, we illustrate that even though a non-linear problem has one and only one solution, the sole solution might have an infinite number of expressions. Finally, to show the validity of the HAM, we apply it to give an explicit, purely analytic solution of the 2D laminar viscous flow over a semi-infinite flat plate. This explicit analytic solution is valid in the whole region η=[0, +∞) and can give, the first time in history (to our knowledge), an analytic value f ″(0)=0.33206 , which agrees very well with Howarth’s numerical result. This verifies the validity and great potential of the proposed homotopy analysis method as a new kind of powerful analytic tool.
TL;DR: In this paper, a similarity transform was used to reduce the Navier-Stokes equations to a set of non-linear ordinary differential equations, which are then integrated numerically.
Abstract: The stagnation flow towards a shrinking sheet is studied. A similarity transform reduces the Navier–Stokes equations to a set of non-linear ordinary differential equations which are then integrated numerically. Both two-dimensional and axisymmetric stagnation flows are considered. It is found that solutions do not exist for larger shrinking rates and may be non-unique in the two-dimensional case. The non-alignment of the stagnation flow and the shrinking sheet complicates the flow structure. Convective heat transfer decreases with the shrinking rate due to an increase in boundary layer thickness.
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