Papers by Keyword: Nonlinear Problem

Abstract: A methodology and a numerical algorithm of solving boundary problems of mechanics of deformable crystallizing elastic polymer media have been developed. A class of problems describing processes taking place in polymer products during their manufacturing is considered. Due to the significance of shrinking deformations the problem is considered within finite deformations theory. Constitutive relations are built on base of Peng-Landel potential. A ‘weak’ variation problem statement based on Galerkin approach is used. The offered algorithm is based on linearization methodology when small deformations are applied to finite ones. Deformation process is considered as a sequence of transitions through intermediate configurations. This approach makes possible to bring the received solution to the sequence of linearized boundary problems for which effective numerical algorithms have been designed. Numerical procedure is based on the technology of finite element method. Increments of displacements on the considered time step are taken to be nodal unknowns. The offered algorithm is applied to solution of the problem concerning the polyethylene pipe deformation during its manufacturing. Main advantages of the proposed algorithm have been defined.

Abstract: By choosing deferent initial approximation solutions and deferent linear operators, the nonlinear equation of the jamming transition problem (JTP), which is based on the Lorentz system, in traffic flow is discussed. The approximation solutions of the JTP are obtained using the homotopy analysis method (HAM). The method of choosing the linear operators and the initial approximation solutions, the corresponding residual errors and the influence of the boundary condition to the solution are studied respectively. By comparing the present results with the previous related studies, the conclusion is drawn that the HAM is superior to the differential transform method. The correctness of the theoretical analysis is confirmed by numerical simulation and the analysis of the residual errors.

Abstract: This paper describes a development of a new method (: Cantilever Method) to measure Young’s modulus of flexible materials. The method is based on a nonlinear deformation theory that takes into account large deformation behaviors. A set of testing devices was designed and machined. Measurements were carried out on two kinds of flexible materials (PVC: a high-polymer material and SWPA: a steel material). The modulus measured by this method is “Secant modulus”. The results of my evaluation confirm that the new method is suitable for flexible thin plates or rods. Based on the assessments made the method can be further applied to thin sheet and fiber materials (e.g., steel belt, glass fiber, carbon fiber, optical fiber, etc.).