Based on the Boltzmann’s superposition principles of linear viscoelastic materials and the von K*-rm*-n’s hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelas...Based on the Boltzmann’s superposition principles of linear viscoelastic materials and the von K*-rm*-n’s hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelastic thin plates was given. By the Galerkin method in spatial domain, the original integro-partial-differential system could be transformed into an integral system. The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper. Numerical results show that compared with the ordinary finite difference method, the new method in this paper is simpler to operate and has some advantages, such as, no storage and quicker computational speed etc.展开更多
The asymptotic behaviour of solutions of three-dimensional nonlinear elastodynamics in a thin shell is considered,as the thickness h of the shell tends to zero.Given the appropriate scalings of the applied force and o...The asymptotic behaviour of solutions of three-dimensional nonlinear elastodynamics in a thin shell is considered,as the thickness h of the shell tends to zero.Given the appropriate scalings of the applied force and of the initial data in terms of h,it’s verified that three-dimesional solutions of the nonlinear elastodynamic equations converge to solutions of the time-dependent von Kármán equations or dynamic linear equations for shell of arbitrary geometry.展开更多
In this paper,a newly developed second order temporally and spatially accurate finite difference scheme for biharmonic semi linear equations has been employed in simulating the time evolution of viscous flows past an ...In this paper,a newly developed second order temporally and spatially accurate finite difference scheme for biharmonic semi linear equations has been employed in simulating the time evolution of viscous flows past an impulsively started circular cylinder for Reynolds number(Re)up to 9,500.The robustness of the scheme and the effectiveness of the formulation can be gauged by the fact that it very accurately captures complex flow structures such as the von Kármán vortex street through streakline simulation and the a and b-phenomena in the range 3,000≤Re≤9,500 among others.The main focus here is the application of the technique which enables the use of the discretized version of a single semi linear biharmonic equation in order to efficiently simulate different fluid structures associated with flows around a bluff body.We compare our results,both qualitatively and quantitatively,with established numerical and more so with experimental results.Excellent comparison is obtained in all the cases.展开更多
文摘Based on the Boltzmann’s superposition principles of linear viscoelastic materials and the von K*-rm*-n’s hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelastic thin plates was given. By the Galerkin method in spatial domain, the original integro-partial-differential system could be transformed into an integral system. The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper. Numerical results show that compared with the ordinary finite difference method, the new method in this paper is simpler to operate and has some advantages, such as, no storage and quicker computational speed etc.
基金the National Science Foundation of China under Grant Nos.61473126 and61573342Key Research Program of Frontier Sciences+1 种基金CASunder Grant No.QYZDJ-SSW-SYS011。
文摘The asymptotic behaviour of solutions of three-dimensional nonlinear elastodynamics in a thin shell is considered,as the thickness h of the shell tends to zero.Given the appropriate scalings of the applied force and of the initial data in terms of h,it’s verified that three-dimesional solutions of the nonlinear elastodynamic equations converge to solutions of the time-dependent von Kármán equations or dynamic linear equations for shell of arbitrary geometry.
基金The first author would like to express his thanks to the DST,India for supporting his research work under Project No.SR/S4/MS:468/07The second author is thankful to the University Grants Commission,India for supporting a part of the work by providing financial support in the form of a minor project(Project No.F.No.37-537/2009(SR)).
文摘In this paper,a newly developed second order temporally and spatially accurate finite difference scheme for biharmonic semi linear equations has been employed in simulating the time evolution of viscous flows past an impulsively started circular cylinder for Reynolds number(Re)up to 9,500.The robustness of the scheme and the effectiveness of the formulation can be gauged by the fact that it very accurately captures complex flow structures such as the von Kármán vortex street through streakline simulation and the a and b-phenomena in the range 3,000≤Re≤9,500 among others.The main focus here is the application of the technique which enables the use of the discretized version of a single semi linear biharmonic equation in order to efficiently simulate different fluid structures associated with flows around a bluff body.We compare our results,both qualitatively and quantitatively,with established numerical and more so with experimental results.Excellent comparison is obtained in all the cases.
