CAI Yunzhu, WU Yuqing. THE APPLICATION OF VARIATIONAL MULTISCALE METHOD ON A ONE-DIMENSIONAL MECHANICAL MODEL[J]. MECHANICS IN ENGINEERING, 2014, 36(3): 288-293. DOI: 10.6052/1000-0879-13-281
Citation: CAI Yunzhu, WU Yuqing. THE APPLICATION OF VARIATIONAL MULTISCALE METHOD ON A ONE-DIMENSIONAL MECHANICAL MODEL[J]. MECHANICS IN ENGINEERING, 2014, 36(3): 288-293. DOI: 10.6052/1000-0879-13-281

THE APPLICATION OF VARIATIONAL MULTISCALE METHOD ON A ONE-DIMENSIONAL MECHANICAL MODEL

  • The variational multiscale method is applied to a one-dimensional mechanical model of a cable in the paper. With the use of the Green's function, the microscopic shape functions and the theory of residual-free bubbles, the macroscopic finite element model for the cable is established and the solution of the microscopic displacement is obtained. The key problems as well as the shortcomings of the application of the variational multiscale method are revealed. The numerical simulation for the cable model with given boundary conditions and constant rigid modulus is made. By comparing the numerical solution of the macroscopic displacement with the exact solution and the analytical solution of the microscopic displacement with the exact solution, it is demonstrated that the microscopic displacement can be regarded as the posteriori error estimation for the general finite element model. The success of applying the variational multiscale method to a one-dimensional mechanical model shows its practicability to mechanical and engineering problems.
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