引用本文: 蔡云竹, 吴宇清. 变分多尺度方法在一维力学模型中的应用[J]. 力学与实践, 2014, 36(3): 288-293.
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.
 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.

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

• 摘要: 将变分多尺度方法应用于一维缆索模型，导出受力缆索的宏观有限元模型并求得细观位移解析解，总结出变分多尺度方法应用于具体模型的关键点和缺陷. 假定刚度为常值，数值模拟一定边界和受力下的缆索，得到宏观和细观位移. 将细观与宏观位移叠加，相比于精确位移得出：细观位移可视为常规有限元模型的后验误差. 变分多尺度方法在一维力学模型中的成功应用，推进了其实用性，为其在更多力学及工程问题中的运用和发展提供了参考.

Abstract: 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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