数值流形法中“质量守恒”的探讨

Discussion on "mass-conservation" in numerical manifold method

数值流形法是至少包含流形法(NMM)、有限元法(FEM)和非连续变形分析(DDA)的数值方法体系。将数值流形法中物理单元与数学单元完全重合,去掉接触理论,流形元能够回归到有限元,将通过简单的板压缩数值试验验证这一点。在以前的数值流形法法中,质量守恒问题一直被忽视,物理单元的质量会随着单元体积改变,计算结果存在一定的误差。通过改变计算过程中单元密度实现计算过程中的"质量守恒",完善了现有数值流形法的理论基础。

Numerical manifold method（NMM） is a numerical system which contains manifold method,finite elements and discontinuous deformation analysis（DDA）.NMM can return to finite elements when physical elements and mathematical elements in NMM are superposition completely;and contact theory is removed.It will be verified by plate compression numerical experiment in the paper.In previous NNM,the problem of mass-conservation is neglected,which the weight of the physical elements will change with changes in its volume;so there are certain error in the calculation results.Mass-conservation can be realized by changing the elements density in the process of calculation;that will perfect the theoretical basis of numerical manifold methods.