有限元秩亏方程的最小范数问题

Rank-Deficient FEM Equations andIts Minimum Norm Solutions

为避免因确定边界约束条件时的不同而引起的应力、位移解不一致问题，作者认为在无明显稳定边界情况下应采用整体最小范数法解算有限元方程。如存在相对稳定边界，则可采用部分最小范数解。在一定条件下、最小范数解更能反映位移场的真实状态，并使计算误差分布均匀。

In order to avoid difference of solution caused by determining the boundary displacement condi-tions. the minimum norm is introduced in this paper.It is reasonable to employ the minimum normcondition in part region of FEM when stable boundary exists.With this method. the situations of dis-placements and stresses may be shown more exactly and the calculus errors have a even distribution.