Loubignac叠代过程中的自然边界条件

Loubignac叠代法给出连续的位移场和连续的应力场,且其计算结果较经典的位移有限元更精确。文献〔1〕、〔2〕建议在叠代过程中强加自然边界条件来提高计算结果精度和加速收敛。本文阐明,按照最小势能原理,我们不应在叠代过程中强加自然边界条件。数字试验表明,强加自然边界条件有可能降低计算结果精度,减低收敛速度,并可能使叠代不收敛。

Natural Boundary Conditions in Loubignac's Iterative Procedure

Loubignac' s iterative method provides both displacement and stress continuous fields,and computed results are more accurate than those provided by classical displacement finite element method. Reference 1],2]suggest that one may impose natural boundary condition during the iterations to increase the accuracy of computed results, and to speedup the convergence. This paper demonstrates that according to the principle of minimum potential energy, we should not impose natural boundary conditions during the iterations, Numerical tests show that imposing natural boundary conditions decreases the accuracy of computed results, slow s the convergence, and may make iterations diverge.