摘要
本文研究了一般弹性接触问题有限元余能泛函的构造及其求解问题.将一般弹性接触问题数学模型归于二次规划,通过用Lemke法找线性互补问题基本解的方法来获得二次规划的Kuhn-Tucker点,并证明了二者的等价性.本文用Lemke法对不少算例进行了求解,发现此法具有收敛快、精度高等优点,尤其对正定性差的问题也能较好求解,不失为一种求解弹性接触问题的可行方法.
This paper studies the construction of complementary energy functional for general elastic contact problems and its solving. General elastic contact problems are resulted in quadratic programming . With Lemke algorithm, we find Complementary Basic Feasible Solution (CBFS) as the Kuhn-Tucker point for quadratic programming and certificate their equivalence. Several applied problems are solved with Lemke algorithm in the paper. The result shows that the algorithm has rapid convergence and high precision. Specially it can solve well the problems with worse positive definiteness . To elastic contact problems this is a feasible algorithm.
出处
《湖南大学学报》
EI
CAS
CSCD
1990年第4期135-142,共8页
关键词
接触
弹性接触
Lemke法
有限元法
complementary energy method
finite elements
quadratic programming/linear complementary problem
Lemke algorithm
