Splitting elastic modulus finite element method and its application

AbstractTo establish the best precision FEM, the proportion of potential and complementary energy in the functional of the variational principles must be changeable. A new kind of variational principle in linear theory of solid mechanics, called the splitting elastic modulus variational principle, is introduced. Its distinctive feature is that the functional contains one arbitrary additional parameter, called splitting factor; the proportion of potential and complementary energy in the functional can be changed by the splitting factor. Finite element method, which is based on the new principle, is established. It is called splitting modulus FEM, its stiffness can be adjusted by properly selecting the splitting factors, some ill‐conditioned problem can be conquered by it. The methods to choose the splitting factors, reduce the condition number of stiffness matrix and improve the precision of solutions are also discussed. The reason why the new method can transform the ill‐conditioned problems into well‐conditioned ones is analysed finally. Copyright © 2001 John Wiley & Sons, Ltd.