Research on Solution Technology of Large-Scale Joint Elements Based on Augmented Lagrange Theory

The advanced aviation equipment is developing in a complicated and refined direction. There are many kinds of complex and numerous connecting structures between various parts and mechanisms, and the simulation of connecting structures has become an important part of structural analysis software. When dealing with joint element, the existing aviation autonomous structural analysis software SABRE generally adopts the method of linear elimination to eliminate the constraint relation from the total stiffness matrix of the structure. This method is efficient in solving simple models, but when dealing with complex aviation structures containing a large number of connecting structures, it will destroy the sparsity of the total stiffness matrix of the structure, which has a great impact on the efficiency of SABRE. This paper has in-depth research on solution technology of large-scale joint elements based on augmented Lagrange theory, innovatively transformed the constraint relationship into the element stiffness matrix expression form of joint element, and realized the development of a new joint element solving module in SABRE. Finally, the engineering application example test shows that the new method can effectively improve the solving efficiency of the autonomous structural analysis software SABRE without changing the solving accuracy.