On The Complementary Principle And The Order-Flexibility Method

Whether in solid mechanics or in fluid mechanics, the least complementary principle is a basic principle to be applied extensively. Its content is considerable abundance. In this paper, by using the collecting method that was put forward by Hu Haichang, from basic equations of elastic mechanics, the right expression of the least complementary principle is derived, the author points out that the least complementary principle of conservative system does not include volume force terms. The stationary conditions of the least complementary principle had different forms. In this paper, by using the adding zero transformation and the Lagrangian multiplier method, the stationary condition of the least complementary principle is derived and it satisfies the completeness of varied conditions for variational principles in elastic mechanics. From the least complementary principle, several variational principles are derived.The least complementary principle is the foundation of flexibility method, the flexibility method is an important part of structural mechanics, and is an indispensable method of computer analyses for structures. In this paper, the author discourses emphatically on the order-flexibility method. The core of the flexibility method is deformable consistency equations. From the least complementary principle, the general expressions of deformable consistency equations are derived. For realizing the compute processes of the flexibility method, the matrices of internal forces and the coefficient matrices are presented.For spatial thin-walled structure, the simplified dispose method and the method of automatic formed equilibrium amplification matrix are given. Finally, the computer procedure process and compute examples are given.