Symplectic Conservative Substructures Time Integration Method

A symplectic conservative substructures time integration method is presented in thispaper, which bases on Precise Integration Method (PIM) and substructure method. Thismethod is flexible and high precise characteristics. It can be applied to many engineeringaspects, such as dynamics problems, transient heat transfer problems, stiff ordinarydifferential equations etc., and also to large-scale structures and parallel computing.After space-discretization by FEM, dynamics problems and heat transfer problems cangenerally transform into ordinary differential equations. From 50s, many numericalintegration methods have been presented to solve ordinary differential equations, in whichmodal superposition method and direct integration method are two main important methods.With the growing of the number of large-scale structures, substructures method has beenwidely used in modal superposition method, but is seldom used in direct integration method.So establishing substructures method in direct integration method is very theoreticalinterested and the value of the works.It's very important to choose an appropriate direct integration method as the base ofsubstructures method. Although difference methods are the most common in direct integrationmethods, but its numerical instability and long-time divergence are obvious disadvantages.Recently symplectic conservative algorithm is considered by more and more people. PIM canpresent precise numerical results which are almost equal to the exact solutions on computer.So in this paper substructures method which bases on PIM is presented.Main work of this thesis includes:First, according to physical characteristics, the structures can be divided into sub-structures by using the physical quantity at the interface in the spatial domain by FEM. Basedon Hamilton variational principle, we deduce the recursive substructures time integrationmethod for dynamics problems and proof that the method is symplectic conservative.Second, based on the least squares method variational principle, we deduce the recursivesubstructures time integration method for transient heat transfer problems with similarprocess.At last, the simulation of numerical examples demonstrates that the method is superior tothe conventional numerical methods, and is symplectic conservation, efficiency and stability.So the method suggested in this thesis has great promise in applications.