Studies On Crack Tip Fields And Conservation Laws In Hamiltonian System

In this thesis, some basic researches were performed in Hamiltonian system of elastostatics, such as crack tip fields of three basic crack modes, general steps for modeling Hamiltonian function, Hamiltonian principle in augmented phase space, and energy-momentum tensor in elastostatics. The main contents of the thesis are as follows:(1) Some basic problems in fracture mechanics were discussed based on Hamiltonian principle in elastostatics. It proposed the approach of solving three basic crack tip fields in phase space. The results indicated that the series expansion method of stress function in solving crack tip fileds using traditional elasticity is corresponding to the expansion of total-state function vector in eigen solution space. It indicated that the basic equations (namely equilibrium equation, geometry equation and constitutive equation) in elasticity implicitly contain the Hamiltonian canonical equations. Exact definition was presented for Hamiltonian principle in elastostatics.(2) According to analysis mechanics methods, it gave the general steps to modeling the Hamiltonian function in elastostatics. Hamiltonian function was calculated along three axes in rectangular coordinates.(3) In the thesis, it presented that Hamiltonian principle and their extension forms in augmented phase space are variational principles without constitutive equation restraint. Sequentially, it figured out that for the improper choose of solution system in elasticity, there is confusion use of each direction stress in the functional of variational principles, namely introduced generalized momentum in all directions without distinguishing. That's the essential reason for the consideration that stress-strain relationship could not be relieved in generalized variational principles.(4) Using field theory method, the thesis calculated the energy-momentum tensor of elastostatics in three-dimension rectangular coordinates and that in two-dimension polar coordinate system. Also physical meanings were analyzed foreach components of the tensor and the conversation integration existence was argued.