Combination Of Analytical And Finite Element Methods For Plane Elastic-plastic Fracture Analysis And Its Applications To The Fracture Of Concrete Structures

Fracture mechanics is a new branch of solid mechanics, which has developed since 50th. It can be classified as micro-fracture mechanics and macro-facture mechanics. On one hand, it's necessary to make clear the microcosmic mechanism of fracture. On the other hand, macro-fracture mechanics has not developed perfectly and needs to be studied continuatively, especially the application in the practical engineering. Even the plane elastic-plastic fracture mechanics has many unsolved problems. The stress intensity factor (SIF) criterion and crack opening displacement (COD) criterion are very important fracture criterions in the linear elastic fracture mechanics (LEFM) and the elastic-plastic fracture mechanics respectively. The method of determining the stress intensity factors and COD computations are problems still concerned by researchers.With the development of computer, computer technology, computational mathematics and mechanics intercross each other and give birth to a new branch of academic study, that is the computational mechanics. Now computation, experiment and theoretical analysis become the three main supports for mechanics researchers to solve problems in engineering and science. Computational mechanics and fracture mechanics intercross and give birth to a new branch of fracture mechanics-the computational fracture mechanics. The contents of the doctoral dissertation belong to the category. A kind of new combination of analytical and finite element methods-semi-analytical finite element method is presented for a series of problems in the plane elastic-plastic fracture mechanics. Employed the Hamiltonian system theories of elastic mechanics, a series of crack singular analytical elements satisfying different boundary conditions along crack surfaces in the vicinity of crack tip are constructed. These hyper-elements can describe the crack tip fields accurately for different simplified fracture models. Implemented the hyper-elements into ordinate finite element system, a kind of semi-analytical finite element method is then constructed. Using the method, we can evaluate the elastic-plastic field of crack tip easily. This method has both advantages of analytical method and finite element method. It is accurate, simple and efficient. The main research work of the thesis covers the following aspects:1. Special solutions for the ring circular domain with crack surfaces acted on uniform compressive force, linear compressive force and linear shearing force are deduced in polar coordinate employed the eigenfunction expansion technique in the Hamiltonian system of elastic mechanics. Combined with the general solution for the above problems, the analytical solutions for crack tip fields with surfaces acted on the above three kinds of loads are obtained. These solutions offer theoretical basis to construct analytical elements for plastic analysis of crack.2. A kind of crack elastic analytical elements is constructed employed the eigenfunction expansion solutions and variational principle in the Hamiltonian system theory. The formulations for the stiffness matrices of the analytical elements are deduced. These elements can be combined with the ordinary finite elements to form a semi-analytical finite element method. Using the semi-analytical finite element method, we can evaluate the stress intensity factors for cracks of mode I , mode II and mode I + II directly. Many typical problems arestudied and compared with boundary collocation method, traditional finite element method and analytical methods. The results indicate that the method is accurate and simple for stress intensity factor computation and is easy to be used in practical engineering. The influence of the external nodal number of the analytical element on the accuracy of stress intensity factor computation is investigated in detail. The results show that the method has good convergent property.3. Extended the semi-analytical finite element method into the Dugdale model of elastic-plastic fracture mechanics, the analytical elements based on t...