Engineering Structure Of The Fem-mfree Coupling Calculation

MFREE method is a new and promising numerical method appeared after traditional ones such as FEM (Finite Element Method), which has been commonly used nowadays. However, there are still some limitations for this method. For instance, the theory of MFREE method and the default value of the parameters which affect the computation precision are still needed to be improved. In this study, we discussed the advantages and the disadvantages of the new developed method (MFREE) and the classical FEM method on the basis of a series of the previous studies. The theoretical investigations about the whole weak-form MFREE method and the application of the MFREE method in the engineering have also been taken into consideration. Several findings can be drawn from this study:1) We summarized the history of MFREE method and the current research status all over the world. The typical MFREE methods have also been reviewed and evaluated according to the different derivation method of solving formulae. The characteristic and superiority of MFREE method, and its problems existed recently have also been presented in this study.2) We have also summarized the basic theory of the FEM and MFREE methods in detail on the basis of the weighted residual method with compactly supported trial functions. We especially focused on the research on the theory of the radial point interpolation mesh-less method (RPIM) and element-free Galerkin method (EFGM), as well as the application of elasticity in the 2-D problem3) The construction and property of shape function of RPIM have been presented in this study in detail. We have analyzed the effect of the two shape parameters(αc, q), the field nodes non-dimensional size (αs), and the choice of the density of Gaussian integral point in the background cell on the calculation precision, when choosing the multi-quadratic (MQ) function as the base function in this method. To facilitate this analysis, a numerical experiment has been given in this study. This analysis might provide some insights on the choice of parameters, the collocation of node in the solution domain and the method of setup the Gaussian integral point in the background cell. The result of calculation indicates that under the same background cell, the precision of the RPIM with the reasonable choice of parameters is much higher than that of FEM.4) The construction and property of shape function of EFGM has been presented in detail. The effect of the density of nodes in the solution domain, the field nodes non-dimensional size (αs) of influence domain, and the choice of the density of Gaussian integral point in the background cell on the calculation precision has also been analyzed as well. It can provide valuable reference for the collocation of node in the solution domain and the method of setup the Gaussian integral point in the background cell. The result of calculation indicates that under the same background cell, the precision of the EFGM with the reasonable choice of parameters is higher than those of FEM and RPIM for solving the linear-elastic solid mechanics problems.5) We have analyzed and discussed both the advantages and disadvantages of whole weak-form MFREE method and finite element method. Synthesized their application advantages, we developed two coupling calculation methods of FEM-RPIM and FEM-EFGM. We have also developed two FORTRAN programs to implement the linear elastic solid mechanics of the two coupling methods. Finally, the results were given by using the ANSYS finite element analysis software and MATLAB mathematical software.6) Taking the most common building materials in Water Resources and Hydropower Engineering——concrete as an example, we analyzed its destruction type. The fracture toughness (KIC), a parameter for determining the crack growth criterion in the traditional medels of the fracture mechanics, has been found to be of great scale dependency in the real experiments. This will result in significant discrepancies for the numerical simulation of crack propagation. In addition, the traditional methods generally used a constant-step method, which will also affect the computation precision. In order to avoid the influence of scale dependency to simulative crack propagation and increase the speed of simulation, we proposed the crack propagation criterion of 'Maximum circumferential tensile strain'and developed the 'pull-crush' combinative destroy model of concrete on the basis of the crush destroy model. The simulation of the destroy process of 3-point bending freely supported beam is also presented.