Optimization Study Based On The Numerical Calculation Method Of Peridynamics Theory

Peridynamics theory is a molecular dynamic theory of solid mechanics, which is proposed by Professor Silling in recent years, It based on non-local integral principle, to avoid the deformation differential discontinuous and tip singularity in traditional mechanical method, instead it use integral method to solve the material damage deformation, it has much advantage in the research on the reliability of the material. It can be seen that the numerical method in PD theory has a very important role. However, the previous numerical methods based on the consideration of accuracy and efficiency has many limitations, this paper focuses on the optimization of the numerical method of PD theory, and verify its feasibility.In my paper, we briefly recommend the theory of PD theory fristly, and introduce two most important equations in solving the deformation and failure:the equation of motion and the force function for a PMB material.Then introduces the traditional numerical methods of PD theory and their feature, and introduces the optimization results, namely the integration method with fixed Gaussian points. Then we verified the optimization of accuracy and efficiency through several calculation examples to analyze.Then the paper describes the discrete PD theory model : dispersing the homogeneous model into a number of large cube lattice,finding their Gaussian points,and calculate their PD force through C language programming,then importe the calculation results into MATLAB to make the visual analysis.Finally we simulate an I-beam model to see its deformation and failure after apply a fixed load,and then get a gradual destruction process of material damage through different time steps.And then,we get a different deformation of material by different loads and the same time steps, which provides a basis for the safety monitoring of bridges.