Studies On Integral Global Optimal Design Method For The Mechanical Structural Optimization

The purpose of this paper is to combine a kind of integral type optimality conditions and Monte Carlo method, put forward a kind of no need for sensitivity analysis and can obtain the global optimal solution of the mechanical structure optimization design method.The concrete research contents include:firstly, studies the integral type the optimality conditions of Monte Carlo and quasi Monte Carlo numerical implementation method; Secondly, studies the structure analysis agent model Kriging model, in order to reduce the amount of calculation in the process of structure optimization analysis of structure; Finally, the proposed method combined with a general structural analysis software ANSYS, the use of secondary development technique, set up a suitable for the engineering practical problems of structure optimization design program.Firstly, a class of integral optimality conditions derived from the field of mathemaiics proposed the use of Monte Carlo numerical integration to obtain a global optimal solution of the optimization problem; Then, outlining the basic idea of Monte Carlo methods, and discusses the method of generating random numbers in Monte Carlo methods in detail, through the comparison of examples, determines a good random number generation method; Then, discussed several specific numerical difficulties may be encountered in the process, and puts forward the solution; Finally, through several typical mathematical examples and truss structure optimization design example proves the validity and reliability of the proposed method.Secondly, because the structural analysis of practical engineering problems often requires huge amount of calculation, and the use of Monte Carlo method for structure optimization design need for multiple sampling, which is many times of structural reanalysis. This leads to the calculation of the method has increased dramatically. In order to alleviate the problem, this chapter studies using kriging agent model instead of structure analysis, in order to reduce the amount of calculation structure analysis.Then, this paper introduces the finite element analysis software ANSYS secondary development method and the mixed programming of MATLAB and ANSYS method and skill. The method of secondary development through APDL, ANSYS enables repeated analysis,It is an essential part of the realization of Monte Carlo method.Finally, For engineering common truss, frame and continuum problem, based on the integral type global optimality conditions of Monte Carlo optimization method, from the structure size optimization, shape optimization and size optimization and shape optimization of hybrid optimization design of the three levels to solve. Calculation results show that the proposed method can correctly solve the problem of the global optimal solution, and then verify the universality and the feasibility of the method researched in this paper.