Method for optimizing structural parameters based on symbolic operation results of sparse matrix

Abstract

The invention discloses a method for optimizing structural parameters based on symbolic operation results of a sparse matrix and belongs to the technical field of strength analysis of aircraft structures. The method mainly includes firstly generating a stiffness matrix through a finite element analysis method; secondly performing a matrix transformation on the stiffness matrix with a minimum filling element as a target, and establishing a mapping relationship; using the transformation to perform equivalent transformation on the right-end item of a load and then performing numerical decomposition, and forming a triangular decomposition matrix of a sparse matrix of linear equations; using results of matrix decomposition to perform finite element analysis to perform optimization calculation;using updated design variables to perform numerical item replacement operations by using the mapping relationship; and finally repeating the optimization process until the optimization converges. According to the method, the result of the first symbol operation is made full use of to perform the numerical decomposition operation. In the entire design process, only one symbolic operation needs to be performed. Compared with a traditional design process, theoretically the method shortens the design time by about 50%.

Description

technical field [0001] The invention belongs to the technical field of aircraft structural strength analysis, and in particular relates to a method for optimizing structural parameters based on sparse matrix symbolic operation results. Background technique [0002] In order to complete the research and development design of the structure with high quality under the limited time and funds, it is an inevitable choice to design by means of optimization. Optimal design is increasingly becoming an effective means for people to solve the contradictions of safety, performance, time and cost. After decades of hard work, the development of optimization techniques has made great progress in theory and application. [0003] Due to historical reasons, in the traditional optimization design process, the finite element analyzer is artificially isolated from the optimization process, and the results of the optimizer after numerical optimization must be returned to the analyzer for a comple...

AI Technical Summary

Problems solved by technology

At present, with the improvement of computer hardware technology, finely divided finite element grids are often used for increasingly complex structural design forms. The finite element model of millions of nodes in the design is quite common, and the finite element model of this scale is repeatedly called for optimization. The design efficiency is relatively low

refer to figure 2 , the analysis process in the traditional optimization design is used as a black box call, and the response is obtained by repeatedly calling the solver, and the optimization efficiency is low

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