Research On Optimization Algorithm Of Beam Structure Cross-sectional Size Based On Isogeometric Analysis

Beam structure cross-sectional size optimization can effectively reduce the quality of the structure while ensuring the performance of the structure,which has been widely used in automobile,aerospace and many other industrial fields.The isogeometric analysis takes the non-uniform rational B-splines（NURBS）basis function used to express the geometric model as the shape function,realizes the seamless combination of computer aided design and computer aided engineering,and avoids the meshing process and reduces the geometric error compared with the finite element analysis method.Therefore,in this paper,the cross-sectional size of beam structure is optimized based on isogeometric analysis,for which the following research work is carried out:（1）Research on continuous variable optimization design of isogeometric beam structure with cross-sectional size based on the method of moving asymptotes: The mathematical model and solving strategy of general continuous variable optimization problems are studied,and the effectiveness of the solving strategy in solving optimization problems is proved by a numerical example;NURBS is used to describe the precise geometry of the bus frame model,and threedimensional Timoshenko beam theory based on isogeometric analysis is used to carry out static analysis of the frame body.With the minimum mass as the optimization objective,torsional stiffness and bending stiffness as constraints,the optimization design of the cross section size is carried out.（2）Research on discrete variable optimization design of isogeometric beam structure with cross-sectional size based on the relative difference quotient algorithm: In many practical engineering problems,the beam section has a series of standard dimensions.The optimization design results of continuous variables do not set the section size as one of these standard dimensions,and the optimization results often need to be rounded.In this paper,for the discrete variable optimization problem,the mathematical model and solving strategy of the general discrete variable optimization problem are studied.The relative difference quotient algorithm is improved and the effectiveness of the solving strategy is proved by a numerical example;NURBS is used to describe the precise geometry of the bus roof frame model.Based on the isogeometric analysis,the cross-sectional size of the model is optimized with discrete variables.（3）Research on continuous variable interval optimization design of isogeometric beam structure with cross-sectional size based on the method of moving asymptotes: The mathematical model and solving strategy of general continuous variable interval optimization problem are studied.The interval number is used to describe the median and manufacturing error of beam cross-sectional size,and the interval optimization model of beam cross-sectional size is transformed into a deterministic optimization model by Taylor formula and natural interval extension of function;The adjoint sensitivity method is used to calculate the second derivative of displacement with respect to design variables.Based on the isogeometric analysis,the interval optimization design of the cross-sectional size of the bus frame with continuous variables is carried out,and the interval optimization results are compared with the deterministic optimization results.（4）Research on interval optimization design of discrete variables of isogeometric beam structure with cross-sectional size based on the method of moving asymptotes and the relative difference quotient algorithm: The solution strategy of interval optimization problem with discrete variables is studied,demonstrates the effectiveness of the solving strategy by using a numerical example,and compares the results of interval optimization of discrete variables and interval optimization of continuous variables.Based on the isogeometric analysis,the interval optimization design of the section size of the bus roof frame model with discrete variables is carried out,and the results of interval optimization and deterministic optimization are compared.