Research On Isogeometric-analysis-based Efficient Structural Optimization Method

With the deepening of industrial transformation and upgrading,China is transforming from a large manufacturing country to a strong manufacturing country,and high-end manufacturing has put forward higher requirements on product design methods.Structural optimization design is the core component of the digital design in advanced manufacturing.It can automatically search for high-performance structures that meet the requirements in a given design domain according to design requirements,which is of great significance for improving design efficiency and quality.The current structural design schemes of manufacturing companies generally use CAD software for product geometric design and use finite element method-based CAE software for product performance analysis.However,the model representation of CAD and CAE are different,and the model conversion is required.The structural optimization design process involves CAD geometric modeling,CAE performance analysis,optimization iterative search and other processes,where exists bottlenecks such as cumbersome model interaction,low efficiency of large-scale calculations,and slow iteration convergence.In order to improve the efficiency of structural optimization,this paper proposes a series of efficient structural optimization methods.The detail work of the thesis is as follows:(1)Focus on the problem of low computational efficiency and slow iteration convergence,a triple acceleration topology optimization method is proposed,which consists of three parts:multilevel mesh,initial-value-based preconditioned conjugate-gradient(PCG)method,and local-update strategy.This method accelerates TO in three aspects including reducing mesh scale,accelerating solving equations,and decreasing the number of updated elements,which can reduce the calculation time of topology optimization and improve the optimization accuracy.As the mesh scale increases,the speedup ratio becomes more significant,which proves that it has a great speedup effect in large-scale problems,and the efficiency and accuracy of the proposed method are verified through classical numerical examples.(2)The isogeometric analysis framework is utilized to replace the finite element method to realize isogeometric topology optimization.Isogeometric analysis is directly based on the CAD accurate model for structural performance analysis,which can avoid the tedious interaction caused by the difference between the design and the analysis model in the product design,eliminate the geometric error from the source,and improve the analysis accuracy.Focus on the characteristics of isogeometric analysis,improvements have been made in the three aspects of reducing the mesh size,accelerating equation solving and reducing updated design variables,making the triple acceleration method successfully applied to isogeometric topology optimization based on NURBS control points,which further improve the efficiency of isogeometric topology optimization.(3)A framework of high-efficiency isogeometric shape optimization combined with neural networks is proposed.The neural network is used to learn and fit the nonlinear constitutive relationship between the geometric parameters of the auxetic structure and the mechanical properties of the material,and the shape is optimized according to the constitutive fitting function,replacing the complicated and time-consuming computing process of isogeometric homogenization,and avoiding the simulation calculation process of equivalent properties.Based on the shape optimization framework,an inverse design optimization model based on neural network constitutive fitting function is proposed,which can efficiently achieve the programmable design of structural equivalent mechanical properties.To sum up,focus on high-efficiency structural optimization design,this article carries out algorithm research for large-scale topology optimization problems and complex configuration shape optimization design.Exploring methods to improve optimization efficiency from the optimization algorithm itself and machine learning,and forming a set of high-efficiency isogeometric structural optimization methods that integrate design,analysis,and optimization,which breaks through the bottlenecks of current structural optimization,such as the tedious interaction of CAD/CAE model,low efficiency and slow convergence of optimization iterations,provides theoretical support for the development of a new generation of design optimization software systems with domestic independent intellectual property rights,and provides strong support for improving corporate design capabilities and promoting manufacturing upgrades.