Explicit Topology Optimization Of Shell Structure Based On Isogeometric Framework

Topology optimization technology can provide engineers with more economical,efficient and novel product design solutions.In recent years,it has been widely used in many industrial fields such as aerospace,vehicles and ships.However,the traditional implicit topology optimization framework usually has a series of problems such as a large number of design variables,unclear boundary geometry information,a large amount of calculation for structural analysis,and the inability to directly integrate with the CAD system.Even under the explicit topology optimization framework,problems such as gray elements cannot be avoided in structural analysis models based on fixed grids.In order to solve the above-mentioned problems,this paper combines the moving morphable void method with the trimmed surface analysis technology,and develops the corresponding explicit structure optimization framework.Among them,the moving morphable void method uses B-spline curve to describe the void boundary,so it can provide explicit description information of the structure boundary contour,and can establish the direct connection between the optimization results and the CAD system without any post-processing.In addition,this method requires only a small number of geometric parameters to completely determine the shape and layout of the voids,greatly reducing the number of design variables for topology optimization.The trimmed surface analysis method can directly use the void boundary parameters to perform highly accurate structural response analysis,which can effectively avoid the patch division and splicing operations in traditional isogeometric analysis methods for topologically complex structures.It has unique advantages in improving computational efficiency and maintaining structural continuity.Based on the above advantages,this paper applies the moving morphable void method and the trimmed surface analysis method to the shell structure optimization,and researches the corresponding numerical algorithm.The specific research content of this paper can be briefly described as follows:1.An explicit topology optimization method of shell structure based on isogeometric analysis and trimming technology is proposed.In this method,the MMV framework is used to update the structure topology and provide void boundary information,and the TSA technology is used to provide highly accurate structural analysis results for the optimization.Through the discrete,identification and interpolation fitting of the void boundary,the fusion void boundary in the MMV framework can be processed into a trimming curve suitable for TSA,and the fusion processing has extremely high accuracy and robustness.Numerical examples show the effectiveness of the proposed method in topology optimization of shell structures.2.Based on the explicit optimization framework,a simultaneous shape and topology optimization method for shell structures is proposed.By introducing the concept of multi-level design,the lossless conversion between the shape optimization model and the structural analysis model is realized,so both the shape optimization efficiency and the structural analysis accuracy can be taken into account in the optimization process.This method integrates the shape/topology design variables of the shell structure into a unified mathematical problem,which can simultaneously optimize the mid-surface geometry and structural topology of the shell structure in highly consistent models.Compared with the conventional method,this method can effectively save the time cost of structural analysis and optimization calculation.Numerical examples show that the method is effective and reliable in solving the simultaneous optimization problem of shell structures.