复杂二维几何模型等几何形状优化

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中图分类号：TP182 文献标志码：A

Isogeometric shape optimization of complex 2D geometric model

LU Shuaishuai， CHEN Long， LI Tianjian （School of Mechanical Engineering， University ofShanghai for Science and Technology，Shanghai 2Oo093， China）

Abstract： Traditional finite element methods suffer from isues such as geometric description errors and redundant model format conversion. To address these problems， a 2D parametric multi-patch model shape optimization method based on isogeometric analysis was proposed. In the modeling phase， a parametric framework integrating dimension parameters and all-quadrilateral partitioning was adopted. Complex 2D models were divided and constructed into multi-patch models compatible with isogeometric analysis， thus avoiding the model conversion step required by traditional methods. In the optimization calculation phase， a control mechanism combining sensitivity guidance and patch conection constraints was established. The analytical derivation of design variable-compliance sensitivity was performed to guide the iterative optimization of control points and weights.Meanwhile， continuity adjustment of sensitivity was implemented at patch interfaces to ensure the continuity and smoothness of optimization results for adjacent patches. During the optimization process， the bounds of design variables were dynamically updated to guarantee the feasibility and stability of optimization results， thus preventing the failure of optimized model generation. Validated by three numerical examples， the proposed method could efectively reduce model compliance， with a maximum reduction rate of 30.8% . This method provides a novel approach for the efcient shape optimization of complex 2D geometric models. Furthermore， it can be further extended to the shape optimization algorithms of 3D parametric solid models， laying a theoretical foundation for the integration of modeling， simulation and optimization.

Keywords： shape optimization; compliance; parametric model; isogeometric analysis

结构优化根据其设计阶段的不同，可分为多个层次，如尺寸优化、形状优化和拓扑优化。（剩余13325字）