Parametric optimization is an important product design technique, especially in the context of the modern parametric feature-based CAD paradigm. Realizing its full potential, however, requires a closed loop between CAD and CAE (i.e., CAD/CAE integration) with automatic design modifications and simulation updates. Conventionally the approach of model conversion is often employed to form the loop, but this way of working is hard to automate and requires manual inputs. As a result, the overall optimization process is too laborious to be acceptable. To address this issue, a new method for parametric optimization is introduced in this paper, based on a unified model representation scheme called eXtended Voxels (XVoxels). This scheme hybridizes feature models and voxel models into a new concept of semantic voxels, where the voxel part is responsible for FEM solving, and the semantic part is responsible for high-level information to capture both design and simulation intents. As such, it can establish a direct mapping between design models and analysis models, which in turn enables automatic updates on simulation results for design modifications, and vice versa -- effectively a closed loop between CAD and CAE. In addition, robust and efficient geometric algorithms for manipulating XVoxel models and efficient numerical methods (based on the recent finite cell method) for simulating XVoxel models are provided. The presented method has been validated by a series of case studies of increasing complexity to demonstrate its effectiveness. In particular, a computational efficiency improvement of up to 55.8 times the existing FCM method has been seen.

翻译：参数化优化是重要的产品设计技术，尤其在现代基于参数化特征的计算机辅助设计（CAD）范式中。然而，要充分发挥其潜力，需要在计算机辅助设计与计算机辅助工程（CAD/CAE）之间建立闭环（即CAD/CAE集成），实现自动化的设计修改与仿真更新。传统方法常采用模型转换来构建该闭环，但这种工作方式难以自动化，需要人工输入，导致整体优化过程过于繁琐而难以接受。为解决此问题，本文提出了一种基于统一模型表示框架（称为扩展体素）的参数化优化新方法。该框架将特征模型与体素模型混合为语义体素的新概念：其中体素部分负责有限元求解，语义部分负责捕获设计与仿真意图的高层信息。由此，它能够建立设计模型与分析模型之间的直接映射，进而实现设计修改时仿真结果的自动更新，反之亦然——有效形成CAD与CAE的闭环。此外，本文还提供了操作体素模型的高效鲁棒几何算法，以及基于近期发展的有限胞元方法的体素模型高效数值模拟方法。通过一系列复杂度递增的案例研究验证了所提方法的有效性，其中计算效率较现有有限胞元方法最高提升达55.8倍。