Construction of IGA-suitable Volume Parametric Models by the Segmentation–Mapping–Merging Mechanism of Design Features
Graphical abstract
Introduction
The parametric design based on the parametric model which is represented by the boundary such as B-rep, CSG is the core technology of most CAD software, because of the variability and reusability of the parametric model [1], [2], [3]. But the parametric model should be transformed into non-parametric mesh model to adapt to analysis and optimization. So, during the whole design process, the parametric models and the non-parametric models need to be converted back and forth, which takes a lot of time. Meanwhile, it is hard to establish the direct analytic relationship among the geometric parameters, the material parameters and the performance parameters, which makes the integration of modeling, analysis and optimization be a great challenge.
Various methods have been developed to overcome the difficulties in the model conversion among modeling, simulation and optimization. Among them, the IGA method based on the volume parametric model can realize the seamless integration of CAD and CAE [4]. Because of the tensor properties of spline basis, a region that is not quadrilateral or hexahedral in topology cannot be represented by a single spline surface or volume [5]. Therefore, the model suitable for IGA must be volume parameterization as a set of quadrilateral surfaces in two-dimension or hexahedral volumes in three-dimension. While the geometric models designed by most CAD software are based on the boundary representation, so these models do not meet the requirements of IGA.
The lack of available software to construct IGA-suitable models is also a great challenge. In the existing literature, there are two ways to solve the problem above. The first is to integrate CAD with existing commercial finite element software like Abaqus [6], [7], [8], trying to bridge the gap between design and analysis with the help of a mature commercial platform. The second is to develop an open software package [9], [10], generating polycube-based mesh by the given boundary and promoting the use of IGA significantly.
In this paper, a method is proposed to construct complex volume parametric models based on the mechanism called Segmentation–Mapping–Merging of the design features. The method consists of three steps: construction and segmentation of design features, volume parametric mapping and merging of parametric patches. To allow great geometric flexibility, the semantic feature network can be constructed by interactive input. Then the semantic feature network is partitioned into multiple simple sub-network under the constraints of volume parametric modeling. Then the volume parametric mapping constructs each sub-network as a volume parametric patch. Finally, under the constraints of IGA, a volume parametric model is obtained by optimizing and merging operations. The complex models including mechanical parts and free-form models are selected to test and verify our method. The contributions can be concluded here.
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A platform of integration design based on volumetric parameterization is put forward. The ideas and methods of parametric design and feature design, which are widely used in the current CAD and CAE software, are also integrated together.
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A modeling mechanism or operation called segmentation–mapping–merging for the volume parametric patches or primitives is studied. Based on the mechanism, the models suitable to IGA can be directly created other than conversion from the models represented in boundary surfaces.
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The proposed method is realized and verified on the complex three-dimensional mechanical parts and free-form models. This gives an expectation to an extensive application for volume parameterization and IGA on complex shapes.
Section snippets
Related works and overviews
Seamless integration of CAD and CAE is a bottleneck problem in today’s product design and has attracted interest of many researchers. To solve this problem, Gujarathi [11] put forward the concept of “Common Data Model”, containing all the parameter information needed for modeling and analysis to connect CAD and CAE from data. Wassermann [12] and Schillinger [13] proposed the “DESIGN-THROUGH-ANALYSIS” method, which explored hierarchical refinement of NURBS as a basis for adaptive isogeometric
Basic definitions and generation of the semantic feature network
The input of the feature network is the set of various size parameters which describe the topological structure and the shape of the model. They are converted from interactive input or extracted from the existing models.
Generation and segmentation of the geometric feature network
The geometric feature network can be extracted from the semantic feature network. During the extraction, some of the feature curves are treated as paths, and the intersections of paths are taken as feature nodes. The unclosed feature surfaces are selected as the section surfaces. Considering all the cases, the geometric feature network falls into four types:
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Type I, it has multiple section surfaces and zero path.
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Type II, it has a single section surface and one path.
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Type III, it has multiple
Complete feature network and volume parametric mapping
The complete feature network can be achieved after the segmentation operation of the geometric feature network. Then the volume parametric patches can be created by the mapping operation in the following two ways.
Merging of parametric patches
After all the parametric patches are generated, they should be merged to form a whole model. In our modeling process, we require that the adjacent two volume parametric patches share one complete surface. So enhancing the continuity among the patches is a very important thing and to be discussed here. If the designer wants to modify a built model, such as adding some features to the model or cutting some features from the model, in other words, how to merge newly generated features and the
Examples
To demonstrate the effectiveness of our methods, some typical mechanical parts and free-form models are constructed and evaluated by their Jacobian values. What is more, IGA is applied to verify the utilization of the generated models. Due to space limitations, the formulae for only some of the parameters are given. We use C++ for modeling and OpenGL for rendering in VS2017.
Conclusions
This paper presents a volumetric parameterization method for mechanical parts and free-form models. Different from most of the current methods, our method creates a model rather than converts it from a B-rep model. The essence of the parametric design and the feature design is also adopted into our method since their concepts, ideas, methods and technologies are widely employed by the current CAD and CAE software. Besides, the proposed segmentation–mapping–merging mechanism will help generate
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This research is supported by the National Nature Science Foundation of China under Grant No. 52075340, the Zhejiang Provincial Science and Technology Program in China under Grant 2021C01108, and the NSFC-Zhejiang Joint Fund for the Integration of Industrialization and Informatization under Grant No. U1909210.
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