Triangular meshes play a crucial role in finite element analysis, especially when modeling complex geometries with irregular boundaries and fine geometric details. However, mesh quality directly impacts analysis accuracy and efficiency. Existing mesh generation and optimization methods are still unable to meet high-quality requirements, and most mesh topology optimization approaches rely on heuristic strategies and manual expertise, making them vulnerable to local optima. To address this issue, this paper proposes a deep reinforcement learning-based topology optimization framework for triangular meshes. This framework constructs a multi-head graph attention network (GAT) that integrates vertex topological properties with edge geometric features. It designs a reward mechanism that combines irregularity improvement and geometric feature preservation, guiding the agent to independently explore optimal topological adjustment strategies through self-play without prior knowledge. This approach preserves geometric features while approximating the optimal vertex degree distribution and effectively reducing mesh irregularity. Experimental results demonstrate that the method is effective and robust in local adaptive topology optimization, providing new insights into high-quality mesh topology optimization.

Open Knowledge Graph (OpenKG) link prediction is important for using OpenKGs in applications such as question answering and text comprehension. The noun phrases (NPs) and relation phrases in OpenKGs are not canonicalized, making OpenKG link prediction highly challenging. Existing methods addressing this problem infuse canonicalization information into knowledge graph embedding models. However, they still fail to fully exploit the semantics of NPs. First, two different NPs, even referring to the same entity, can carry different versions of information, which has been ignored by previous methods. Second, neighborhood information of NPs in OpenKGs has not been utilized, which contains abundant information for link prediction. Based on these observations, we propose the OpenKG Segmented Embedding (OKGSE) method. Specifically, to fully capture the dissimilarity of NPs belonging to the same cluster, we learn separate parts of embedding for both the NP cluster and NP. Meanwhile, we exploit neighborhood information by integrating graph context into the semantic matching score function. Extensive experiments across four benchmarks show that OKGSE can achieve state-of-the-art performance as well as effectively capture the unique semantics of each NP.

This paper presents a novel evolutionary strategy for multiobjective optimization in which a population's evolution is guided by exploiting the geometric structure of its Pareto front. Specifically, the Pareto front of a particle population is regarded as a set of scattered points on which interpolation is performed using a geometric curve/surface model to construct a geometric parameter space. On this basis, the normal direction of this space can be obtained and the solutions located exactly in this direction are chosen as the guiding points. Then, the dominated solutions are processed by using a local optimization technique with the help of these guiding points. Particle populations can thus evolve toward optimal solutions with the guidance of such a geometric structure. The strategy is employed to develop a fast and robust algorithm based on correlation analysis for solving the optimization problems with more than three objectives. A number of computational experiments have been conducted to compare the algorithm to another three popular multiobjective algorithms. As demonstrated in the experiments, the proposed algorithm achieves remarkable performance in terms of the solutions obtained, robustness, and speed of convergence.

Model integration enables the automated data flow of design changes between multidisciplinary models and improves the efficiency of collaborative multidisciplinary design. In this study, a geometry-related profile of SysML is first proposed to specify the geometric information of mechanical structure to support the generation of initial CAD models from SysML models. Second, a model comparison-based method is introduced to obtain the model changes to facilitate the incremental update between distributed heterogeneous models. Third, a multidisciplinary design optimization based method is introduced to deal with the design conflicts that hinder model integration during multidisciplinary design. Finally, a five-bar robot is used as a case study to demonstrate the whole proposed method.

Medial axis (MA) is widely used in many engineering fields. The difficulty of current methods for the generation of MA of CAD models is how to make balance between the efficiency and quality. In this study, an approach to iteratively generating hierarchical multi-resolution MA is proposed. In each iteration, only local MA needs to be refined, by which the time cost and the space cost are reduced greatly. First, the model is voxelized and its initial MA is generated by the distance dilation method. Meanwhile, the MA quality is computed and evaluated. Second, the MA level is upgraded and the details of the model is re-voxelized if the MA quality doesn't satisfy the requirement. Third, the affected region is computed in which the local MA needs to be refined. Forth, the local MA is re-computed in the affected region, and it is combined to the MA in other regions. Several examples are given to demonstrate the outperformance of the proposed method in terms of time and space.

Model simplification is imperative in the process of Computer aided design (CAD) and Computer aided engineering (CAE) integration. Mid-surface abstraction is the most effective method to simplify the thin-walled models. Many previous research efforts have been focused on the mid-surface abstraction, including the model decomposition based methods, Medial Axis Transform (MAT) based methods and Chordal Axis Transform CAT based methods. However, complex thin-walled models cannot be handled well due to the fact that there are some problems including low geometrical precision, poor topological structure, etc., in the above resultant mid-surface models. Especially, these methods are hard to be reused to generate the mid-surface model efficiently. Therefore, a hierarchical semantic mid-surface abstraction method is proposed for the thin-walled model based on rid feature decomposition in this paper. Firstly, a new hierarchical semantic structure is defined and applied on both the thinwalled models and mid-surface models. After that, the model decomposition is conducted based on the identified rib features and the hierarchical semantic information is obtained at the same time. Then, the offset operation and discretization based methods are used to obtain the mid-surface patch for each sub region with different semantic structure respectively. Finally, the mid-surface model with hierarchical semantic information is generated by stitching each discrete patches. Moreover, the above model can be reused to facilitate the rapid mid-surface abstraction of the changed model based on its hierarchical semantic structure. Several examples are given to demonstrate the outperformance of the proposed method.

Multidisciplinary simulations are becoming imperative for the design of complex products. However, it is not an easy task for designers to quickly view the simulation results. The reason is that the simulation data are usually too huge to be transferred quickly and they are heterogeneous and have to be visualized in specific tools. In this study, a novel CAD-centered method of seamless integration and efficient visualization of multidisciplinary heterogeneous simulation results is proposed based on the intermediate model. Here, a common simplified mesh model is used as the intermediate visualization model in CAD platform by analyzing different simulation requirements. The mapping association is established between the intermediate mesh and the simulation meshes of different disciplines based on relative coordinates. Based on the mapping association, an interpolation approach is proposed to achieve the simulation results for visualization in CAD platform. To accelerate the transmission speed, several strategies are deliberately devised: parallel mapping, parallel interpolation and incremental transmission. Several examples are provided to demonstrate the out performance of the proposed approach.

Mesh editing can provide various models for FEA-simulation in industry. This paper proposes a framework for FEA-mesh editing with feature constrained. In the framework, cage-based technique is first used to edit the base-decomposition model. Vertices of the constrained feature are transformed into a local form. Parameters are analyzed before editing operation, and our method permits the user to add constraints on the parameters of the feature. This framework can also keep consistence for the disconnected assembly mesh model. Experimental results show that constrained features are kept precisely after mesh editing. Additionally, experimental data indicate our method is efficient and achieves real-time response.

In this paper, we present a semantic-based partial retrieval approach of CAD models for design reuse. Based on the observation of reusable regions for design of 3D CAD models, for each model in the model library, we propose an algorithm that automatically extracts its reusable regions for partial retrieval. To further effectively support the partial retrieval of these reusable regions through simple queries, we represent each reusable region by all its local matching regions and describe each local matching region in a hierarchical way. Based on the hierarchical descriptor, a partial retrieval method for reusable regions is put forward. The approach proposed is implemented and tested by hundreds of mechanical parts. Preliminary results show that the method can effectively support partial retrieval for design reuse.

The significance of tolerance is obvious and undoubted for product design and manufacturing. However, it is not intuitionistic for the computer to understand the tolerance semantics, which heavily baffles the integration of CAD and CAM. In this paper, a uniform approach to interpreting the rigorous tolerance semantics for complicated tolerance specification (CTS) is proposed with the help of reclassification of tolerance based on tolerance zone (TZ). First, the tolerance is reclassified into three categories: Immovable-TZ (ITZ) tolerance, Translational-TZ (TTZ) tolerance and Floatable-TZ (FTZ) tolerance. Second, a uniform method of interpreting the rigorous tolerance semantics is presented based on the variation along degrees of freedom direction (VDOF) for CTSs. To improve the computational efficiency of implementation of interpreting rigorous tolerance semantics, a novel method is proposed to determine the TZ boundary without performing Boolean intersection operations in 3-D CAD systems. Finally, the algorithm is implemented and some test results are given.

In this paper, a multi-mode retrieval approach of solid models is presented. First, a local feature determination method based on wavelet transform is given, which makes the local feature agree with the human perception of resemblance; then a uniform and efficient DBMS (dilation based multiresolutional skeleton) generation method for global model and local feature using adaptive voxelization and local dilation is proposed; finally a flexible similarity assessment is proposed which supports both global matching and partial matching effectively and further supports different retrieval requires. Preliminary experiment results show that a multi-mode retrieval approach can describe user's retrieval intent more precisely and return retrieval results more properly.

A parallel global optimal approach of feedback is proposed for 3D CAD model retrieval in this study. First, a novel unified mathematical model with multi-object for similarity field modification based relevance feedback is brought forward and the simplification is also given. Second, a new algorithm based on particle swarm optimization is proposed to optimize above model. In this algorithm, the particle can fly under the guide of its experience and a leader queue helps to avoid immature convergence. At last, an implementation is given and the results show that better feedback results are obtained for CAD model retrieval with the proposed method.

Medial axis (MA) is widely used in many fields nowadays. However, the efficiency of generating MA of complicated models with current methods is still not satisfactory. A novel approach to constructively generate MA is proposed in this paper. With this method, the MA of the resultant model set up with two primitives and a Boolean operation upon them is generated by combining the MAs of the two primitives in a certain way instead of regenerating from scratch. First, the properties of MA are investigated. During Boolean operation, the boundaries that will vanish are found and the region of the model on the basis of which some new MA segments(MASs) need to be generated is determined, and the new MASs are generated based on the region using tracing method. The MA of the resultant model is constructed by combining the new generated MASs with the reserved MASs of the two primitives at last.

Tolerance is almost ubiquitous during the whole product life. However how to effectively embody and interpret the semantics of tolerance in three-dimensional computer-aided design systems is still an open issue. Variational geometry is recognized as one of the most promising solution for it. And the methods for systematically and efficiently generating the variational geometries of all kinds of geometric entities with tolerances are imperative. In this paper, a degree-of-freedom (DOF)-based approach is proposed for generating variational geometry of a hole with composite tolerances imposed on its centerline and surface at the same time. All possible combinations of tolerance requirements for a hole are discussed. And the mathematical models for variational geometries of the centerline and the surface of a hole are deduced. Furthermore two strategies for improving the efficiency of generating the variational geometry of a hole are presented. Finally, the algorithm is implemented and some test results are given. Note to Practitioners-This paper is motivated by the problem that the tolerance information in the current computer-aided-design CAD systems lacks the necessary engineering semantics, which causes tolerance information that cannot be correctly used and impedes the integration of CAD and computer-aided manufacturing (CAM). Existing approaches have partially solved the problem for the pattern of holes (POH) and plane feature based on variational geometry. But the computational efficiency with the variational geometry method is very insufferable due to a lot of Boolean intersection operation. In this paper, the hole feature is mainly considered because its tolerance specification is quite different from other features and is imposed on the centerline and the surface of a hole at the same time. First, the mathematical model is given for interpreting the engineering semantics of the tolerance of the centerline and the surface based on the variational geometry, respectively. Then, the tolerance principles are further considered for compensation between the above two types of tolerance. More important, a direct method, which can largely avoid the Boolean intersection operation, is proposed for generating the variational geometry. The computational efficiency is thus improved dramatically and the variational geometry is generated almost in real time. This enables virtual assembly and virtual inspection with the tolerance information to be possible.