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This paper presents methods for preparing a geometry model for finite element mesh generation in a Mechanical Computer-Aided Design (MCAD) environment. It works by creating a new representation of the model through the application of virtual topology operators. The resulting “analysis topology” description is used to abstract the analysis model, enabling automated tools and experts to apply an incremental strategy to decompose the model for meshing, without modifying the original CAD model. This work also demonstrated how virtual topology enables the integration of multiple model decomposition tools to expand the capabilities of the hosting CAD environment, providing support for more meshing strategies and more freedom in how they are applied, while bridging the gap between the CAD and analysis models. Herein, the virtual topology operators used to decompose the model are checked and propagated based on the required mesh constraints to ensure the resulting mesh is conformal at the interfaces. Finally, the methods required to decompose the original CAD model using the analysis topology description and “virtual geometry curves” are presented, enabling downstream automation of the mesh.

Generating hexahedral meshes is often an expensive process, which limits the use of high-fidelity numerical simulation methods for design. Hexahedral meshes can be generated by decomposing a geometric model into simpler meshable regions, but robustly propagating design modifications to the decomposed representation makes any attempt to update the mesh very challenging. In this paper, a virtual topology workflow enabling automatic generation of hex-dominant meshes is extended to propagate parametric modifications and feature changes to the decomposition and resulting mesh. Geometric and topological modifications are identified and linked to the decomposition through virtual topology relationships. Modified regions are localized and reasoning on the virtual decomposition enables their definition and associated meshing strategy to be updated. Instead of starting the meshing process from the beginning, only modified cells are re-meshed. This provides an efficient and automated method to propagate design changes down to the analysis model.

Generating fit-for-purpose CAD models from complex assemblies is time consuming for analysts. Tedious tasks include to identify and isolate the components of interest for the analysis, remove duplicate components, or correct inconsistent components’ interfaces are common for large assemblies during the product development process. In this paper a new approach to help engineers analyse the consistency of CAD assembly models is proposed. The method utilises a tensor factorisation technique developed for relational machine learning and applies it on B-Rep topological and geometrical relations. The generated decomposition is used to identify which entities in the assembly are similar (within a threshold) to a selected input entity. The factorisation model regards globally all input relationships, e.g. the connections between components, to identify similar entities based on their relationships in the relational domain. It is shown that a hierarchical clustering method can group entities based on the similarities of their attributes and relationships.

In this work, a novel method for creating decompositions of general 3D domains, suitable for hexahedral mesh generation is presented. To accomplish this, frames and cross-fields are generated on top of the medial object of the domain. The geometrical and topological information carried by the medial object, together with the directional information of the frames/crosses help analyze the domain. By generating frames and cross fields on medial vertices, edges and faces based on touching vectors, a directional field is constructed on top of the medial object. Based on it, critical lines in the domain called, singularity lines, are identified. Starting from these, a complete line network is created on the interior of the domain. This network is extruded to the boundary in order to create the boundary of high-quality partitioning surfaces that are used to decompose the domain into regions appropriate for a high-quality hexahedral mesh. Examples are given to validate the method.

Adjoint methods have proven to be an efficient way of calculating the gradient of an objective function with respect to a shape parameter for optimisation, with a computational cost nearly independent of the number of the design variables [1]. The approach in this paper links the adjoint surface sensitivities (gradient of objective function with respect to the surface movement) with the parametric design velocities (movement of the surface due to a CAD parameter perturbation) in order to compute the gradient of the objective function with respect to CAD variables. For a successful implementation of shape optimization strategies in practical industrial cases, the choice of design variables or parameterisation scheme used for the model to be optimized plays a vital role. Where the goal is to base the optimization on a CAD model the choices are to use a NURBS geometry generated from CAD modelling software, where the position of the NURBS control points are the optimisation variables [2] or to use the feature based CAD model with all of the construction history to preserve the design intent [3]. The main advantage of using the feature based model is that the optimized model produced can be directly used for the downstream applications including manufacturing and process planning.This paper presents an approach for optimization based on the feature based CAD model, which uses CAD parameters defining the features in the model geometry as the design variables. In order to capture the CAD surface movement with respect to the change in design variable, the “Parametric Design Velocity” is calculated, which is defined as the movement of the CAD model boundary in the normal direction due to a change in the parameter value.The approach presented here for calculating the design velocities represents an advancement in terms of capability and robustness of that described by Robinson et al. [3]. The process can be easily integrated to most industrial optimisation workflows and is immune to the topology and labelling issues highlighted by other CAD based optimisation processes. It considers every continuous (“real value”) parameter type as an optimisation variable, and it can be adapted to work with any CAD modelling software, as long as it has an API which provides access to the values of the parameters which control the model shape and allows the model geometry to be exported. To calculate the movement of the boundary the methodology employs finite differences on the shape of the 3D CAD models before and after the parameter perturbation. The implementation procedure includes calculating the geometrical movement along a normal direction between two discrete representations of the original and perturbed geometry respectively. Parametric design velocities can then be directly linked with adjoint surface sensitivities to extract the gradients to use in a gradient-based optimization algorithm.The optimisation of a flow optimisation problem is presented, in which the power dissipation of the flow in an automotive air duct is to be reduced by changing the parameters of the CAD geometry created in CATIA V5. The flow sensitivities are computed with the continuous adjoint method for a laminar and turbulent flow [4] and are combined with the parametric design velocities to compute the cost function gradients. A line-search algorithm is then used to update the design variables and proceed further with optimisation process.

The aim of this work is to investigate an efficient CAD based adjoint process chain for calculating sensitivities of the objective function to the CAD parameter in time scales acceptable for industrial design processes.