CAD/CAE integration: Updating the CAD Model after a Finite Element Method analysis

An RPI is a blog article introducing Research Papers and  Research Patent Application Publications realized by researchers from École de technologie supérieure (ÉTS) de Montréal, Québec, Canada.

The improvement of the simulation process requires an integration of the design and analysis models. There are two essential tasks in the design analysis process: (i) Computer Aided Design (CAD) which provides the geometric description of the model and (ii) the Finite Element Method (FEM) used for mechanical behaviour simulations. The interoperability between these two tasks reduces costs and improves product quality through the acceleration of design analysis loops. Our activity fits into this research orientation by providing a method to link the Finite Element (FE) analysis and the CAD model. This is done by reconstructing the CAD model from the FE analysis results (deformed mesh).  This paper proposes a method to update the CAD geometry from the deformed mesh. This approach allows for rebuilding the CAD model after analysis by extracting geometric information from the deformed mesh. An illustration of the developed method is discussed at the end of this paper.

1. Reconstruction of the CAD model from FEM results

The general algorithm allows for the reconstruction of CAD model as a Boundary Representation (BREP model). The BREP model describes not only geometrical information (surfaces, curves and points), but also topological information (faces, edges and vertices). The proposed algorithm is based on two main parts: to determine the topology and rebuild the geometry. We first build the BREP entities and then join them to build the deformed CAD model. BREP entities are defined using deformed mesh boundary nodes (faces mesh).

Fig. 2: Reconstruction algorithm

The general algorithm (Fig. 2) of reconstruction exploits information extracted from a triangulated surface obtained from the deformed mesh. In addition, a topological model describing how surfaces are inter-connected is provided. The main steps of the reconstruction algorithm are as follows:

• Identification of the mesh information for each CAD entity;
• Reconstruction of the CAD edges and vertices;
• Reconstruction of the CAD faces.

The last step is the most complicated phase in the CAD model reconstruction. Indeed, there are many difficulties in using  a direct interpolation method to generate the CAD face (surface) from the mesh: (i) the data modeling the surface consists of a triangulation of an unorganized set of points in the parametric space (u,v) of the reconstructed surface; (ii) the density of information (triangles, points) is not constant over the surface; (iii) in the case of faces with inner loops it is not easy to evaluate the surface, and mesh information (nodes) is not sufficient to calculate  B-Spline shape functions. Thus the weighted displacement estimation (WDE) method is used to solve any encountered difficulties and update the CAD surfaces (faces) after deformation.

2. Illustration

The proposed approach is developed by using Matlab and The Solidworks Application Programming Interface (API). The development is based on three main steps:

• Extraction of the mesh information from the FE results obtained by Solidworks Simulation and identification of the mesh information corresponding to each CAD entity (face, edge, vertex). This step is developed by using Solidworks API;
• Computation of the CAD entities (interpolation points, control points…) by using the information extracted in the last step. This step is developed under Matlab;
• Generation of the geometry and the topology of the CAD entity to obtain the final CAD model. This step is developed by using Solidworks API.

2.1 Example – crankshaft assembly

The first case represents the connecting rod of a crankshaft assembly. Figure 3 (b) presents the board conditions defined on the connecting rod CAD model. The connecting rod is loaded in compression (under prevailing gas pressure) and in tension (primarily due to inertia force).The analysis is realized in the compression phase (Fig 4 c-d).

After the extraction of the deformed mesh, the reconstruction of the curves (edges) is realised. It is a direct interpolation from the mesh information (section 3-2). To rebuild the surfaces (faces), the WDE method is used to move a regular lattice (computed on the initial surface) representing the interpolation points of the B-Spline surface. Face reconstruction is based on three steps:

• Generation of a regular lattice (in the u,v parametric space) of points on the initial CAD face before deformation (Fig. 3 (a));
• Moving the regular lattice of points by using the WDE method to fit the deformed mesh corresponding to face (Fig. 3 (c));
• Computation of the B-Spline surface parameters and reconstruction of the deformed CAD face (surface limited by loops – Fig. 3 (d)).

Fig. 3: Connecting rod model.

Figure 4 (e) presents a rebuilding of the deformed CAD model of the connecting rod.  New axes are computed on the deformed connecting rod model. This allows defining new mating constraints between the deformed part (connecting rod) and other parts of the assembly.

The assembly with deformed parts allows a virtual simulation of the assembly functioning (rod – crankshaft) with the deformed model (realistic model in the operating conditions). According to this simulation, the designer can discern possible collisions between parts, particularly between the connecting rod and crankshaft, and between the connecting rod and piston axis (Fig 4(f)).

Fig. 4: Illustration method – crankshaft assembly.

Table 1, Fig. 5, Fig.6, and Fig. 7 illustrate many quantitative criteria and results obtained by the reconstruction algorithm of the previous example (Fig.3). The reconstruction error is the distance between the interpolation point (node) and its projection on the reconstructed surface. The calculated errors are negligible compared to the node displacements.

Fig. 5: Colormap and its distribution of the surface nodes FEA displacements
results in 10-1 mm.

Fig. 6: Colormap and its distribution of error results in 10-4 mm.

Fig. 7: Error results (Red) and FEA displacement results (Bleu) of each surface nodes in millimeters. Vertical axis is the nodes identification number; the logarithmic horizontal axis is in millimeters.

Table 1: Quantitative criteria and results (Connecting rod).

 3. Research Paper

For a more comprehensive discussion about “CAD/CAE integration: Updating the CAD Model after a FEM analysis”, we invite you to read the following Research Paper:
Borhen Louhichi, Gad N. Abenhaim, Antoine S. Tahan. CAD/CAE integration: Updating the CAD Model after a FEM analysis. The International Journal of Advanced Manufacturing Technology, August 2014, DOI: 10.1007/s00170-014-6248-y. (PDF)