Mesh morphing also offers the ability to guide the modification of the shape of the numerical model using the physics of the model itself. The morpher tool described next is the RBF Morph™ ACT extension for the ANSYS® Mechanical™ environment. The software was released in 2015 and is based on the ANSYS® Fluent™ Add On technology that has been available on the market since 2009 (www.rbf-morph.com). Since the first version, several features have been added to help engineers in their numerical simulation activities. One of the latest features introduced is the Biological Growth Method (BGM) approach for surface sculpting. The BGM was inspired by the observation of the behavior of biological tissues: in nature, the number of tissues increases if the stresses on the surfaces reach an activation value, which changes with the type of tissue. The same approach can be applied to structural components. Furthermore, material layers are added if the stress levels are above a threshold value, and eliminated when the stresses are below the threshold.

Fig. 3 - Parameters set-up in BGM sequential analysis

Fig. 4 - BGM surface sculpting applied to a cantilevered beam

Using the BGM approach for surface sculpting has two advantages: the maximum peak stresses can be reduced and the stress distribution in the model becomes more uniform. However, since the surface sculpting is guided by the stress distribution, the resulting shape can be very complex, and can only be created on the real physical object by using innovative additive manufacturing technologies. If the manufacturing process concerned is a traditional one (such as casting, machining, etc.), RBF Morph offers an additional
function that allows engineers to respect their manufacturing constraints. The coordinate filtering option allows engineers to replicate the modification of the shape in a specific position (e.g. the position in which the maximum stress was evaluated) and to apply it along a user-defined axis (Fig.2). Both Cartesian and cylindrical coordinates can be used as filters. The highest degree of automation can be achieved by linking RBF Morph surface sculpting based on BGM with the definition of the parameter-based Design Point in ANSYS® Workbench™. The analysis can be set up so that, after solving the baseline configuration (DP 0), the analysis results are used to perform the surface sculpting. The subsequent Design Point (DP 1) is generated from the morphed configuration of the previous DP. That is then resolved and the evaluated stress distribution is used to set up another surface sculpting step. Using Workbench parameters, this procedure can be repeated until the stress levels reach the desired optimal values, as shown in Fig.3. For example, it is possible to consider the problem of a cantilevered beam: beam theory tells us that the optimal configuration for this simple static structure has a parabolic profile. If BGM sculpting is performed on a beam of constant thickness where the upper and lower surfaces are those to be sculpted, it is possible to automatically reach the shape depicted in Fig.4, which has a parabolic profile, a uniform stress distribution and a reduction in mass of 33% compared to the initial configuration.

A second approach to surface sculpting with RBF Morph mesh morphing is the Adjoint approach. The Adjoint method is widely used in CFD simulations and has recently also been introduced in CSM problems. The output of the Adjoint solution consists of sensitivity to a defined objective function of a set of input parameters. If nodal surface displacements are set as input parameters, with the Adjoint method engineers can determine which surface node should be moved inwards or outwards. This information can be transferred to the RBF Morph set-up so that an automatic surface sculpting approach can be used.

Fig. 5 - BGM surface sculpting applied to a cantilevered beam

With the Adjoint approach, it is possible to define and use several objective functions as an optimization objective: not only stress level reduction (as in the BGM approach), but also mass reduction, compliance, and so on. For example, the optimization of a thick plate is shown in Fig.5. The free and undamped modes of the plate are extracted using an eigenvalue analysis. The optimization task aims to reduce the mass of the component by keeping the first eigenvalue above 1220Hz. Adjoint data was used to set up the mesh morphing, resulting in the optimized shape shown in Fig.5, which produced an initial eigenvalue of 1351.5Hz and a 20% mass reduction.

SACMI, an early adopter of the RBF Morph optimization since 2015, successfully used automated surface sculpting procedures in an exploratory study. The Italian company SACMI Imola S.C. is an international leader in the design of industrial plants. It supplies both machines and complete systems for the ceramics, metals, packaging, and food and beverage industries, and for the production of containers made of plastic and advanced materials. Due to the confidential industrial nature of the component analyzed (Fig.6), it is not possible to provide detailed data on the model. However, both automatic sculpting approaches were used to optimize the component’s stress levels. The Adjoint-based approach was successfully applied to the area identified in Fig.7a and resulted in a maximum stress reduction of 11.6% on the surface shown in Fig.7b.
The BGM approach was applied to three zones of the component (Fig.8), using the linear manufacturing constraint in hot spot area 1, the circular manufacturing constraint in hot spot area 2, and leaving the BGM algorithm free to sculpt the surface in hot spot 3 area. After 8 sequential steps, the maximum surface stress was reduced by 2.76% for hot spot 1, by 7.84% for hot spot 2, and by 8.12% for hot spot 3. Fig.9 shows the baseline and final meshes respectively, and the initial and final surface stress distributions for the three hot spots.

Fig. 6 - SACMI industrial component

Fig.7 - a) Area in which Adjoint-based sculpting was applied, b) resulting stress distribution

Fig.8 - Optimization of SACMI industrial component hot spots