• 1

# Mesh morphing

In the field of numerical simulation, mesh-morphing is a technique to change an existing geometry or an existing FEM or CFD mesh by applying a specific distortion. In the original form of this method, the changes only apply to the positions of the nodes, so the connectivity of the elements is retained. The same applies to all other model definitions, such as loads, boundary conditions, contact settings, material data. In this way, a simulation model can be quickly adapted to a changed CAD geometry or a new geometry can be created without using a CAD model.

Change of geometry by mesh-morphing without re-meshing of the modified areas

If the method is limited to the pure re-positioning of the nodal points, sometimes strongly distorted elements occur with increasing deformation of the mesh. The area for possible modifications is thus limited. In order to overcome this limitation, morphing is often extended in practice by a re-meshing operation of the affected areas. In this way, even large changes in geometry can be implemented.

Change of geometry by mesh-morphing with re-meshing of the modified areas

An additional model description is required for mesh-morphing. This defines the rules according to which nodes of individual model areas can be distorted and under which conditions a re-meshing is carried out. There are two main variants for this approach, box-morphing and direct-morphing.

## Box-Morphing

In this variant of the method, one or more control volumes or control domains are created first, each enclosing a part of the original mesh. The simplest form of a control volume is a cube. The morphing domain can be adjusted by changing the position of the corner or control points. The nodes of the mesh enclosed in it follow this distortion in relation to their individual distances to the control points. The nodes belonging to adjacent control volumes only change their position if their control points have also undergone a change. The construction and division of the model into suitable control volumes depends on the task and requires some experience. The handling and parameterization of the morphing model can be simplified by taking into account symmetry conditions and the possibility to represent patterned arrangements, but also by nested control volumes.

## Direct-Morphing

In contrast to the practice described previously, direct-morphing does not create control volumes. Instead, the element area to be modified is defined directly on the model. The nodes belonging to the elements can be divided into three categories. The nodes that must not change their position form a subgroup. These are usually the boundary nodes at the interface to neighboring elements and other predefined areas that are subject to any restrictions. On the other hand, there are the nodes whose coordinates should be changed directly and specifically. The last group are the remaining nodes, which move with the changing ones. The amount and direction of the movement also depend here on the individual distances to the directly variable nodes.

Both variants offer advantages depending on the application and can be used in parallel in one model. In both cases, each morphing operation is also defined using different parameters. These can be addressed individually or grouped by an optimization algorithm which can be used to search for an optimal geometry.

## Relevance

Morphing has been a powerful alternative to the CAD-based approach of geometry adaptation for many years. By foregoing the step back into the CAD system, some time-consuming work steps are no longer necessary. Among other things, the required export from CAD and re-import into the preprocessor is no longer needed. The subsequent processes such as the cleaning of geometry, a complete or partial re-meshing and finally the assignment of all other model definitions are not necessary either.

Especially when it comes to complex models with many components and definitions or complicated geometries with many free-form surfaces, this method therefore offers big advantages. In addition to the pure working speed, the work quality is also increased in this way, as the number of work steps saved also reduces the possibility of errors.

Morphing is mainly used in the automotive industry, aerospace and in the development of rail vehicles. This is mainly due to the fact that the preprocessors that offer and support morphing are most widespread in these industries.

• 1

Warmesberg 24, 9450 Altstätten, Switzerland

+41 79 471 1612