## 2 Fundamentals and State of the Art
### Morphing  
As this paper focuses on morphing FE models in the digital design phase, we give a brief overview over morphing techniques with special application on FE meshes. Morphing is also called mesh warping or mesh moving in the literature [10] and originates from animations or special effects, where meshes change from a source to a target shape [3]. In this paper, we do not go into mathematical detail, as there are many specific publications on this topic, for example [11]. Volumetric FE meshes consist of nodes that define volumetric elements like e.g., tetrahedrons or hexahedrons [11]. We call this set of elements, forming the component, FE mesh. Besides volumetric elements, there are also 1D and 2D FE elements like beams or shells. We do not mention them separately here, but all used methods in this paper apply to them, too. Morphing FE meshes usually only moves its nodes in space [3] (p. 4), without changing the element connectivity [6] (p. 1653). As long as the mesh quality stays inside defined boundaries, no remeshing, mesh relaxation or smoothing is necessary [3; 12]. This is especially problematic, when morphing distances become large or areas with different morphing directions collide. Due to that, a constant monitoring of mesh quality criteria is required [3]. Those include for example distortion on element level or smoothness and cross sections on component level [3] (p. 21), [8] (p. 307), [13] (p. 22). Moreover, [11] uses morphing to find the transition process from an initial to a target 3D model. For our application, only the resulting 3D model is relevant, not the transition. Nevertheless, the feature preservation described by [11] (p. 180) is necessary in our approach, too. His example of the feature preservation directly transfers to technical features like screw holes or bushings. In order to control the morphing process, there are three types of nodes: control nodes, free nodes and fixed nodes [3] (p. 6). The second type receives different names in literature, for example deformable nodes. As we deform the mesh but not the node itself, we prefer the term free. In literature, there are mainly two different approaches for morphing FE meshes with varying naming. For example, [3] distinguish between Direct Morphing and a control-based approach. In this paper, we use both methods and explain our implementations in Sections 3.1 and 3.2 respectively. We compare their application and results in Sections 3 and 4 respectively. The Direct Morphing approach is slightly altered here. We label our two approaches Direct Morphing and Box Morphing. Application of Morphing  
Morphing techniques serve many different applications and purposes. The following examples are relevant for our work and thus presented here. In automotive applications, [3] investigate the influences of the roof curvature, the windshield angle, the wheel base and the subframe shape on eigenfrequencies, airborne and structure-born noise. These are large-scale investigations on a full vehicle level, contrary to the approach presented in this paper, where we focus on component level. They use their control block morphing model as a direct input into the optimization chain, which differs from the approach presented in this paper using metamodels. Similarly, [14] perform an investigation on a body in white. They use and compare morphing approaches to modify connection elements between 1D FE elements. They use _NX NASTRAN_'s _SOL200_[15] to optimize geometry parameters [14]. Furthermore, [12] use a morphing approach to implement geometric imperfections onto an FE mesh. This enables them to perform a robustness evaluation of the geometrical tolerances on brake squeal and vibration transfer through the knuckle [12; 16]. In another publication, [13] use a statistical approach to approximate random brake pad designs in order to investigate robustness [13]. They change FE nodes according to identified distribution parameters [16].