In adjoint based shape optimization problems, after the sensitivities have been computed, there are two ways of dealing with the necessary changes to the mesh. The first one is re-meshing based on the new shape, while the second one is adapting the existing mesh (by moving the nodes) to fit the new shape. Re-meshing may be time consuming, as it is introduced as a separate step inside the optimization loop, and tedious as it may require by-hand manipulation. It also introduces inconsistencies in the process as the sensitivities have been computed at isoconnectivity. Morphing also has its share of challenges, namely maintaining the mesh quality (avoiding distorted and negative cells) while deforming it. Within this context, various mesh morphing techniques have been developed. The Spring Analogy [1] is simple but may suffer robustness issues. Laplacian smoothing [11] is suitable for translation but does not account for rotation. The linear elasticity approach [3] does not account for mesh anisotropy and is difficult to implement for general meshes because finite elements are used to solve the equations. Finally, the Radial Basis Functions [7] are promising but computationally heavy as the matrices involved are full, restricting the mesh size and complicating the implementation. The Rigid Motion Mesh Morpher approach, proposed in the present study, aims at overcoming the above-mentioned limitations, being more flexible and essentially mesh-less, since it does not require any inertial quantities or cell connectivities related to the mesh. Firstly, the set of boundary nodes (nodes defining the shape) of the mesh is identified. The prescribed motion of these nodes (their velocities) is known. Then, all nodes are grouped into “stencils” which are required to deform in an as-rigid-as-possible way. Hence, every stencil has a rotation velocity and a translation velocity. Those, along with the velocities of all internal nodes, form the set of unknowns. The as-close-to-rigid-as-possible motion is ensured by attempting to minimize a metric representing the difference of the actual deformation from a perfectly rigid motion (a translation plus a rotation). It will be shown that this quantity is related to the anisotropic deformation energy. Next, the resulting system of equations is solved, having the prescribed motion of the boundary nodes as boundary conditions. more...