Shape-adaptive structures can be designed using topology optimization. In the literature, linear assumptions (small distortions and linear-elastic material behavior) are often made for this purpose. For the function of compliant structures, however, it is important to also realize large deformations. Therefore, non-linear assumptions are required for topology optimization (large distortions and non-linear material behavior). Similarly to conventional mechanisms, compliant structures are designed to map certain desired kinematics. This is already challenging when designing shape-adaptive compliant structures under linear assumptions. This is due to the fact that deformations of elastic structures are in principle load-dependent. The deformation can be divided into a desired (load-independent) and undesired (load-dependent) component. The desired deformations must be optimized so that they represent the desired kinematics. In order to suppress the undesired component, all possible load cases must be included in the optimization. However existing approaches only optimize the deformations for certain load cases and therefore cannot guarantee this. The authors have already solved this problem with the modal approach for the synthesis of structures with selective compliance [1]. Here, the eigenbehavior of the compliant structure is made the subject of the synthesis, which is why no load cases need to be included. In the case of non-linear assumptions, deformation states are specified during optimization that are located on the desired kinematics. The compliant structure is then optimized so that the desired deformation passes through these deformation states and is referred to as a path-generating structure. To the best of the authors' knowledge, an optimization approach for path-generating shape-adaptive structures is still missing in the literature. Therefore, the modal approach [1] is extended to non-linear assumptions in order to close this gap in the state of the art. For this purpose, it is equally applied to deformation states on the desired kinematics. The modified modal approach presented in this contribution is tested on a shape-adaptive path-generating structure whose surface is to deform independently of the direction of the applied load using a sinusoidal curve.