## 4 Conclusions  
The results of this work clearly demonstrate the necessity of both nonlinear finite-element analysis and stress constraints in the topology optimization of compliant mechanisms. To achieve this, multiresolution stress-constrained topology optimization with nonlinear finite-element analysis has been implemented for maximum displacement and path-generation mechanisms. Without stress constraints, the resulting topologies of the introduced problems exhibit stresses well beyond the limits, especially because of the formation of one-node hinges. Through proper choice of stress limits in concert with filtering parameters, designs were found that can function without violation of strength limits. As large displacements and rotations are actually desired with this design problem,  
Figure 11: Comparison of solutions for the compliant mechanism rib example. Figure 12: Morphing wing demonstrator based on topology optimization results showing undeformed and deformed states. nonlinear finite-element analysis is necessary to properly represent deformations, strains and stresses. These two aspects represent a challenge to its implementation, not only for the primal analysis but also in the calculation of the sensitivities. Based on a total Lagrangian formulation, we have derived the sensitivities of the objective and constraint functions via an adjoint methodology. The introduced topology optimization methodology is applied to two numerical examples with different objective functions: maximum displacement and path-following designs. For the former, we clearly show the different resulting optimal topologies from  
* linear finite-element analysis with volume constraint;
* linear finite-element analysis with volume and stress constraints;
* nonlinear finite-element analysis with volume constraint;
* nonlinear finite-element analysis with volume and stress constraints. Nonlinear analysis is necessary for the path-following design as linear analysis will not follow a curved path. By applying stress constraints to the path-generation design problem, an approach for the synthesis of fatigue resistant prescribed path following mechanisms is shown. Moreover, a novel methodology for the consideration of stress constraints in multiresolution topology optimization is introduced and applied to the examples for the path-generation mechanisms. As a conclusion, an engineering example of a mechanism designed for a morphing wing application is discussed, showing a possible practical application of the introduced methods. Future work will explore the reduction in the large amount of iterations (ca. 250) to increase computational efficiency, the extension of the path generation problem formulation to multiple output nodes as well as the expansion to a geometrically robust formulation. Other challenges include the high number of parameter values in the optimization formulation that have a large influence on the resulting topology and convergence. More specific knowledge about the influence and mutual interference of these parameters must be gained. Furthermore, the issue of unstable behavior in void elements and resulting ill-convergence is still not fully resolved for all types of problems. Although the interpolation scheme based on [PERSON] et al. [47] and applied in this work significantly improved the stability of the finite-element analysis, instabilities still occur in intermediate density elements. This problem could be resolved by a thorough study of the interpolation parameters of Equation (15). However, there are also promising recent approaches based on contact modeling theory, as shown by [PERSON] et al. [57], where the material strain energy function has been augmented with an energy associated with higher order strains. This approach penalizes only mesh bending and warping distortion in high strained low density elements and not homogeneous deformation states. It also introduces self-contact modeling with low additional computational cost, paving the way for the synthesis of compliant mechanisms making use of self-contact.