Multiresolution Topology Optimization of Large-Deformation Path-Generation Compliant Mechanisms with Stress Constraints

Topology optimization is a powerful numerical tool in the synthesis of lightweight structures and compliant mechanisms. Compliant mechanisms present challenges for topology optimization, as they typically exhibit large displacements and rotations. Path-generation mechanisms are a class of mechanisms that are designed to follow an exact path. The characteristics of compliant mechanisms therefore exclude the validity of linear finite-element analysis to ensure the proper modeling of deformation and stresses. As stresses can exceed the limit when neglected, stress constraints are needed in the synthesis of compliant mechanisms. Both nonlinear finite-element analysis as well as the consideration of stress constraints significantly increase computational cost of topology optimization. Multiresolution topology optimization, which employs different levels of discretization for the finite-element analysis and the representation of the material distribution, allows an important reduction of computational effort. A multiresolution topology optimization methodology is proposed integrating stress constraints based on nonlinear finite-element analysis for path-generation mechanisms. Two objective formulations are used to motivate and validate this methodology: maximum-displacement mechanisms and path-generation mechanisms. The formulation of the stress constraints and their sensitivities within nonlinear finite-element analysis and multiresolution topology optimization are explained. We introduce two academic benchmark examples to demonstrate the results for each of the objective formulations. To show the practical, large-scale application of this method, results for the compliant mechanism structure of a droop-nose morphing wing concept are shown.

Design of Phononic Materials Using Multiresolution Topology Optimization

In this work the Multiresolution Topology Optimization (MTOP) scheme is investigated to obtain high resolution designs of phononic (elastic) materials, focusing primarily on acoustic waveguides. We demonstrate via numerical examples that the resolution of the design can be significantly improved without refining the finite element mesh. The first one is the simplest case where one might be interested in maximizing the energy reaching certain parts of the domain. The second and more interesting example is the creation of different propagation patterns for different frequencies, thus creating smart filters. The results demonstrate the power and potential of our computational framework to design sophisticated acoustic wave devices.