Multiscale Topology Optimization With a Strong Dependence on Complementary Energy

A discrete approach introduces a novel deep learning approach for generating fine resolution structures that preserve all the information from the topology optimization (TO). The proposed approach utilizes neural networks (NNs) that map the desired engineering properties to seed for determining optimized structure. This framework relies on utilizing parameters such as density and nodal deflections to predict optimized topologies. A three-stage NN framework is employed for the discrete approach to reduce computational runtime while maintaining physics constraints.A continuous representation that uses complementary energy (CE) methods to solve a representative element's homogenized properties consists of an embedded structure that is parametrically defined. Defining the meso-scale structure as a swept cross-section makes it possible to solve for force/displacement interactions by leveraging Castigliano's second theorem. Homogenization is used to find the equivalent material properties of a representative element; the properties are used to solve a compliant mechanism TO (CMTO). A direct stiffness method is used to provide a better alternative to homogenization by directly finding the force/displacement relationships. An RBF surrogate model is used in a multi-variate TO (MVTO) framework to find the relationship between the design parameter vector and the stiffness values, the sensitivities for the design parameter vector can be found by taking the derivate of the RBFs. The MVTO framework is compared against the homogenized approach to demonstrate the algorithm's efficacy. A visualization framework is presented that can display high-resolution textures on low-triangulation meshes to show regions of high stress or deformation.