Numerical Design of Compliant Lattice Structures

Abstract

The ultimate goal of engineering is to propose technological solutions that are as effective and efficient as possible. Popular approaches are Computer Aided Design (CAD), i.e., virtual design of products, and Computer Aided Engineering (CAE), i.e., virtual analysis of products. Within CAD, parameterized designs can be obtained based on splines – which also serve as a basis for isogeometric analysis, thereby not only enabling the seamless integration of CAD and CAE but even the adjoint-based numerical optimization of the proposed technological solutions.The performance of engineered solutions can often also be improved by incorporating lattice structures. One example from the field of structural mechanics are compliant lattices that result in desired mechanical properties of the overall structure. While complex lattice structures cannot be easily realized by conventional manufacturing processes, they are much more readily available since the advent of additive manufacturing. Furthermore, computational geometries of complex lattice structures can be generated by tiling, during which a desired shape is filled with varying instances of parameterized tiles.The integration of adjoint-based numerical optimization and compliant lattice structures is facilitated by utilizing a parameter spline. On the one hand, the parameter spline controls the resulting lattice structure; for example, when it represents a spatially-dependent thickness parameter used for tiling. On the other hand, the parameter spline also controls the size of the optimization problem when choosing its control variables as the optimization variables; for example, when they represent the thickness of a lattice which is to be optimized.The aim of this work is to advance the numerical design of compliant lattice structures. An existing framework is extended to also allow for more complex, multi-patch structural designs. Furthermore, the structural analysis is enhanced by adding the output of mechanical stresses. These additions enable the optimization of a complex structural design with respect to an appropriate objective.