Topology and geometry optimization of grid-shells incorporating design-dependent self-weight loading

This manuscript presents the first approach that is capable of finding the optimal connectivity and elevation of grid-shell structures acting in pure compression (or pure tension) for long-span scenarios; i.e., under the combined effects of a prescribed external loading and the design-dependent self-weight of the structure itself. The method derived herein involves solving a second-order cone optimization problem, thereby ensuring convexity and obtaining globally optimal results for a given discretization of the design domain. Several numerical examples are presented, illustrating hitherto unknown or unconfirmed characteristics of this class of optimal structures. For example, it is found that, as self-weight becomes more significant, both the optimal topology and the optimal elevation profile of the structure change, highlighting the importance of optimizing both topology and geometry simultaneously from the earliest stages of design. It is shown that this approach can obtain solutions with greater accuracy and several orders of magnitude more quickly than a standard 3D layout/truss topology optimization approach. Python scripts and Rhino/Grasshopper files are provided for the examples shown.