🤖 AI Summary
This work addresses self-weight-dominated gridshell structures by simultaneously optimizing topological connectivity and surface elevation to ensure all members carry purely compressive or tensile forces, thereby achieving both mechanical efficiency and geometric buildability. Methodologically, self-weight is innovatively modeled as a design-variable-dependent load, enabling—for the first time—the joint convex optimization of topology and geometry, thus overcoming the limitations of conventional sequential design paradigms. The approach integrates parametric surface discretization with the force density method within a second-order cone programming (SOCP) framework, guaranteeing global optimality and computational efficiency. Compared to standard 3D layout optimization, the proposed method achieves speedups of several orders of magnitude while delivering higher accuracy. Furthermore, it uncovers the nonlinear morphological evolution of optimal forms under increasing self-weight, directly generating lightweight, buildable shell geometries.
📝 Abstract
This manuscript presents an approach for simultaneously optimizing the connectivity and elevation of grid-shell structures acting in pure compression (or pure tension) 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 characteristics of this class of optimal structures. 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.