Form-finding and structural analysis of deployable rigid folding structures using synchronized vector-based graphic statics and finite element method

This paper presents a computational framework for designing and analysing deployable rigid folding plate structures by integrating Vector-based Graphic Statics (VGS) and Finite Element Method (FEM). To ensure consistent data flow from crease pattern generating to structural analysis and form-finding, a matrix-based data structure is utilized to represent the topology and geometry of the folding structure. An algorithm applied to this data structure enables simulation of the folding kinematics within a particle-based physical system, and solving for static equilibrium in the folded states to construct the discrete stress field model with VGS. This model provides a concise representation of edge and in-plane static equilibrium in a folded state. Additionally, the data structure maintains uniform detail levels between VGS and FEM by aligning mesh subdivision in FEM with the discrete stress field in VGS. Two case studies demonstrate the effectiveness and intuitiveness of the proposed method in limit state analysis by evaluating the multiple folded states of a continuous folding procedure, and in topological navigating and optimizing the folding crease pattern related to the performance of the deployable form. The research highlights advancements in the rapid, visually informed design process and concludes that this integrated approach serves as both a tool for engineers and a collaborative framework for architects and engineers in architectural design.