Accurate Discrete Simulation of Plates and Shells via Mid-Edge Formulation

Abstract Thin plates and shells are central to emerging technologies such as deployable space structures, wearable devices, and flexible electronics, where large geometric nonlinearities are not only unavoidable but often exploited for functionality. While the widely used bar-and-hinge model in the discrete differential geometry approach offers computational simplicity, it lacks physical consistency and suffers from mesh-dependent artifacts, limiting its predictive capability. In this technical brief, we show that the mid-edge-based formulation can provide an accurate and consistent simulation for thin plates and shells. By constructing discrete analogs of the first and second fundamental forms from a mesh and its edge-adjacent neighbors, the method naturally recovers in-plane and bending strain tensors and their associated strain energy. Benchmark comparisons against finite element simulations demonstrate that the mid-edge model achieves superior accuracy, stronger consistency, and faster convergence than the bar-and-hinge formulation. Crucially, the method delivers mesh-shape-independent convergence, enabling robust modeling of geometrically nonlinear responses on arbitrary meshes. These advantages make the framework highly suitable for rapid simulation, optimization, and inverse design of morphable and programmable plate structures, with potential applications in metasurfaces, kirigami, and origami-inspired systems.