A mesh-free single spline subdomain method for static analysis of Multi-Span Doubly Curved Arch structures

Purpose This study proposes a meshless Single Spline Subdomain Method (SSSM) for the static analysis of Multi-Span Doubly Curved Arch structures, aiming to overcome limitations of traditional finite element methods such as mesh sensitivity and computational intensity. Design/methodology/approach The SSSM divides the arch into subdomains discretized by uniformly distributed spline nodes. Displacement fields are approximated using cubic B-spline functions combined with orthogonal trigonometric series. The stiffness equations are derived and assembled without meshing, and the method is validated against ABAQUS simulations. Findings The proposed method demonstrates high accuracy, with relative errors below 7.5% for displacements, axial forces and bending moments. It also shows robustness in parametric analyses of thickness, elastic modulus, rise-span ratios and arch-foot dimensions. Originality/value This work introduces a novel semi-analytical and semi-numerical approach that eliminates traditional meshing, reduces modeling complexity and is applicable to irregular shell geometries, offering a computationally efficient alternative to conventional finite element analysis.