A Meshfree RBF Partition-of-Unity Collocation Method for Structural Yield Design

This paper presents a radial basis function partition-of-unity method (RBF–PUM) nodal collocation framework for structural yield design based on kinematic limit analysis under monotonic proportional loading. Localised meshfree approximations are combined with nodal evaluation of the kinematic relations and a nodal area approximation of the dissipation and external-work functionals. The resulting norm-constrained optimisation problem is recast as a second-order cone programming (SOCP) problem without conventional element-wise Gauss quadrature. The numerical results show favourable resistance to volumetric locking under the investigated plane strain conditions while retaining the geometric flexibility of meshfree discretisations for complex geometries and localised collapse phenomena. Benchmark examples demonstrate stable numerical convergence, close agreement with analytical and published reference solutions, and consistent representation of localised plastic collapse mechanisms. A parametric investigation further clarifies the influence of the RBF shape parameter and support domain size on solution accuracy, dissipation-field localisation, numerical stability, and computational cost. Because the continuous functionals and incompressibility condition are enforced through discrete nodal approximations, the computed values are interpreted as kinematic collocation estimates rather than mathematically rigorous upper bounds in all parameter regimes. Overall, the results indicate that the proposed RBF–PUM–SOCP framework is an accurate and promising computational approach for structural yield design.