Error analysis of the element-free Galerkin method for a nonlinear plate problem

In this work, we derive a geometrically nonlinear plate model based on the Kirchhoff hypothesis and the large deflection hypothesis, and provide an error analysis of the corresponding element-free Galerkin method. The penalty method is employed to enforce boundary conditions. The error estimate explicitly depends on nodal spacing, number of monomial basis functions, continuity of weight functions, and penalty factors, which provides some practical choices among these key parameters in engineering applications. In addition, we offer guidance on selecting appropriate penalty factors to improve numerical accuracy. Numerical experiments, involving clamped square and circle plates with uniform and nonuniform nodes, as well as a plate model with a corner singularity, are presented to validate the theoretical results.