A meshless method for the nonlinear von Kármán plate with multiple folds of complex shape: A bridge between cracks and folds

Abstract

We present a meshless discretisation method for the solution of the non-linear equations of the von Kármán plate containing folds. The plate has Mindlin–Reissner kinematics where the rotations are independent of the derivatives of the normal deflection, hence discretised with different shape functions. While in cracks displacements are discontinuous, in folds, rotations are discontinuous. To introduce a discontinuity in the rotations, we use an enriched weight function previously derived by the authors for cracks (Barbieri et al. in Int J Numer Methods Eng 90(2):177–195, 2012). With this approach, there is no need to introduce additional degrees of freedom for the folds, nor the mesh needs to follow the folding lines. Instead, the folds can be arbitrarily oriented and have endpoints either on the boundary or internal to the plate. Also, the geometry of the folds can be straight or have kinks. The results show that the method can reproduce the sharp edges of the folding lines, for various folding configurations and compare satisfactorily with analytical formulas for buckling or load-displacement curves from reference solutions.