A mesh-free minimum length method for 2-D problems

A mesh-free minimum length method (MLM) has been proposed for 2-D solids and heat conduction problems. In this method, both polynomials as well as modified radial basis functions (RBFs) are used to construct shape functions for arbitrarily distributed nodes based on minimum length procedure, which possess Kronecker delta property. The shape functions are then used to formulate a mesh-free method based on weak-form formulation. Both Gauss integration (GI) and stabilized nodal integration (NI) are employed to numerically evaluate Galerkin weak form. The numerical examples show that the MLM achieves better accuracy than the 4-node finite elements especially for problems with steep gradients. The method is easy to implement and works well for irregularly distributed nodes. Some numerical implementation issues for MLM are also discussed in detail.