A meshfree minimum length method

Abstract

A meshfree minimum length method (MLM) has been proposed for solids mechanics and heat conduction problems. In this method, both polynomial terms as well as modified radial basis functions (RBFs) are used to construct shape functions using arbitrarily distributed nodes based on the minimum length procedure. The shape functions constructed possess delta function property. The numerical examples show that the method achieves better accuracy than the finite element method especially for problems with steep gradients. Some numerical implementation issues for MLM are also discussed in detail.