Blending isogeometric analysis and local maximum entropy meshfree approximants

A stabilized formulation with maximum entropy meshfree approximants for viscoplastic flow simulation in metal forming

The finite element method is the reference technique in the simulation of metal forming and provides excellent results with both Eulerian and Lagrangian implementations. The latter approach is more natural and direct but the large deformations involved in such processes require remeshing-rezoning algorithms that increase the computational times and reduce the quality of the results. Meshfree me...

Smooth, second order, non-negative meshfree approximants selected by maximum entropy

We present a family of approximation schemes, which we refer to as second-order maximum-entropy (max-ent) approximation schemes, that extends the first-order local max-ent approximation schemes to second-order consistency. This method retains the fundamental properties of first-order max-ent schemes, namely the shape functions are smooth, non-negative, and satisfy a weak Kronecker-delta propert...

Maximum-entropy meshfree coordinates in computational mechanics

Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods

We present a one-parameter family of approximation schemes, which we refer to as local maximumentropy approximation schemes, that bridges continuously two important limits: Delaunay triangulation and maximum-entropy (max-ent) statistical inference. Local max-ent approximation schemes represent a compromise—in the sense of Pareto optimality—between the competing objectives of unbiased statistica...

Maximum-Entropy Meshfree Method for Compressible and Near-Incompressible Elasticity

Numerical integration errors and volumetric locking in the near-incompressible limit are two outstanding issues in Galerkin-based meshfree computations. In this paper, we present a modified Gaussian integration scheme on background cells for meshfree methods that alleviates errors in numerical integration and ensures patch test satisfaction to machine precision. Secondly, a lockingfree small-st...