  We present the Cell-based Maximum Entropy (CME) approximants in E3 space by
constructing the smooth approximation distance function to polyhedral surfaces.
CME is a meshfree approximation method combining the properties of the Maximum
Entropy approximants and the compact support of element-based interpolants. The
method is evaluated in problems of large strain elastodynamics for
three-dimensional (3D) continua using the well-established Meshless Total
Lagrangian Explicit Dynamics (MTLED) method. The accuracy and efficiency of the
method is assessed in several numerical examples in terms of computational
time, accuracy in boundary conditions imposition, and strain energy density
error. Due to the smoothness of CME basis functions, the numerical stability in
explicit time integration is preserved for large time step. The challenging
task of essential boundary conditions imposition in non-interpolating meshless
methods (e.g., Moving Least Squares) is eliminated in CME due to the weak
Kronecker-delta property. The essential boundary conditions are imposed
directly, similar to the Finite Element Method. CME is proven a valuable
alternative to other meshless and element-based methods for large-scale
elastodynamics in 3D.
