Cell-based Maximum Entropy Approximants for Three-Dimensional Domains: Application in Large Strain Elastodynamics using the Meshless Total Lagrangian Explicit Dynamics Method

We present the Cell-based Maximum Entropy (CME) approximants inE3space by constructing thesmooth approximation distance function to polyhedral surfaces. CME is a meshfree approximation methodcombining the properties of the Maximum Entropy approximantsand the compact support of element-basedinterpolants. 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. Theaccuracy and efficiency of the method is assessed in several numerical examples in terms of computationaltime, accuracy in boundary conditions imposition, and strain energy density error. Due to the smoothnessof CME basis functions, the numerical stability in explicittime 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 essentialboundary conditions are imposed directly, similar to the Finite Element Method. CME is proven a valuablealternative to other meshless and element-based methods for large-scale elastodynamics in 3D. Copyrightc©2019 John Wiley & Sons, Ltd