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We present the Cell-based Maximum Entropy (CME) approximants in E3 space byconstructing the smooth approximation distance function to polyhedral surfaces.CME is a meshfree approximation method combining the properties of the MaximumEntropy approximants and the compact support of element-based interpolants. Themethod is evaluated in problems of large strain elastodynamics forthree-dimensional (3D) continua using the well-established Meshless TotalLagrangian Explicit Dynamics (MTLED) method. The accuracy and efficiency of themethod is assessed in several numerical examples in terms of computationaltime, accuracy in boundary conditions imposition, and strain energy densityerror. Due to the smoothness of CME basis functions, the numerical stability inexplicit time integration is preserved for large time step. The challengingtask of essential boundary conditions imposition in non-interpolating meshlessmethods (e.g., Moving Least Squares) is eliminated in CME due to the weakKronecker-delta property. The essential boundary conditions are imposeddirectly, similar to the Finite Element Method. CME is proven a valuablealternative to other meshless and element-based methods for large-scaleelastodynamics in 3D.

international journal for numerical methods in engineering

Cell‐based maximum entropy approximants for three‐dimensional domains: Application in large strain elastodynamics using the meshless total Lagrangian explicit dynamics method