Abstract
AbstractThis work presents a meshfree particle scheme designed for arbitrary deformations that possess the accuracy and properties of the Finite-Element-Method. The accuracy is maintained even with arbitrary particle distributions. Mesh-based methods mostly fail if requirements on the location of evaluation points are not satisfied. Hence, with this new scheme not only the range of loadings can be increased but also the pre-processing step can be facilitated compared to the FEM. The key to this new meshfree method lies in the fulfillment of essential requirements for spatial discretization schemes. The new approach is based on the correspondence theory of Peridynamics. Some modifications of this framework allows for a consistent and stable formulation. By applying the peridynamic differentiation concept, it is also shown that the equations of the correspondence theory can be derived from the weak form. Likewise, it is demonstrated that special moving least square shape functions possess the Kronecker-$$\delta $$
δ
property. Thus, Dirichlet boundary conditions can be directly applied. The positive performance of this new meshfree method, especially in comparison to the Finite-Element-Method, is shown in the calculation of several test cases. In order to guarantee a fair comparison enhanced finite element formulations are also used. The test cases include the patch test, an eigenmode analysis as well as the investigation of loadings in the context of large deformations.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Mechanical Engineering,Ocean Engineering,Computational Mechanics
Reference52 articles.
1. Bathe KJ (2006) Finite Element Procedures. Pearson, 1995
2. Bazeley GP, Cheung YK, Irons BM, Zienkiewicz OC (1965) Triangular elements in bending-conforming and nonconforming solutions. In Proc. Conf. Matrix Methods in Structural Mechanics, Air Forces Inst. of Tech., Wright Patterson AF Base, Ohio
3. Belytschko T, Krongauz Y, Dolbow J, Gerlach C (1998) On the completeness of meshfree particle methods. Int J Numer Meth Eng 43(5):785–819
4. Belytschko T, Guo Y, Liu WK, Xiao SP (2000) A unified stability analysis of meshless particle methods. Int J Numer Meth Eng 48(9):1359–1400
5. Bode T (2021) Peridynamic Galerkin methods for nonlinear solid mechanics. Dissertation, Institut für Kontinuumsmechanik at Leibniz Universität Hannover
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