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Title: A meshfree cell-based smoothed point interpolation method for solid mechanics problems
Authors: Zhang, G.
Liu, G.-R. 
Keywords: meshfree methods
numerical methods
point interpolation method
strain smoothing
weakened weak form
Issue Date: 2010
Citation: Zhang, G.,Liu, G.-R. (2010). A meshfree cell-based smoothed point interpolation method for solid mechanics problems. AIP Conference Proceedings 1233 (PART 1) : 887-892. ScholarBank@NUS Repository.
Abstract: In the framework of a weakened weak (W2) formulation using a generalized gradient smoothing operation, this paper introduces a novel meshfree cell-based smoothed point interpolation method (CS-PIM) for solid mechanics problems. The W2 formulation seeks solutions from a normed G space which includes both continuous and discontinuous functions and allows the use of much more types of methods to create shape functions for numerical methods [1]. When PIM shape functions are used, the functions constructed are in general not continuous over the entire problem domain and hence are not compatible. Such an interpolation is not in a traditional H1 space, but in a G 1 space. By introducing the generalized gradient smoothing operation properly, the requirement on function is now further weakened upon the already weakened requirement for functions in a H1 space and G1 space can be viewed as a space of functions with weakened weak (W2) requirement on continuity [1-3]. The cell-based smoothed point interpolation method (CS-PIM) is formulated based on the W2 formulation, in which displacement field is approximated using the PIM shape functions, which possess the Kronecker delta property facilitating the enforcement of essential boundary conditions [3]. The gradient (strain) field is constructed by the generalized gradient smoothing operation within the cell-based smoothing domains, which are exactly the triangular background cells. A W2 formulation of generalized smoothed Galerkin (GS-Galerkin) weak form is used to derive the discretized system equations [2]. It was found that the CS-PIM possesses the following attractive properties: (1) It is very easy to implement and works well with the simplest linear triangular mesh without introducing additional degrees of freedom; (2) it is at least linearly conforming; (3) this method is temporally stable and works well for dynamic analysis; (4) it possesses a close-to-exact stiffness, which is much softer than the overly-stiff FEM model and much stiffer than the overly-soft node-based smoothed point interpolation method (NS-PIM) [4]; (5) the results of the present method are of better accuracy and higher convergence rate than the linear FEM model using the same set of triangular meshes. © 2010 American Institute of Physics.
Source Title: AIP Conference Proceedings
ISBN: 9780735407787
ISSN: 0094243X
DOI: 10.1063/1.3452296
Appears in Collections:Staff Publications

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