Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC‐PIM)

By Guirong Liu, Guiyong Zhang. 2008

203 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/22662fa843a0081a8e7eaf30062493ef9766d569

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

An edge-based smoothed finite element method for visco-elastoplastic analyses of 2D solids using triangular mesh (2009, result): “The upper bound property shown in the NS-PIM [16] was also found in the NS-FEM [15].”
Analysis of plates and shells using an edge-based smoothed finite element method (2009, background): “X. Cui · G. Li (B) · G. Zheng State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, 410082 Changsha, People’s Republic of China e-mail: gyli@hnu.cn X. Cui · G.-R. Liu Department of Mechanical Engineering, Centre for Advanced Computations in Engineering Science”
An edge-based smoothed finite element method (ES-FEM) for analyzing three-dimensional acoustic problems (2009, background): “More importantly, it has been found that LC-PIM can provide upper bound solution in energy norm for elasticity problems with homogeneous essential boundary conditions [15].”
Assessment of smoothed point interpolation methods for elastic mechanics (2010, background): “The strain smoothing operation in the smoothed PIMs creates an ‘equilibrium’ state of stress locally inside the smoothing domains and the ‘compatible’ displacements on all interfaces of the smoothing domains [53].”
A normed G space and weakened weak (W2) formulation of a cell-based smoothed point interpolation method (2009, methodology): “…edge-based domains, the edge-based smoothed finite element method (ES-FEM) [Liu, Nguyen and Lam (2008); Nguyen and Liu et al. (2008)] and the edge-based smoothed point interpolation method (ES-PIM) [Liu and Zhang (2008b)] have been developed in the settings of FEM and meshfree methods respectively.”
A GENERALIZED GRADIENT SMOOTHING TECHNIQUE AND THE SMOOTHED BILINEAR FORM FOR GALERKIN FORMULATION OF A WIDE CLASS OF COMPUTATIONAL METHODS (2008, methodology): “We found the results are good for these cases, as presented in this paper and in [Liu and Zhang (2005, 2008); Liu and Li (2006); Zhang et al. (2007); Li et al. (2007)], but we do not know precisely how good and why they are good.”
A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part I theory (2010, methodology): “Typical proven divisions that give sufficient number of independent smoothing domains are cell/element based as in the smoothed FEM or SFEM [7, 10] and CS-PIM [21], node based as in the NS-PIM [19, 26] and NS-FEM [27], as well as the edge/face based as in the ES-FEM [28, 29].”
A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements (2009, background): “DOI: 10.1002/nme.2491 A face-based smoothed finite element method (FS-FEM) for 3D linear and geometrically non-linear solid mechanics problems using 4-node tetrahedral elements T. Nguyen-Thoi1,∗,†, G. R. Liu1,2, K. Y. Lam3 and G. Y. Zhang1,2 1Center for Advanced Computations in Engineering Science (”
A novel twice-interpolation finite element method for solid mechanics problems (2010, background): “The simplex elements, including three-node triangle and four-node tetrahedron, have the simplest topological shape and good flexibility and adaptability to complex geometry [ 17 ].”
A novel singular node‐based smoothed finite element method (NS‐FEM) for upper bound solutions of fracture problems (2010, background): “The NS-FEM produces the upper-bound solutions, and is found in general to be overly soft [40], due to many elements participating in the node-based strain smoothing operation.”
An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields (2010, methodology): “[14,15] proposed a node-based smoothed point interpolation method (NS-PIM), which is formulated using the polynomial point interpolation method (PIM) [8] or the radial point interpolation method (RPIM) [16].”