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Tian, R.; Yagawa, Genki
International Journal for Numerical Methods in Engineering, 71(4), p.473 - 503, 2007/07
Times Cited Count：16 Percentile：69.76(Engineering, Multidisciplinary)Rewards of using non-matching meshes are great in many aspects: sub-meshing a complex structure in a sub-structure-wise manner separately; selective local refinement; unlimited scalability guarantee for generating meshes, etc. However, when meshes do not match, a gluing algorithm is required to enforce inter-domain continuity. The non-matching mesh issue is avoidable or does not exist in a node-based or meshless discretization in meshless methods. Motivated by this, a gluing algorithm is developed based on meshless interpolation. The gluing is accomplished by continuous trial and test functions across non-matching meshes constructed using nodes only. Compared with Lagrange multiplier gluing - one of the most common approaches - the current algorithm has two significant benefits: (1) easier implementation in any dimension and (2) positive definite banded system matrices, not acting against equation solvers, and hence better suited for large-scale finite element analysis.
Tian, R.; Yagawa, Genki
International Journal for Numerical Methods in Engineering, 69(4), p.837 - 858, 2007/01
Times Cited Count：19 Percentile：73.54(Engineering, Multidisciplinary)A simplification of the 1984 Allman triangle is presented. It is found that this old element takes a typical form of the partition of unity approximation. The Allman's rotation presented in the partition of unity form offers merits and convenience in formulation and practical applications. The stiffness matrix of the 1984 Allman triangle, which is originally computed from the linear strain triangular element, can be obtained instead in a cheaper way from that of the constant strain triangular element. The constraint of the rotational terms during essential boundary treatment, which remains equivocal and ambiguous, is understood to be mandatory. The partition of unity notion enables a straightforward extension of the Allman's rotational dof to meshfree approximations.
Tian, R.; Matsubara, Hitoshi; Yagawa, Genki
International Journal for Numerical Methods in Engineering, 68(12), p.1209 - 1231, 2006/12
Times Cited Count：30 Percentile：79.75(Engineering, Multidisciplinary)Tetrahedral elements are indispensable to complex finite element structural analysis. Two existing and two newly developed advanced 4-node tetrahedrons are studied in this paper. The existing elements that use complicated displacement fields are significantly simplified. The spurious zero-energy modes typical of all these elements are identified to be rigid-body-alike modes and are found to be naturally suppressible, making it possible to avoid any stabilization techniques and unknown parameters in formulation. Through the simplified form, we connect these four tetrahedrons and view them in a general framework of the partition-of-unity-based approximation. This general view allows us to reveal many promising features of the newly developed tetrahedrons by comparing them with their existing counterparts: the newly developed tetrahedrons have straightforward formulation.
; Ninokata, Hisashi
International Journal for Numerical Methods in Engineering, 37(20), p.3397 - 3415, 1994/00
Times Cited Count：1 Percentile：34.3(Engineering, Multidisciplinary)None
