Analysis of anisotropic Mindlin plate model by continuous and non-continuous GFEM

Effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for GFEM/XFEM stress approximations around brittle cracks

“…Extrinsic enrichment is characterized by adding unknowns to the nodes, such that each additional unknown is associated with a new applied enrichment functions (see, for instance, [24][25][26][27][28]). Therefore, the PoU functions can be called "pasting functions" as they bring about implicit domain discretization (defining compact supports), merge various local approximations by performing an unbiased average, and determine their order or continuity across element boundaries [29].…”

“…In the former method, the resultant PoU exhibits C 0 regularity while the exponential edge functions in the Edwards method lead to C ∞ PoU. It is also clear that Wachspress-based smoothed FEM and the C k -GFEM are completely free of geometrical restrictions and, as both are directly computed in physical coordinates, they can be highly appropriate for distorted meshes (see [34,27]). …”

“…Furthermore, imposing an essential boundary condition is difficult in both PoU constructions. For example, a strong-form essential boundary condition enforcement is not trivial for general boundaries and even homogeneous conditions demand some care in conventional GFEM approximations [26,27].…”

Comparative Analysis of Ck- and C0-GFEM Applied to Two-dimensional Problems of Confined Plasticity

“…Figure 3 and Table 1 show the norm of the relative error of the radial displacement at outer face versus degrees of freedom obtained via C 0 -GFEM and C k -GFEM for the maximum pressure level (P = 0.18 GPa). On notice that b = p +1 to C 0 PoU and b = p to C k PoU, where p is the degree of the polynomial enrichment, as identified in Mendonça et al (2011). The relative error of the radial displacement is computed by , where and are the exact (Hill, 1950) and approximated displacements, respectively.…”

“…Some C 1 approximants applied to problems that require such regularity, as Hermitian functions commonly used in thin plate bending problems, for instance, are very restrictive and do not favor a systematic procedure for building such functions for general element shapes or to allow p-refinement. Some approaches that exploit some benefits of C k -GFEM approximations in plate bending problems were presented in Barcellos et al (2009), Mendonça et al (2011 and Mendonça et al (2013).…”