Finite Element Analysis

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A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics (2013, neutral): “The weak formulation of the problem above is given by the Principle of Virtual Work, which reads: Find u ∈ E (Ω) such that, ∀ v ∈ E (Ω) B(u,v) = F(v) (9) where B(u,v) = ∫ Ω σ (u) : ε (v)dA F(v) = ∫ ∂Ω t̄ · vds and E (Ω) is the energy space [39] with norm ‖ ·‖E (Ω) = √ B(·, ·)”
Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method (2012, methodology): “The high-order basis originally applied in the FCM [28, 29] uses a regular mesh of elements of the p-version of the finite element method, introduced by Szabó and Babuška [30,31,49,50].”
Extraction of stress intensity factors from generalized finite element solutions (2005, methodology): “The inverted S-curve, typical of p-convergence of the error in energy norm when geometric meshes are used [12,13], is clearly visible in the results obtained with the GFEM.”
The p-Version of the Finite Element and Finite Cell Methods (2017, methodology): “When the material is isotropic, φi(ν) are polynomials; when the shell is laminated, φi(ν) are piecewise polynomials (Szabó and Babuška, 1991; Actis et al., 1999).”