The Finite Element Method

By R. W. Lewis, Perumal Nithiarasu, K. N. Seetharamu. 2005

2,787 citations recorded by the source corpus.

Subfields: Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/d1cc6fc43c535899a31568669524d25908ca19af

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In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

Simulation Methods for Guided Wave-Based Structural Health Monitoring: A Review (2015, methodology): “A wide variety of books and articles have been published on this topic to date, including Bathe [20], Hughes [105], Reddy [212], Zienkiewicz and Taylor [280–282], etc.”
Optimal convergence analysis for the extended finite element method (2011, positive): “Without loss of generality we may assume that γ1 ≥ γ2, and therefore γ1 ≥ α0 2 , where α0 ∈ (0, π3 ) is the minimal angle of all triangles of Th (equivalent to the regularity of the mesh thanks to Zlamal’s result [39]).”
Coupling of the meshfree and finite element methods for determination of the crack tip fields (2008, neutral): “The meshfree shape functions have been given in Section 2, and the interpolation formulation of FEM can be written as [22]”
Three-dimensional optimization of staggered finned circular and elliptic tubes in forced convection (2004, methodology): “D isoparametric, four-noded, linear element was implemented for the finite element analysis program, FEAP [10].”
Multiscale modeling and characterization of granular matter: From grain kinematics to continuum mechanics (2011, methodology): “So far, the backbone of our models has been furnished by numerical techniques such as the finite element method (FEM) (Belytschko et al., 2000; Hughes, 1987) and the discrete element method (DEM) (Cundall and Strack, 1979).”
A mortar method for energy‐momentum conserving schemes in frictionless dynamic contact problems (2009, methodology): “whereA denotes the standard assembly operator (see, for example, [21]).”
Reproducing kernel element method Part III: Generalized enrichment and applications (2004, methodology): “In the Part II of this work [27], two arbitrarily smooth, globally conforming, Im=Cn interpolation hierarchies have been constructed based on a so-called reproducing kernel element method (RKEM) [34], which combines the advantages of both the finite element method [5,10,24,32,33] and the meshfree me”
Theoretical and numerical analyses of chemical‐dissolution front instability in fluid‐saturated porous rocks (2008, methodology): “derive the analytical solution for the propagation of a planar dissolution front within a benchmark problem, the geometry of which can be accurately simulated using numerical methods such as the finite element method [28, 29] and the finite difference method.”
Efficient Analysis of High Dimensional Data in Tensor Formats (2012, methodology): “Zander the use of numerical integration in the usual FEM [46, 7, 51].”
On the numerical integration of three-invariant elastoplastic constitutive models (2003, neutral): “b Eigenvalues/eigenbases calculated from closed-form solution [16].”
Thermodynamic framework for coupling of non-local viscoplasticity and non-local anisotropic viscodamage for dynamic localization problems using gradient theory (2004, neutral): “…b nþ1 ¼ unþ1 ð166Þ having set ¼ 2Dt2 ; b nþ1 ¼ bnþ1 þ 1 u€n þ 1 2Dt u : n þ 1 2Dt2 un ð167Þ The above integration algorithm belongs to the popular class of time integrators termed the Newmark b-method using the generalized mid-point rule algorithm (e.g. Houghs, 1987; Zienkiewicz and Taylor, 1989).”
Dynamics of porous media at finite strain (2004, background): “Note that for the linear theory, 2b P c P 1=2 results in an unconditionally stable algorithm [58].”
Stress Intensity Factor Gauging by Digital Image Correlation: Application in Cyclic Fatigue (2007, neutral): “Q4P1-shape functions in the language of the finite element method [22]).”
Boussinesq-type modelling using an unstructured finite element technique (2004, methodology): “A description of the basic theory of the Galerkin approach may be found, for example, in Zienkiewikz and Taylor (1989).”