Finite Element Method

By Eiki Yamaguchi. 2014

2,756 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/cbbc8ed995eb3a18a00135edd72c5e82edf8b98c

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In Civil and Structural Engineering

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Citations in the corpus

Coupled hydromechanical‐fracture simulations of nonplanar three‐dimensional hydraulic fracture propagation (2018, background): “where C is the elasticity tensor in matrix form.(43) Matrix Kn+1 c is given by”
Accuracy and convergence properties of the fixed‐stress iterative solution of two‐way coupled poromechanics (2015, neutral): “Specifically, the mechanical problem employs a continuous Galerkin formulation [36] to track the deformation field.”
Next-Generation Parametric Reduced-Order Models (2013, neutral): “To that aim, let us first revisit the formulation used to derive stiffness matrices for brick-type elements [14, 15].”
Design of manufacturable 3D extremal elastic microstructure (2014, methodology): “It is discretized using finite elements and the stiffness matrix of the discretized structure (Zienkiewicz et al., 2005) can be written as K ¼ XN e¼1 Z Ve BT CeBdVe; ðA:1Þ where N denotes the finite elements number.”
Computation of limit and shakedown loads using a node‐based smoothed finite element method (2012, methodology): “Variational formulation of the NS-FEM In this section, we show that the variational basis of the NS-FEM can be derived from the modified Hellinger–Reissner variational principle [32].”
An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures (2015, methodology): “Finite element method [47,48] is used to solve Eq.”
Comparison of Local and Global Approaches to Digital Image Correlation (2012, background): “They are based upon variational formulations (as one would use in solid mechanics when resorting to, say, nite element formulations [22]).”
Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis (2015, background): “More detailed information on this formulation is found in standard textbooks on nonlinear finite element analysis [30, 31, 32].”
Estimation of the Compressive Strength of Corrugated Cardboard Boxes with Various Openings (2020, background): “where J is the in-plane Jacobian matrix [37,44,45]:”
Implementation of regularized isogeometric boundary element methods for gradient‐based shape optimization in two‐dimensional linear elasticity (2016, methodology): “Although different in the way of formulating shape and test functions, they share the same characteristic of lifting the strict connectivity requirements posed by the FEM.”
A Nitsche‐type formulation and comparison of the most common domain decomposition methods in isogeometric analysis (2014, methodology): “The variational formulation of the initial BVP (5a)–(5g) without consideration of the interface conditions is written as follows [41]: Find u 2 V such that h R u, vi0, C a.”
Single-variable formulations and isogeometric discretizations for shear deformable beams (2015, background): “, reduced integration and B̄-methods [8], assumed natural strain [9] and enhanced natural strain methods [10].”
Element differential method and its application in thermal‐mechanical problems (2018, background): “The stress tensor σij can be expressed in terms of the strain tensor εkl and the temperature T through the following constitutive relationship17: σij ¼ Dijklεkl−~kTδij; (2) where εkl ¼ 12 ∂uk ∂xl þ ∂ul ∂xk ; (3) Dijkl ¼ λδijδkl þ μ δikδjl þ δilδjk ; (4a) λ ¼ 2μν 1−2νð Þ ; (4b) ~k ¼ 2μ 1þ νð Þ 1−2ν k”
Cell‐centered finite volume discretizations for deformable porous media (2014, methodology): “the spatial terms in equations (4-5) are well established, and are the method of choice for most mechanical problems [25].”
Comparison of the absolute nodal coordinate and geometrically exact formulations for beams (2014, methodology): “This observation also explains the different continuity requirements at inter-element boundaries [10, 11]: because second derivatives appear in the ANCF strain-displacement relationships, C1 continuity is required at inter-element boundaries, whereas C0 continuity only is required for GEBF.”
The hp‐d‐adaptive finite cell method for geometrically nonlinear problems of solid mechanics (2012, background): “The best approximation property to the total strain energy states that the solution of a Galerkin FE scheme represents a least-squares best fit to the exact solution in terms of Equation (8) [2, 47].”
Finite strain fracture of 2D problems with injected anisotropic softening elements (2014, neutral): “[40]): ui 1⁄4 gi on Cgi ð3Þ rijnj 1⁄4 hi on Chi ð4Þ”