Nonlinear Finite Elements for Continua and Structures

By Ted Belytschko, Wing Kam Liu, Brian Moran. 2000

4,270 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Control and Systems Engineering, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/bed02db81d718d4173e61ab496d6ea686370d3eb

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In Civil and Structural Engineering

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Citations in the corpus

Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods (2012, background): “However, Rayleigh’s nested eigenvalue theorem [42] states that the maximum eigenvalue of a constrained system is always bounded by the maximum eigenvalue of an unconstrained system.”
Director‐based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates (2014, neutral): “[6].”
Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods (2008, background): “[26] for a discussion on the applications of multi-field methods.”
A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations (2011, methodology): “Both of them are used successfully with the FEM formulations, and solutions from both forms are equivalent [32].”
PHYSICS-BASED SIMULATION OF HIGH SPEED MACHINING (2002, methodology): “The most widely used explicit method is the central difference method with a diagonal or lumped mass matrix.([21]) When using the central difference method, the velocity is approximated using Eq.”
Cracking node method for dynamic fracture with finite elements (2009, neutral): “The strong form of the linear momentum equation in the current configuration can easily be developed by changing the kinetic and kinematic quantities of the strong form in the reference configuration 0; see Belytschko et al. [ 42 ] for a text-book account.”
A simplified mesh‐free method for shear bands with cohesive surfaces (2007, background): “[33]: A = C + σ ⊗ I (8) The vector n defines the direction of propagation and h is the polarization of the wave.”
Bridging Scale Methods for Nanomechanics and Materials (2006, methodology): “One possible approach that can be applied to many problems is to use MD only in localized regions in which the atomic-scale dynamics are important, and a continuum simulation method, such as the finite element (FE) [1,2] or meshfree methods [3–5] everywhere else.”