Energy Theorems and Structural Analysis

Argyris, John; Kelsey, S. J.

doi:10.1108/eb032502

Cited by 56 publications

(42 citation statements)

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“…The concept of finite element analysis (FEA) can be seen as an extension of a common method in structural analysis: the division of a complex geometry into a series of smaller, geometrically simpler elements that possess joint continuity . Modern FEA is the culmination of the convergence of a number of developments taking place during the 1940s–1950s that included the development of matrix formulations for structural problems, the advancement of computers and computer based methods, methods of discretization, and stress analysis . FEA has expanded beyond its early limitations to become a relatively common technique in stress analysis as well as heat transfer, fluid flow, and electro‐magnetic field problems .…”

Section: Overview Of Finite Element Modeling and Analysismentioning

confidence: 99%

Finite Element Analysis as a Method to Study Molluscan Shell Mechanics

Lemanis

Zlotnikov

2017

Adv Eng Mater

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The clade Mollusca is a highly diverse and disparate group of terrestrial and aquatic invertebrates, the taxon containing over 100 000 known species including some of the most intelligent invertebrate animals. Their shells are exemplar systems in the study of biomechanics, biomineralization, and biomimetics. Research into understanding the superior biomechanical properties of the shell and how these properties relate to the animals ecology have required a diverse range of methods at multiple length scales; one particularly powerful method is finite element analysis. Finite element analysis is a robust engineering method that has a long-standing history in biomechanical research. This review summarizes the application of finite element analysis in the study of both the mechanical properties of different molluscan shell ultrastructures as well as macro-scale modeling of the shell. From the calculation of elastic constants to the origins of the strength of nacre and the relationship between shell folding and ecology, this article provides a window into how finite element analysis can further our understanding of mechanics and functional morphology.

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Section: Overview Of Finite Element Modeling and Analysismentioning

confidence: 99%

Finite Element Analysis as a Method to Study Molluscan Shell Mechanics

Lemanis

Zlotnikov

2017

Adv Eng Mater

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“…The challenge is to meld them into a seamless, monolithic simulation. The first such proposal implemented a coupling between molecular dynamics 18,19 (MD) and a finite element model 20,21 (FEM) implementation of continuum elastic theory using stress consistency as the boundary condition at the interface. 22 More recently, a dynamical instability in the original formulation has been eliminated through the use of a mean force boundary condition together with uniform symplectic time evolution.…”

Section: 2mentioning

confidence: 99%

Coarse-grained molecular dynamics: Nonlinear finite elements and finite temperature

2005

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Coarse-grained molecular dynamics (CGMD) is a technique developed as a concurrent multiscale model that couples conventional molecular dynamics (MD) to a more coarse-grained description of the periphery. The coarse-grained regions are modeled on a mesh in a formulation that generalizes conventional finite element modeling (FEM) of continuum elasticity. CGMD is derived solely from the MD model, however, and has no continuum parameters. As a result, it provides a coupling that is smooth and provides control of errors that arise at the coupling between the atomistic and coarse-grained regions. In this article, we elaborate on the formulation of CGMD, describing in detail how CGMD is applied to anharmonic solids and finite temperature simulations. As tests of CGMD, we present in detail the calculation of the phonon spectra for solid argon and tantalum in 3D, demonstrating how CGMD provides a better description of the elastic waves than that provided by FEM. We also present elastic wave scattering calculations that show the elastic wave scattering is more benign in CGMD than FEM. We also discuss the dependence of scattering on the properties of the mesh. We introduce a rigid approximation to CGMD that eliminates internal relaxation, similar to the Quasicontinuum technique, and compare it to the full CGMD.

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“…Courant [19431 first used such principles to solve the St. Venant torsion problem. It was, however, the works done by Turner et al [1956] and Argyris [1960], to name a few, which gave the finite element method impetus.…”

Section: Introductionmentioning

confidence: 99%