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Assessment of Thermal Influence on an Orthodontic System by Means of the Finite Element Method. [PDF]

Bioengineering (Basel)
Petrescu SM, Rauten AM, Popescu M, Popescu MR, Popa DL, Ilie D, Duță A, Răcilă LD, Vintilă DD, Buciu G.   +9 more
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Generalizing the finite element method: Diffuse approximation and diffuse elements

Computational Mechanics, 1992
B. Nayroles, G. Touzot, P. Villon
semanticscholar   +3 more sources

Introduction to the finite element method

Finite Element Analysis, 2021
1. Let Ω = (−1, 1)× (0, 1). We consider the initial boundary value problem ut − uxx = 0, in Ω, (1a) u(±1, t) = 0, for 0 ≤ t ≤ 1, (1b) u(x, 0) = sin(nπx), n ∈ N. (1c) a) Give the analytical solution u(x, t) for general n ∈ N.
G. Nikishkov
semanticscholar   +1 more source

A new eigenvalue problem solver for thermo‐mechanical vibration of Timoshenko nanobeams by an innovative nonlocal finite element method

Mathematical methods in the applied sciences, 2021
In this study, size‐dependent thermo‐mechanical vibration analysis of nanobeams is examined. Size‐dependent dynamic equations are obtained by implementing Hamilton's principle based on Timoshenko beam theory and then combined with stress equation of ...
Hayri Metin Numanoğlu, H. Ersoy, B. Akgöz, Ö. Civalek   +3 more
semanticscholar   +1 more source

Finite element method for PCM solidification in existence of CuO nanoparticles

Journal of Molecular Liquids, 2018
In this investigation, CuO nanoparticles with various shapes are dispersed into the base fluid (water) to augment conduction mode during solidification process.
M. Sheikholeslami
semanticscholar   +1 more source

The Scaled Boundary Finite Element Method

, 2018
In the finite element method, a problem domain is divided into elements of simple geometries. The shapes of the finite elements are typically limited to triangles and quadrilaterals in 2D and tetrahedrons, wedges and hexahedrons in 3D. On these elements,
Chongmin Song
semanticscholar   +1 more source

A Multiscale Finite-Element-Method

Civil-Comp Proceedings, 1997
Abstract This paper describes a hierarchical overlay of a p -version finite element approximation on a coarse mesh and an h -approximation on a geometrically independent fine mesh. The length scales of the local problem may be some orders of magnitude below the scale of the global problem.
Rank, E., Krause, R.
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Curved Elements in the Finite Element Method. II

SIAM Journal on Numerical Analysis, 1973
Curved elements, introduced by the author in [13] and [14], which are suitable for solving boundary value problems of the second order in plane domains with an arbitrary boundary are discussed. An approximation theorem is proved, the Dirichlet problem for a ${\mathop W\limits^{\circ}} _2^{(1)} $-elliptic equation is considered as a model problem and ...
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An Introduction to Finite Element Methods

Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation, 2015
The most common techniques for obtaining numerical solutions to partial differential equations on non-trivial domains are (high order) finite element methods. The given domain is subdivided into simple geometric objects and an approximate solution is computed as a linear combination of locally supported basis functions.
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Nonconforming Elements in the Finite Element Method with Penalty

SIAM Journal on Numerical Analysis, 1973
Summary: A penalty method approach is used for achieving convergence of a finite element method using nonconforming elements. Error estimates are given.
Babuška, Ivo, Zlámal, Milos
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