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Minimum norm solutions to linear elastic analysis problems

International Journal for Numerical Methods in Engineering, 1984
AbstractA basic problem in the linear elastic analysis is that of finding the vectors of stresses and strains, given a finite element model of a structure and a set of external loads. One purpose of this paper is to show that the problem is a special case of the minimum norm problem for underdetermined systems of linear equations.
Kaneko, I., Plemmons, R. J.
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Asymptotic analysis and boundary homogenization in linear elasticity

Mathematical Methods in the Applied Sciences, 2000
The authors consider a linear elastic problem posed in a domain of \(\mathbb{R}^3\) with homogeneous Dirichlet conditions imposed on small zones of \(\varepsilon\)-size \((\varepsilon\to 0)\) distributed on the boundary of the domain. Using the concept of a rich family of Borel subsets of the boundary and the epi-convergence arguments, they obtain the ...
El Jarroudi, M., Addou, A., Brillard, A.
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Analysis of a Staggered Discontinuous Galerkin Method for Linear Elasticity

Journal of Scientific Computing, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jeonghun J. Lee, Hyea Hyun Kim
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Material sensitivity analysis in homogenization of linear elastic composites

Archive of Applied Mechanics (Ingenieur Archiv), 2001
The author considers an heterogeneous elastic material assuming that the inclusions, which are periodically distributed, are built of a finite number of different disjoint materials. All the materials which are involved (the matrix and the inclusions) are supposed to be linear and transversely isotropic elastic materials.
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Linear Elastic Finite Element Analysis of Torsion

2013
In the following we shall see how finite elements based on the stress function concept may be derived in a fairly simple fashion.
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Shape sensitivity analysis in linear elastic fracture mechanics

Computer Methods in Applied Mechanics and Engineering, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Linear Elastic Stress Analysis of 2D Cracks

2012
To begin to understand fracture of materials, one must first know the stress and deformation fields near the tips of cracks. Thus the first topic in fracture mechanics is the linear elastic analysis of crack tip fields. The solutions derived here will be seen to violate the assumptions upon which linear elasticity theory is grounded.
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Mapped infinite elements in linear elastic stress analysis

1985
This paper considers the use of mapped infinite elements for modelling the far field response. The applicability of the technique is examined and the benefits of employing a combined finite/infinite element approach to the solution of unbounded geomechanical problems is then illustrated by one numerical example.
Marović, Pavao, Damjanić, Frano
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Design sensitivity analysis of multi-span non-linear elastic beam–columns with elastic supports

Structural and Multidisciplinary Optimization, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Linear dynamics of elastic helical springs: asymptotic analysis of wave propagation

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2009
Helical springs serve as vibration isolators in virtually any suspension system. A variety of theories to describe the dynamic behaviour of these structural elements, which involves interaction of flexural, torsion and longitudinal waves, can be found in the literature.
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