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Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.


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TL;DR: In this article, a 3D low-order element, identified as HIS, is proposed for analysis of both linear and non-linear problems including finite strain plasticity, which is shown to be suitable in the analysis of linear problems and general nonlinear problems.
Abstract: The now classical enhanced strain technique, employed with success for more than 10 years in solid, both 2D and 3D and shell finite elements, is here explored in a versatile 3D low-order element which is identified as HIS. The quest for accurate results in a wide range of problems, from solid analysis including near-incompressibility to the analysis of locking-prone beam and shell bending problems leads to a general 3D element. This element, put here to test in various contexts, is found to be suitable in the analysis of both linear problems and general non-linear problems including finite strain plasticity. The formulation is based on the enrichment of the deformation gradient and approximations to the shape function material derivatives. Both the equilibrium equations and their variation are completely exposed and deduced, from which internal forces and consistent tangent stiffness follow. A stabilizing term is included, in a simple and natural form. Two sets of examples are detailed: the accuracy tests in the linear elastic regime and several finite strain tests. Some examples involve finite strain plasticity. In both sets the element behaves very well, as is illustrated in numerous examples. Copyright © 2003 John Wiley & Sons, Ltd.

104 citations

Journal ArticleDOI
TL;DR: In this paper, structural and loading uncertainties, bounded from above and below, are considered within a finite-element formulation to determine conservative bounds for the displacement and force response quantities, illustrated using a linear elastic beam.
Abstract: Structural and loading uncertainties, bounded from above and below, are considered within a finite-element formulation to determine conservative bounds for the displacement and force response quantities. Discretization of a continuum with material uncertainties is illustrated using a linear elastic beam. This yields the elements of the stiffness matrix with uncertainties and the components of the force vector with uncertainties, to be defined in bounded intervals. Then, the response quantities become uncertain, yet bounded, in a multidimensional rectangular prism. The discretized linear static interval equation is solved using the triangle inequality and linear programming to determine the conservative bounds for the response quantities. For the case when only loading uncertainties are considered, the problem reduces to the pattern loading problem of structural design. The proposed formulation is applied to the structural analysis of frames with material uncertainty under static loads with uncertainties.

104 citations

Journal ArticleDOI
TL;DR: In this article, an incrementally linear elastic, orthotropic constitutive model is suggested to represent the equivalent continuum pre-failure mechanical behavior of the jointed rock mass by incorporating the effect of joint geometry network by the fracture tensor components.

104 citations

Journal ArticleDOI
TL;DR: A large strain nonlinear elastic isotropic "split" law is proposed for modeling the behaviour of the periodontal ligament for a better description of the stiffening response of this tissue and, concomitantly, for a more accurate calibration of its elastic properties.
Abstract: A large strain nonlinear elastic isotropic "split" law is proposed for modeling the behaviour of the periodontal ligament. This law allows for a better description of the stiffening response of this tissue and, concomitantly, for a more accurate calibration of its elastic properties. Indeed, fine finite element simulations of an upper human incisor attached to its surrounding alveolar bone by an intermediate layer of ligament were run using that "split" law for the ligament. A good correlation was established with available experimental data on such a tooth under axial loading. Values of 0.010-0.031 MPa for the initial Young's modulus and of 0.45-0.495 for Poisson's ratio were determined. A sensitivity analysis of the results with respect to material and numerical parameters of the model was also carried out. Finally, a comparison of the simulation results using this "split" law with standard ones obtained with the linear elastic law, shows a significant improvement.

104 citations

Journal ArticleDOI
TL;DR: It is shown that the homogeneous least-squares functional is elliptic and continuous in the H({\rm div};\,\Omega)^d \times H^1(\Omega]^d$ norm, which immediately implies optimal error estimates for finite element subspaces of the L2 norm.
Abstract: This paper develops least-squares methods for the solution of linear elastic problems in both two and three dimensions. Our main approach is defined by simply applying the L2 norm least-squares principle to a stress-displacement system: the constitutive and the equilibrium equations. It is shown that the homogeneous least-squares functional is elliptic and continuous in the $H({\rm div};\,\Omega)^d \times H^1(\Omega)^d$ norm. This immediately implies optimal error estimates for finite element subspaces of $H({\rm div};\,\Omega)^d \times H^1(\Omega)^d$. It admits optimal multigrid solution methods as well if Raviart--Thomas finite element spaces are used to approximate the stress tensor. Our method does not degrade when the material properties approach the incompressible limit. Least-squares methods that impose boundary conditions weakly and use an inverse norm are also considered. Numerical results for a benchmark test problem of planar elasticity are included in order to illustrate the robustness of our ...

103 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202386
2022223
2021318
2020317
2019312
2018335