207 research outputs found
Differential Geometry applied to Acoustics : Non Linear Propagation in Reissner Beams
Although acoustics is one of the disciplines of mechanics, its
"geometrization" is still limited to a few areas. As shown in the work on
nonlinear propagation in Reissner beams, it seems that an interpretation of the
theories of acoustics through the concepts of differential geometry can help to
address the non-linear phenomena in their intrinsic qualities. This results in
a field of research aimed at establishing and solving dynamic models purged of
any artificial nonlinearity by taking advantage of symmetry properties
underlying the use of Lie groups. The geometric constructions needed for
reduction are presented in the context of the "covariant" approach.Comment: Submitted to GSI2013 - Geometric Science of Informatio
A comparison of Finite Elements for Nonlinear Beams: The absolute nodal coordinate and geometrically exact formulations
Two of the most popular finite element formulations for solving nonlinear beams are the absolute nodal coordinate and the geometrically exact approaches. Both can be applied to problems with very large deformations and strains, but they differ substantially at the continuous and the discrete levels. In addition, implementation and run-time computational costs also vary significantly. In the current work, we summarize the main features of the two formulations, highlighting their differences and similarities, and perform numerical benchmarks to assess their accuracy and robustness. The article concludes with recommendations for the choice of one formulation over the other
Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration Control
An embedded cohesive crack model for finite element analysis of quasi-brittle materials
This paper presents a numerical implementation of the cohesive crack model for the anal-ysis of quasibrittle materials based on the strong discontinuity approach in the framework of the finite element method. A simple central force model is used for the stress versus crack opening curve. The additional degrees of freedom defining the crack opening are determined at the crack level, thus avoiding the need for performing a static condensation at the element level. The need for a tracking algorithm is avoided by using a consistent pro-cedure for the selection of the separated nodes. Such a model is then implemented into a commercial program by means of a user subroutine, consequently being contrasted with the experimental results. The model takes into account the anisotropy of the material. Numerical simulations of well-known experiments are presented to show the ability of the proposed model to simulate the fracture of quasibrittle materials such as mortar, concrete and masonry
Existence theorems in the geometrically non-linear 6-parametric theory of elastic plates
In this paper we show the existence of global minimizers for the
geometrically exact, non-linear equations of elastic plates, in the framework
of the general 6-parametric shell theory. A characteristic feature of this
model for shells is the appearance of two independent kinematic fields: the
translation vector field and the rotation tensor field (representing in total 6
independent scalar kinematic variables). For isotropic plates, we prove the
existence theorem by applying the direct methods of the calculus of variations.
Then, we generalize our existence result to the case of anisotropic plates. We
also present a detailed comparison with a previously established Cosserat plate
model.Comment: 19 pages, 1 figur
An embedded cohesive crack model for finite element analysis of brickwork masonry fracture
This paper presents a numerical procedure for fracture of brickwork masonry based on the strong discontinuity approach. The model is an extension of the cohesive model prepared by the authors for concrete, and takes into account the anisotropy of the material. A simple central-force model is used for the stress versus crack opening curve. The additional degrees of freedom defining the crack opening are determined at the crack level, thus avoiding the need of performing a static condensation at the element level. The need for a tracking algorithm is avoided by using a consistent procedure for the selection of the separated nodes. Such a model is then implemented into a commercial code by means of a user subroutine, consequently being contrasted with experimental results. Fracture properties of masonry are independently measured for two directions on the composed masonry, and then input in the numerical model. This numerical procedure accurately predicts the experimental mixed-mode fracture records for different orientations of the brick layers on masonry panels
Minimum Energy Configurations in the -Body Problem and the Celestial Mechanics of Granular Systems
Minimum energy configurations in celestial mechanics are investigated. It is
shown that this is not a well defined problem for point-mass celestial
mechanics but well-posed for finite density distributions. This naturally leads
to a granular mechanics extension of usual celestial mechanics questions such
as relative equilibria and stability. This paper specifically studies and finds
all relative equilibria and minimum energy configurations for and
develops hypotheses on the relative equilibria and minimum energy
configurations for bodies.Comment: Accepted for publication in Celestial Mechanics and Dynamical
Astronom
Relative Equilibria for General Gravity Fields in the Sphere-Restricted Full 2-Body Problem
Reduction, Linearization, and Stability of Relative Equilibria for Mechanical Systems on Riemannian Manifolds
Análise não linear de chapas através de uma formulação do método dos elementos de contorno com convergência quadrática
No presente trabalho foi desenvolvida a formulação nĂŁo-linear do mĂ©todo dos elementos de contorno para a análise estrutural de chapas escrita em termos de deslocamentos e forças nas direções normal e tangencial ao contorno da sua superfĂcie. A equação integral do deslocamento Ă© deduzida a partir do Teorema de Reciprocidade de Betti, considerando-se espessura constante na chapa. Para calcular a integral de domĂnio envolvendo o campo de esforços iniciais (ou inelásticos) deve-se discretizar o domĂnio em cĂ©lulas. A solução nĂŁo linear se obtĂ©m por uma formulação implĂcita, na qual as correções das deformações sĂŁo feitas atravĂ©s do operador tangente consistente que se atualiza a cada nova iteração, tendo como referĂŞncia os valores das variáveis internas referentes ao incremento convergido, o que leva a uma convergĂŞncia quadrática do processo iterativo. Utilizou-se como critĂ©rio de ruptura o de von Misses e exemplos foram analisados a fim de mostrar a convergĂŞncia quadrática no processo iterativo e tambĂ©m a convergĂŞncia dos resultados numĂ©ricos a medida que se refinava a discretização do contorno em elementos e do domĂnio em cĂ©lulas
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