8,896 research outputs found
Application of Inverse Finite Element Method to Shape Sensing of Curved Beams
Curved beam, plate, and shell finite elements are commonly used in the finite element modeling of a wide range of civil and mechanical engineering structures. In civil engineering, curved elements are used to model tunnels, arch bridges, pipelines, and domes. Such structures provide a more efficient load transfer than their straight/flat counterparts due to the additional strength provided by their curved geometry. The load transfer is characterized by the bending, shear, and membrane actions. In this paper, a higher-order curved inverse beam element is developed for the inverse Finite Element Method (iFEM), which is aimed at reconstructing the deformed structural shapes based on real-time, in situ strain measurements. The proposed two-node inverse beam element is based on the quintic-degree polynomial shape functions that interpolate the kinematic variables. The element is C2 continuous and has rapid convergence characteristics. To assess the element predictive capabilities, several circular arch structures subjected to static loading are analyzed, under the assumption of linear elasticity and isotropic material behavior. Comparisons between direct FEM and iFEM results are presented. It is demonstrated that the present inverse beam finite element is both efficient and accurate, requiring only a few element subdivisions to reconstruct an accurate displacement field of shallow and deep curved beams
Reliable a-posteriori error estimators for -adaptive finite element approximations of eigenvalue/eigenvector problems
We present reliable a-posteriori error estimates for -adaptive finite
element approximations of eigenvalue/eigenvector problems. Starting from our
earlier work on adaptive finite element approximations we show a way to
obtain reliable and efficient a-posteriori estimates in the -setting. At
the core of our analysis is the reduction of the problem on the analysis of the
associated boundary value problem. We start from the analysis of Wohlmuth and
Melenk and combine this with our a-posteriori estimation framework to obtain
eigenvalue/eigenvector approximation bounds.Comment: submitte
Optimal Reconstruction of Inviscid Vortices
We address the question of constructing simple inviscid vortex models which
optimally approximate realistic flows as solutions of an inverse problem.
Assuming the model to be incompressible, inviscid and stationary in the frame
of reference moving with the vortex, the "structure" of the vortex is uniquely
characterized by the functional relation between the streamfunction and
vorticity. It is demonstrated how the inverse problem of reconstructing this
functional relation from data can be framed as an optimization problem which
can be efficiently solved using variational techniques. In contrast to earlier
studies, the vorticity function defining the streamfunction-vorticity relation
is reconstructed in the continuous setting subject to a minimum number of
assumptions. To focus attention, we consider flows in 3D axisymmetric geometry
with vortex rings. To validate our approach, a test case involving Hill's
vortex is presented in which a very good reconstruction is obtained. In the
second example we construct an optimal inviscid vortex model for a realistic
flow in which a more accurate vorticity function is obtained than produced
through an empirical fit. When compared to available theoretical vortex-ring
models, our approach has the advantage of offering a good representation of
both the vortex structure and its integral characteristics.Comment: 33 pages, 10 figure
Effect of Ductile Damage Evolution in Sheet Metal Forming: Experimental and Numerical Investigations
The numerical simulation based on the Finite Element Method (FEM) is widely used in academic institutes and in the industry. It is a useful tool to predict many phenomena present in the classical manufacturing forming processes such as necking, fracture, springback, buckling and wrinkling. But, the results of such numerical model depend strongly on the parameters of the constitutive behavior model. In the first part of this work, we focus on the traditional identification of the constitutive law using oriented tensile tests (0°, 45°, and 90° with respect to the rolling direction). A Digital Image Correlation (DIC) method is used in order to measure the displacements on the surface of the specimen and to analyze the necking
evolution and the instability along the shear band. Therefore, bulge tests involving a number of die shapes
(circular and elliptic) were developed. In a second step, a mixed numerical–experimental method is used for the identification of the plastic behavior of the stainless steel metal sheet. The initial parameters of the
inverse identification were extracted from a uniaxial tensile test. The optimization procedure uses a
combination of a Monte-Carlo and a Levenberg-Marquardt algorithm. In the second part of this work, according to some results obtained by SEM (Scaning Electron Microscopy)
of the crack zones on the tensile specimens, a Gurson Tvergaard Needleman (GTN) ductile model of damage
has been selected for the numerical simulations. This model was introduced in order to give informations concerning crack initiations during hydroforming. At the end of the paper, experimental and numerical comparisons of sheet metal forming applications are presented and validate the proposed approach
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