- Modified Finite Particle Method: applications to elasticity and plasticity problems
- D. Asprone ; F. Auricchio ; A. Reali
- Book Title / Journal: International Journal of Computational Methods
- Year: 2013 , Volume: , Series:
- Structural Analysis
- Keywords: Meshless methods ; Particle methods
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- Approximation of incompressible large deformation elastic problems: some unresolved issues
- F. Auricchio ; L. Beirão da Veiga ; C. Lovadina ; A. Reali ; R. Taylor ; P. Wriggers
- Book Title / Journal: Computational Mechanics
- Year: 2013 , Volume: 52 , Series:
- Structural Analysis
- Keywords: Incompressible nonlinear elasticity ; Stability ; Mixed finite elements
- Description
- Several finite element methods for large deformation elastic problems in the nearly incompressible and purely incompressible regimes are considered. In particular, the method ability to accurately capture critical loads for the possible occurrence of bifurcation and limit points, is investigated. By means of a couple of 2D model problems involving a very simple neo-Hookean constitutive law, it is shown that within the framework of displacement/pressure mixed elements, even schemes that are inf-sup stable for linear elasticity may exhibit problems when used in the finite deformation regime.The roots of such troubles are identified but a general strategy to cure them is still missing. Furthermore,
a comparison with displacement-based elements,
especially of high order, is presented.
- Abstract
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- The dimensional reduction modelling approach for 3D beams: Differential equations and finite-element solutions based on Hellinger–Reissner principle
- F. Auricchio ; G. Balduzzi ; C. Lovadina
- Book Title / Journal: International Journal of Solids and Structures
- Year: 2013 , Volume: 50 , Series:
- Structural Analysis
- Keywords: Linear elastic beam ; Mixed variational modelling ; Beam analytical solution ; Beam analytical solution Static analysis
- Description
- This paper illustrates an application of the so-called dimensional reduction modelling approach to obtain a mixed, 3D, linear, elastic beam-model.
We start from the 3D linear elastic problem, formulated through the Hellinger–Reissner functional, then we introduce a cross-section piecewise-polynomial approximation, and finally we integrate within the cross section, obtaining a beam model that satisfies the cross-section equilibrium and could be applied to inhomogeneous bodies with also a non trivial geometries (such as L-shape cross section). Moreover the beam model can predict the local effects of both boundary displacement constraints and non homogeneous
or concentrated boundary load distributions, usually not accurately captured by most of the
popular beam models.
We modify the beam-model formulation in order to satisfy the axial compatibility (and without violating equilibrium within the cross section), then we introduce axis piecewise-polynomial approximation, and finally we integrate along the beam axis, obtaining a beam finite element. Also the beam finite elements have the capability to describe local effects of constraints and loads. Moreover, the proposed beam finite element describes the stress distribution inside the cross section with high accuracy.
In addition to the simplicity of the derivation procedure and the very satisfying numerical performances, both the beam model and the beam finite element can be refined arbitrarily, allowing to adapt the model accuracy to specific needs of practitioners.
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- Mixed 3D Beam Models: Differential Equation Derivation and Finite Element Solutions
- F. Auricchio ; G. Balduzzi ; C. Lovadina
- Book Title / Journal: European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012)
- Year: 2012 , Volume: , Series:
- Structural Analysis
- Keywords: Hellinger-Reissner principle ; 3D beam model ; dimensional reduction ; mixed beam finite element
- Description
- In this document we illustrate the dimensional-reduction approach applied to 3D solid elastic equations in order to obtain a beam model.
We start from the Hellinger-Reissner (HR) principle, in a formulation which guarantees the selection of a compatible solution in a family of equilibrated fields. Then, we introduce a semidiscretization within the cross-section, this allows to reduce the problem’s dimension from 3D to 1D and to formulate the beam model. After a manipulation of the 1D weak model (done in order to guarantee the selection of an axis-equilibrated solution in a family of axis-compatible fields), we introduce a discretization along the beam axis obtaining the related beam Finite Element (FE).
On one hand, the initial HR principle formulation leads to an accurate stress analysis into the cross-section, on the other hand, the 1D model manipulation leads to an accurate displacement
analysis along the beam-axis. Moreover, the manipulation allows to statically condensate
stresses out at element level, improving the numerical efficiency of the FE algorithm.
In order to illustrate the capability of the method, we consider a slim cross-section beam that shows non trivial behaviour in bending and for which the analytical solution is available in literature. Numerical results are accurate in description of both displacement and stress variables, the FE solution converges to the analytical solution, and the beam FE models complex phenomena like anticlastic bending and boundary effects.
- Abstract
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- A finite strain kinematic hardening constitutive model based on Hencky strain: General framework, solution algorithm and application to shape memory alloys
- J. Arghavani ; F. Auricchio ; R. Naghdabadi
- Book Title / Journal: International Journal of Plasticity
- Year: 2011 , Volume: 27 , Series:
- Structural Analysis
- Keywords: Kinematic hardening ; Shape memory alloys ; Logarithmic strain
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- Performance evaluation of shape-memory-alloy superelastic behavior to control a stay cable in cable-stayed bridges
- O.B. Mekki ; F. Auricchio
- Book Title / Journal: International Journal of Non-Linear Mechanics
- Year: 2010 , Volume: , Series:
- Bridge management ; Bridges
- Keywords: Shape-memory alloys ; Superelastic
- Description
- This paper focuses on introducing and investigating the performance of a new passive control device for
stay cable in cable-stayed bridges made with shape-memory alloys (SMA). The superelasticity and
damping capability of SMA is sought in this study to develop a supplementary energy dissipation device
for stay cable. A linear model of a sag cable and a one-dimensional constitutive model for the SMA are
used. The problem of the optimal design of the device is studied. In the optimization problem, an energy criterion associated with the concept of optimal performance of the hysteretic connection is used. The maximum dissipation energy depends on the cross-sectional area, the length, and the location of the SMA on the cable. The effectiveness of the SMA damper in controlling the cable displacement is assessed. Furthermore, a study is conducted to determine the sensitivity of the cable response to the properties of the SMA device. The comparison between the SMA damper and a more classical passive control energy dissipation device, i.e., the tuned mass damper (TMD), is carried out. The numerical results show the effectiveness of the SMA damper to damp the high free vibration and the harmonic vibration better than an optimal TMD.
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- A new modeling approach for planar beams: finite-element solutions based on mixed variational derivations
- F. Auricchio ; G. Balduzzi ; C. Lovadina
- Book Title / Journal: Journal of Mechanics of Materials and Structures
- Year: 2010 , Volume: 5 , Series:
- Structural Analysis
- Keywords: planar beams ; Finite elements
- Description
- This paper illustrates a new modeling approach for planar linear elastic beams. Referring to existing
models, we first introduce the variational principles that could be adopted for the beam model derivation, discussing their relative advantages and disadvantages. Then, starting from the Hellinger–Reissner functional we derive some homogeneous and multilayered beam models, discussing some properties of their analytical solutions. Finally, we develop a planar beam finite element, following an innovative approach that could be seen as the imposition of equilibrium in the cross-section and compatibility along the axis. The homogeneous model is capable of reproducing the behavior of the Timoshenko beam, with the advantage that the shear correction factor appears naturally from the variational derivation; the multilayered beam is capable of capturing the local effects produced by boundary constraints and load distributions; the finite element is capable of predicting the cross-section stress distribution with high accuracy, and more generally the behavior of planar structural elements.
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- Particle Methods for a 1D Elastic Model Problem: Error Analysis and Development of a Second-Order Accurate Formulation
- D. Asprone ; F. Auricchio ; G. Manfredi ; A. Prota ; A Reali ; G Sangalli
- Book Title / Journal: Computer Modeling in Engineering & Sciences
- Year: 2010 , Volume: 62 , Series:
- Structural Analysis
- Keywords: Meshless methods ; Particle methods ; Error Evaluation ; Kernel Particle Methods
- Description
- Particle methods represent some of the most investigated meshless approaches, applied to numerical problems, ranging from solid mechanics to fluiddynamics and thermo-dynamics. The objective of the present paper is to analyze some of the proposed particle formulations in one dimension, investigating in particular how the different approaches address second derivative approximation.
With respect to this issue, a rigorous analysis of the error is conducted and a novel second-order accurate formulation is proposed. Hence, as a benchmark, three numerical experiments are carried out on the investigated formulations, dealing
respectively with the approximation of the second derivative of given functions, as well as with the numerical solution of the static problem and with the approximation of the vibration frequencies for an elastic rod. In each test, the obtained numerical results are compared with exact solutions and the main criticalities of each formulation are addressed.
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- A metric approach to plasticity via Hamilton-Jacobi equation
- F. Auricchio ; E. Bonetti ; A. Marigonda
- Book Title / Journal: Mathematical Models and Methods in Applied Sciences
- Year: 2009 , Volume: 20 , Series:
- Structural Analysis
- Keywords: plasticity models ; dissipative metric ; energetic formulation
- Description
- Thermodynamical consistency of plasticity models is usually written in terms of the so-called \maximum dissipation principle". In this paper, we discuss constitutive relations for dissipative materials writ-
ten through suitable generalized gradients of a (possibly non-convex) metric. This new framework allows us to generalize the classical results
providing an interpretation of the yield function in terms of Hamilton-Jacobi Equations theory.
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