GENERALIZED FINITE ELEMENT METHOD FOR NONLINEAR THREE-DIMENSIONAL ANALYSIS OF SOLIDS

The Generalized Finite Element Method (GFEM) is employed in this paper for the numerical analysis of three-dimensional solids tinder nonlinear behavior. A brief summary of the GFEM as well as a description of the formulation of the hexahedral element based oil the proposed enrichment strategy are initially presented. Next, in order to introduce the nonlinear analysis of solids, two constitutive models are briefly reviewed: Lemaitre`s model, in which damage and plasticity are coupled, and Mazars`s damage model suitable for concrete tinder increased loading. Both models are employed in the framework of a nonlocal approach to ensure solution objectivity. In the numerical analyses carried out, a selective enrichment of approximation at regions of concern in the domain (mainly those with high strain and damage gradients) is exploited. Such a possibility makes the three-dimensional analysis less expensive and practicable since re-meshing resources, characteristic of h-adaptivity, can be minimized. Moreover, a combination of three-dimensional analysis and the selective enrichment presents a valuable good tool for a better description of both damage and plastic strain scatterings.

Numerical analysis of the modal coupling at low resonances in a Colombian Andean Bandola in C using the finite element method

The work presented in this thesis is concerned with the dynamical behavior of a CBandola's acoustical box at low resonances -- Two models consisting of two and three coupled oscillators are proposed in order to analyse the response at the first two and three resonances, respectively -- These models describe the first resonances in a bandola as a combination of the lowest modes of vibration of enclosed air, top and back plates -- Physically, the coupling between these elements is caused by the fluid-structure interaction that gives rise to coupled modes of vibration for the assembled resonance box -- In this sense, the coupling in the models is expressed in terms of the ratio of effective areas and masses of the elements which is an useful parameter to control the coupling -- Numerical models are developed for the analysis of modal coupling which is performed using the Finite Element Method -- First, it is analysed the modal behavior of separate elements: enclosed air, top plate and back plate -- This step is important to identify participating modes in the coupling -- Then, a numerical model of the resonance box is used to compute the coupled modes -- The computation of normal modes of vibration was executed in the frequency range of 0-800Hz -- Although the introduced models of coupled oscillators only predict maximum the first three resonances, they also allow to study qualitatively the coupling between the rest of the computed modes in the range -- Considering that dynamic response of a structure can be described in terms of the modal parameters, this work represents, in a good approach, the basic behavior of a CBandola, although experimental measurements are suggested as further work to verify the obtained results and get more information about some characteristics of the coupled modes, for instance, the phase of vibration of the air mode and the radiation e ciency

Complex modal analysis of a vertical rotor through finite element method

Natural frequencies were analyzed (axial, torsional and flexural) and frequency response of a vertical rotor with a hard disk at the edge through the classical and complex modal analysis. The mathematical modeling was based on the theory of Euler-Bernoulli beam. The equation that rules the movement was obtained through the Lagrangian formulation. The model considered the effects of bending, torsion and axial deformation of the shaft, besides the gravitational and gyroscopic effects. The finite element method was used to discretize the structure into hollow cylindrical elements with 12 degrees of freedom. Mass, stiffness and gyroscopic matrices were explained consistently. This type of tool, based on the use of complex coordinates to describe the dynamic behavior of rotating shaft, allows the decomposition of the system in two submodes, backward and forward. Thus, it is possible to clearly visualize that the orbit and direction of the precessional motion around the line of the rotating shaft is not deformed. A finite element program was developed using Matlab ®, and numerical simulations were performed to validate this model.

NUMERICAL SIMULATION of CONVECTION-DIFFUSION PROBLEMS BY THE CONTROL-VOLUME-BASED FINITE-ELEMENT METHOD

This work presents a numerical study of the tri-dimensional convection-diffusion equation by the control-volume-based on finite-element method using quadratic hexahedral elements. Considering that the equation governing this problem in its main variable may represent several properties, including temperature, turbulent kinetic energy, viscous dissipation rate of the turbulent kinetic energy, specific dissipation rate of the turbulent kinetic energy, or even the concentration of a contaminant in a given medium, among others, the wide applicability of this problem is thus evidenced. Three cases of temperature distributions will be studied specifically in this work, in addition to one case of pollutant dispersion upon analysis of the concentration of a contaminant in a fixed flow point. Some comparisons will be carried out against works found in the open literature, while others will be done according to each phenomenon characteristics.

Modal analysis of anisotropic diffused-channel waveguide by a scalar finite element method

A procedure to model optical diffused-channel waveguides is presented in this work. The dielectric waveguides present anisotropic refractive indexes which are calculated from the proton concentration. The proton concentration inside the channel is calculated by the anisotropic 2D-linear diffusion equation and converted to the refractive indexes using mathematical relations obtained from experimental data, the arbitrary refractive index profile is modeled by a. nodal expansion in the base functions. The TE and TM-like propagation properties (effective index) and the electromagnetic fields for well-annealed proton-exchanged (APE) LiNbO3 waveguides are computed by the finite element method.

Investigations into the use of the finite element method and artificial neural networks in the non-destructive analysis of metallic tubes

This work presents an investigation into the use of the finite element method and artificial neural networks in the identification of defects in industrial plants metallic tubes, due to the aggressive actions of the fluids contained by them, and/or atmospheric agents. The methodology used in this study consists of simulating a very large number of defects in a metallic tube, using the finite element method. Both variations in width and height of the defects are considered. Then, the obtained results are used to generate a set of vectors for the training of a perceptron multilayer artificial neural network. Finally, the obtained neural network is used to classify a group of new defects, simulated by the finite element method, but that do not belong to the original dataset. The reached results demonstrate the efficiency of the proposed approach, and encourage future works on this subject.

Electroosmotic pumping in rectangular microchannels: A numerical treatment by the finite element method

In this work, the analysis of electroosmotic pumping mechanisms in microchannels is performed through the solution of Poisson-Boltzmann and Navier Stokes equations by the Finite Element Method. This approach is combined with a Newton-Raphson iterative scheme, allowing a full treatment of the non-linear Poisson-Boltzmann source term which is normally approximated by linearizations in other methods.

Influence of the implant diameter with different sizes of hexagon: Analysis by 3-dimensional finite element method

The aim of this study was to evaluate the stress distribution in implants of regular platforms and of wide diameter with different sizes of hexagon by the 3-dimensional finite element method. We used simulated 3-dimensional models with the aid of Solidworks 2006 and Rhinoceros 4.0 software for the design of the implant and abutment and the InVesalius software for the design of the bone. Each model represented a block of bone from the mandibular molar region with an implant 10 mm in length and different diameters. Model A was an implant 3.75 mm/regular hexagon, model B was an implant 5.00 mm/regular hexagon, and model C was an implant 5.00 mm/ expanded hexagon. A load of 200 N was applied in the axial, lateral, and oblique directions. At implant, applying the load (axial, lateral, and oblique), the 3 models presented stress concentration at the threads in the cervical and middle regions, and the stress was higher for model A. At the abutment, models A and B showed a similar stress distribution, concentrated at the cervical and middle third; model C showed the highest stresses. On the cortical bone, the stress was concentrated at the cervical region for the 3 models and was higher for model A. In the trabecular bone, the stresses were less intense and concentrated around the implant body, and were more intense for model A. Among the models of wide diameter (models B and C), model B (implant 5.00 mm/regular hexagon) was more favorable with regard to distribution of stresses. Model A (implant 3.75 mm/regular hexagon) showed the largest areas and the most intense stress, and model B (implant 5.00 mm/regular hexagon) showed a more favorable stress distribution. The highest stresses were observed in the application of lateral load.

Influence of Tapered and External Hexagon Connections on Bone Stresses Around Tilted Dental Implants: Three-Dimensional Finite Element Method With Statistical Analysis

Background: The purpose of this study is to analyze the tension distribution on bone tissue around implants with different angulations (0 degrees, 17 degrees, and 30 degrees) and connections (external hexagon and tapered) through the use of three-dimensional finite element and statistical analyses.Methods: Twelve different configurations of three-dimensional finite element models, including three inclinations of the implants (0 degrees, 17 degrees, and 30 degrees), two connections (an external hexagon and a tapered), and two load applications (axial and oblique), were simulated. The maximum principal stress values for cortical bone were measured at the mesial, distal, buccal, and lingual regions around the implant for each analyzed situation, totaling 48 groups. Loads of 200 and 100 N were applied at the occlusal surface in the axial and oblique directions, respectively. Maximum principal stress values were measured at the bone crest and statistically analyzed using analysis of variance. Stress patterns in the bone tissue around the implant were analyzed qualitatively.Results: The results demonstrated that under the oblique loading process, the external hexagon connection showed significantly higher stress concentrations in the bone tissue (P < 0.05) compared with the tapered connection. Moreover, the buccal and mesial regions of the cortical bone concentrated significantly higher stress (P < 0.005) to the external hexagon implant type. Under the oblique loading direction, the increased external hexagon implant angulation induced a significantly higher stress concentration (P = 0.045).Conclusions: The study results show that: 1) the oblique load was more damaging to bone tissue, mainly when associated with external hexagon implants; and 2) there was a higher stress concentration on the buccal region in comparison to all other regions under oblique load.

3-D Boundary element-finite element method for the dynamic analysis of piled buildings.

[EN]A boundary element-finite element model is presented for the three-dimensional dynamic analysis of piled buildings in the frequency domain. Piles are modelled as compressible Euler-Bernoulli beams founded on a linear, isotropic, viscoelastic, zoned-homogeneous, unbounded layered soil, while multi-storey buildings are assumed to be comprised of vertical compressible piers and rigid slabs.

Slope stability analysis of the Pacaya Volcano, Guatemala, using limit equilibrium and finite element method

The Pacaya volcanic complex is part of the Central American volcanic arc, which is associated with the subduction of the Cocos tectonic plate under the Caribbean plate. Located 30 km south of Guatemala City, Pacaya is situated on the southern rim of the Amatitlan Caldera. It is the largest post-caldera volcano, and has been one of Central America’s most active volcanoes over the last 500 years. Between 400 and 2000 years B.P, the Pacaya volcano had experienced a huge collapse, which resulted in the formation of horseshoe-shaped scarp that is still visible. In the recent years, several smaller collapses have been associated with the activity of the volcano (in 1961 and 2010) affecting its northwestern flanks, which are likely to be induced by the local and regional stress changes. The similar orientation of dry and volcanic fissures and the distribution of new vents would likely explain the reactivation of the pre-existing stress configuration responsible for the old-collapse. This paper presents the first stability analysis of the Pacaya volcanic flank. The inputs for the geological and geotechnical models were defined based on the stratigraphical, lithological, structural data, and material properties obtained from field survey and lab tests. According to the mechanical characteristics, three lithotechnical units were defined: Lava, Lava-Breccia and Breccia-Lava. The Hoek and Brown’s failure criterion was applied for each lithotechnical unit and the rock mass friction angle, apparent cohesion, and strength and deformation characteristics were computed in a specified stress range. Further, the stability of the volcano was evaluated by two-dimensional analysis performed by Limit Equilibrium (LEM, ROCSCIENCE) and Finite Element Method (FEM, PHASE 2 7.0). The stability analysis mainly focused on the modern Pacaya volcano built inside the collapse amphitheatre of “Old Pacaya”. The volcanic instability was assessed based on the variability of safety factor using deterministic, sensitivity, and probabilistic analysis considering the gravitational instability and the effects of external forces such as magma pressure and seismicity as potential triggering mechanisms of lateral collapse. The preliminary results from the analysis provide two insights: first, the least stable sector is on the south-western flank of the volcano; second, the lowest safety factor value suggests that the edifice is stable under gravity alone, and the external triggering mechanism can represent a likely destabilizing factor.

Analysis of the stress state of a halved and tabled traditional timber scarf joint with the Finite Element Method

The purpose of this study is to determine the stress distribution in the carpentry joint of halved and tabled scarf joint with the finite element method (FEM) and its comparison with the values obtained using the theory of Strength of Materials. The stress concentration areas where analyzed and the influence of mesh refinement was studied on the results in order to determine the mesh size that provides the stress values more consistent with the theory. In areas where stress concentration is lower, different mesh sizes show similar stress values. In areas where stress concentration occurs, the same values increase considerably with the refinement of the mesh. The results show a central symmetry of the isobar lines distribution where the centre of symmetry corresponds to the geometric centre of the joint. Comparison of normal stress levels obtained by the FEM and the classical theory shows small differences, except at points of stress concentration.

Application of the finite element method in cold forging processes

The demand for more efficient manufacturing processes has been increasing in the last few years. The cold forging process is presented as a possible solution, because it allows the production of parts with a good surface finish and with good mechanical properties. Nevertheless, the cold forming sequence design is very empirical and it is based on the designer experience. The computational modeling of each forming process stage by the finite element method can make the sequence design faster and more efficient, decreasing the use of conventional "trial and error" methods. In this study, the application of a commercial general finite element software - ANSYS - has been applied to model a forming operation. Models have been developed to simulate the ring compression test and to simulate a basic forming operation (upsetting) that is applied in most of the cold forging parts sequences. The simulated upsetting operation is one stage of the automotive starter parts manufacturing process. Experiments have been done to obtain the stress-strain material curve, the material flow during the simulated stage, and the required forming force. These experiments provided results used as numerical model input data and as validation of model results. The comparison between experiments and numerical results confirms the developed methodology potential on die filling prediction.

A finite element method for nonlinear elliptic problems

We present a Galerkin method with piecewise polynomial continuous elements for fully nonlinear elliptic equations. A key tool is the discretization proposed in Lakkis and Pryer, 2011, allowing us to work directly on the strong form of a linear PDE. An added benefit to making use of this discretization method is that a recovered (finite element) Hessian is a byproduct of the solution process. We build on the linear method and ultimately construct two different methodologies for the solution of second order fully nonlinear PDEs. Benchmark numerical results illustrate the convergence properties of the scheme for some test problems as well as the Monge–Amp`ere equation and the Pucci equation.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.