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.

Simulations of incompressible fluid flows by a least squares finite element method

In this work simulations of incompressible fluid flows have been done by a Least Squares Finite Element Method (LSFEM) using velocity-pressure-vorticity and velocity-pressure-stress formulations, named u-p-ω) and u-p-τ formulations respectively. These formulations are preferred because the resulting equations are partial differential equations of first order, which is convenient for implementation by LSFEM. The main purposes of this work are the numerical computation of laminar, transitional and turbulent fluid flows through the application of large eddy simulation (LES) methodology using the LSFEM. The Navier-Stokes equations in u-p-ω and u-p-τ formulations are filtered and the eddy viscosity model of Smagorinsky is used for modeling the sub-grid-scale stresses. Some benchmark problems are solved for validate the numerical code and the preliminary results are presented and compared with available results from the literature. Copyright © 2005 by ABCM.

Simulation of needle-type corona electrodes by the finite element method

This paper describes a software tool, called LEVSOFT, suitable for the electric field simulations of corona electrodes by the Finite Element Method (FEM). Special attention was paid to the user friendly construction of geometries with corners and sharp points, and to the fast generation of highly refined triangular meshes and field maps. The execution of self-adaptive meshes was also implemented. These customized features make the code attractive for the simulation of needle-type corona electrodes. Some case examples involving needle type electrodes are presented.

Study of the phenomena of fatigue using the finite element method

About 99% of mechanical failures are consequence of the phenomena of fatigue, which consists on the progressive weakening of the resistant section of a mechanical component due to the growing of cracks caused by fluctuating loadings. A broad diversity of factors influences the fatigue life of a mechanical component, like the surface finishing, scale factors, among others, but none is as significantly as the presence of geometric severities. Stress concentrators are places where fatigue cracks have a greater probability to occur, and so on, the intuit of this work is to develop a consistent and trustfully methodology to determine the theoretical stress concentration factor of mechanical components. Copyright © 2007 SAE International.

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.

Application of the finite element method in Dentistry

The finite element method (FEM) involves a series of computational procedures to calculate the stress in each element, which performs a model solution. Such a structural analysis allows the determination of stress resulting from external force, pressure, thermal change, and other factors. This method is extremely useful for indicating mechanical aspects of biomaterials and human tissues that can hardly be measured in vivo. The results obtained can then be studied using visualization software within the FEM environment to view a variety of parameters, and to fully identify implications of the analysis. Objective: An overview to show application of FEM in dentistry was undertaken. Literature review: This paper shows the basic concept, advances, advantages, limitations and applications of finite element method (FEM) in dentistry. Conclusion: It is extremely important to verify what the purpose of the study is in order to correctly apply FEM.

Application of hte finite element method in Dentistry

Introduction: The finite element method (FEM) involves a series of computational procedures to calculate the stress in each element, which performs a model solution. Such a structural analysis allows the determination of stress resulting from external force, pressure, thermal change, and other factors. This method is extremely useful for indicating mechanical aspects of biomaterials and human tissues that can hardly be measured in vivo. The results obtained can then be studied using visualization software within the FEM environment to view a variety of parameters, and to fully identify implications of the analysis. Objective: An overview to show application of FEM in dentistry was undertaken. Literature review: This paper shows the basic concept, advances, advantages, limitations and applications of finite element method (FEM) in dentistry. Conclusion: It is extremely important to verify what the purpose of the study is in order to correctly apply FEM.

Scientific use of the finite element method in Orthodontics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

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.

GENERALIZED FINITE ELEMENT METHOD ON NONCONVENTIONAL HYBRID-MIXED FORMULATION

The generalized finite element method (GFEM) is applied to a nonconventional hybrid-mixed stress formulation (HMSF) for plane analysis. In the HMSF, three approximation fields are involved: stresses and displacements in the domain and displacement fields on the static boundary. The GFEM-HMSF shape functions are then generated by the product of a partition of unity associated to each field and the polynomials enrichment functions. In principle, the enrichment can be conducted independently over each of the HMSF approximation fields. However, stability and convergence features of the resulting numerical method can be affected mainly by spurious modes generated when enrichment is arbitrarily applied to the displacement fields. With the aim to efficiently explore the enrichment possibilities, an extension to GFEM-HMSF of the conventional Zienkiewicz-Patch-Test is proposed as a necessary condition to ensure numerical stability. Finally, once the extended Patch-Test is satisfied, some numerical analyses focusing on the selective enrichment over distorted meshes formed by bilinear quadrilateral finite elements are presented, thus showing the performance of the GFEM-HMSF combination.

Numeric reconstruction of cytoskeleton with finite element method and topology optimization method

The importance of mechanical aspects related to cell activity and its environment is becoming more evident due to their influence in stem cell differentiation and in the development of diseases such as atherosclerosis. The mechanical tension homeostasis is related to normal tissue behavior and its lack may be related to the formation of cancer, which shows a higher mechanical tension. Due to the complexity of cellular activity, the application of simplified models may elucidate which factors are really essential and which have a marginal effect. The development of a systematic method to reconstruct the elements involved in the perception of mechanical aspects by the cell may accelerate substantially the validation of these models. This work proposes the development of a routine capable of reconstructing the topology of focal adhesions and the actomyosin portion of the cytoskeleton from the displacement field generated by the cell on a flexible substrate. Another way to think of this problem is to develop an algorithm to reconstruct the forces applied by the cell from the measurements of the substrate displacement, which would be characterized as an inverse problem. For these kind of problems, the Topology Optimization Method (TOM) is suitable to find a solution. TOM is consisted of an iterative application of an optimization method and an analysis method to obtain an optimal distribution of material in a fixed domain. One way to experimentally obtain the substrate displacement is through Traction Force Microscopy (TFM), which also provides the forces applied by the cell. Along with systematically generating the distributions of focal adhesion and actin-myosin for the validation of simplified models, the algorithm also represents a complementary and more phenomenological approach to TFM. As a first approximation, actin fibers and flexible substrate are represented through two-dimensional linear Finite Element Method. Actin contraction is modeled as an initial stress of the FEM elements. Focal adhesions connecting actin and substrate are represented by springs. The algorithm was applied to data obtained from experiments regarding cytoskeletal prestress and micropatterning, comparing the numerical results to the experimental ones