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.

Three-Dimensional Finite Element Analysis of Stress Distribution on Different Bony Ridges With Different Lengths of Morse Taper Implants and Prosthesis Dimensions

This finite element analysis (FEA) compared stress distribution on different bony ridges rehabilitated with different lengths of morse taper implants, varying dimensions of metal-ceramic crowns to maintain the occlusal alignment. Three-dimensional FE models were designed representing a posterior left side segment of the mandible: group control, 3 implants of 11 mm length; group 1, implants of 13 mm, 11 mm and 5 mm length; group 2, 1 implant of 11 mm and 2 implants of 5 mm length; and group 3, 3 implants of 5 mm length. The abutments heights were 3.5 mm for 13- and 11-mm implants (regular), and 0.8 mm for 5-mm implants (short). Evaluation was performed on Ansys software, oblique loads of 365N for molars and 200N for premolars. There was 50% higher stress on cortical bone for the short implants than regular implants. There was 80% higher stress on trabecular bone for the short implants than regular implants. There was higher stress concentration on the bone region of the short implants neck. However, these implants were capable of dissipating the stress to the bones, given the applied loads, but achieving near the threshold between elastic and plastic deformation to the trabecular bone. Distal implants and/or with biggest occlusal table generated greatest stress regions on the surrounding bone. It was concluded that patients requiring short implants associated with increased proportions implant prostheses need careful evaluation and occlusal adjustment, as a possible overload in these short implants, and even in regular ones, can generate stress beyond the physiological threshold of the surrounding bone, compromising the whole system.

Assessment of nose protector for sport activities: finite element analysis

There has been a significant increase in the number of facial fractures stemming from sport activities in recent years, with the nasal bone one of the most affected structures. Researchers recommend the use of a nose protector, but there is no standardization regarding the material employed. Clinical experience has demonstrated that a combination of a flexible and rigid layer of ethylene vinyl acetate (EVA) offers both comfort and safety to practitioners of sports. The aim of the present study was the investigation into the stresses generated by the impact of a rigid body on the nasal bone on models with and without an EVA protector. For such, finite element analysis was employed. A craniofacial model was constructed from images obtained through computed tomography. The nose protector was modeled with two layers of EVA (1 mm of rigid EVA over 2 mm of flexible EVA), following the geometry of the soft tissue. Finite element analysis was performed using the LS Dyna program. The bone and rigid EVA were represented as elastic linear material, whereas the soft tissues and flexible EVA were represented as hyperelastic material. The impact from a rigid sphere on the frontal region of the face was simulated with a constant velocity of 20 m s-1 for 9.1 mu s. The model without the protector served as the control. The distribution of maximal stress of the facial bones was recorded. The maximal stress on the nasal bone surpassed the breaking limit of 0.130.34 MPa on the model without a protector, while remaining below this limit on the model with the protector. Thus, the nose protector made from both flexible and rigid EVA proved effective at protecting the nasal bones under high-impact conditions.

Interpolation estimate for a finite-element space with embedded discontinuities

We consider a recently proposed finite-element space that consists of piecewise affine functions with discontinuities across a smooth given interface Γ (a curve in two dimensions, a surface in three dimensions). Contrary to existing extended finite element methodologies, the space is a variant of the standard conforming Formula space that can be implemented element by element. Further, it neither introduces new unknowns nor deteriorates the sparsity structure. It is proved that, for u arbitrary in Formula, the interpolant Formula defined by this new space satisfies Graphic where h is the mesh size, Formula is the domain, Formula, Formula, Formula and standard notation has been adopted for the function spaces. This result proves the good approximation properties of the finite-element space as compared to any space consisting of functions that are continuous across Γ, which would yield an error in the Formula-norm of order Graphic. These properties make this space especially attractive for approximating the pressure in problems with surface tension or other immersed interfaces that lead to discontinuities in the pressure field. Furthermore, the result still holds for interfaces that end within the domain, as happens for example in cracked domains.

Finite element analysis of stress distribution in anchor teeth in surgically assisted rapid palatal expansion

The treatment of a transverse maxillary deficiency in skeletally mature individuals should include surgically assisted rapid palatal expansion. This study evaluated the distribution of stresses that affect the expander's anchor teeth using finite element analysis when the osteotomy is varied. Five virtual models were built and the surgically assisted rapid palatal expansion was simulated. Results showed tension on the lingual face of the teeth and alveolar bone, and compression on the buccal side of the alveolar bone. The subtotal Le Fort I osteotomy combined with intermaxillary suture osteotomy seemed to reduce the dissipation of tensions. Therefore, subtotal Le Fort I osteotomy without a step in the zygomaticomaxillary buttress, combined with intermaxillary suture osteotomy and pterygomaxillary disjunction may be the osteotomy of choice to reduce tensions on anchor teeth, which tend to move mesiobuccally (premolar) and distobuccally (molar)

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

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.

Local scale finite element modelling of stack pollutant emissions

Congresos y conferencias

Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner.

Comparison between analytical and numerical methods for the assessment of masonry arch bridges: Case study of Clemente Bridge on Savio river

This research has focused on the study of the behavior and of the collapse of masonry arch bridges. The latest decades have seen an increasing interest in this structural type, that is still present and in use, despite the passage of time and the variation of the transport means. Several strategies have been developed during the time to simulate the response of this type of structures, although even today there is no generally accepted standard one for assessment of masonry arch bridges. The aim of this thesis is to compare the principal analytical and numerical methods existing in literature on case studies, trying to highlight values and weaknesses. The methods taken in exam are mainly three: i) the Thrust Line Analysis Method; ii) the Mechanism Method; iii) the Finite Element Methods. The Thrust Line Analysis Method and the Mechanism Method are analytical methods and derived from two of the fundamental theorems of the Plastic Analysis, while the Finite Element Method is a numerical method, that uses different strategies of discretization to analyze the structure. Every method is applied to the case study through computer-based representations, that allow a friendly-use application of the principles explained. A particular closed-form approach based on an elasto-plastic material model and developed by some Belgian researchers is also studied. To compare the three methods, two different case study have been analyzed: i) a generic masonry arch bridge with a single span; ii) a real masonry arch bridge, the Clemente Bridge, built on Savio River in Cesena. In the analyses performed, all the models are two-dimensional in order to have results comparable between the different methods taken in exam. The different methods have been compared with each other in terms of collapse load and of hinge positions.

Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics

Over the years the Differential Quadrature (DQ) method has distinguished because of its high accuracy, straightforward implementation and general ap- plication to a variety of problems. There has been an increase in this topic by several researchers who experienced significant development in the last years. DQ is essentially a generalization of the popular Gaussian Quadrature (GQ) used for numerical integration functions. GQ approximates a finite in- tegral as a weighted sum of integrand values at selected points in a problem domain whereas DQ approximate the derivatives of a smooth function at a point as a weighted sum of function values at selected nodes. A direct appli- cation of this elegant methodology is to solve ordinary and partial differential equations. Furthermore in recent years the DQ formulation has been gener- alized in the weighting coefficients computations to let the approach to be more flexible and accurate. As a result it has been indicated as Generalized Differential Quadrature (GDQ) method. However the applicability of GDQ in its original form is still limited. It has been proven to fail for problems with strong material discontinuities as well as problems involving singularities and irregularities. On the other hand the very well-known Finite Element (FE) method could overcome these issues because it subdivides the computational domain into a certain number of elements in which the solution is calculated. Recently, some researchers have been studying a numerical technique which could use the advantages of the GDQ method and the advantages of FE method. This methodology has got different names among each research group, it will be indicated here as Generalized Differential Quadrature Finite Element Method (GDQFEM).

Fluid-structure interaction by a coupled lattice Boltzmann-finite element approach

In this thesis, a strategy to model the behavior of fluids and their interaction with deformable bodies is proposed. The fluid domain is modeled by using the lattice Boltzmann method, thus analyzing the fluid dynamics by a mesoscopic point of view. It has been proved that the solution provided by this method is equivalent to solve the Navier-Stokes equations for an incompressible flow with a second-order accuracy. Slender elastic structures idealized through beam finite elements are used. Large displacements are accounted for by using the corotational formulation. Structural dynamics is computed by using the Time Discontinuous Galerkin method. Therefore, two different solution procedures are used, one for the fluid domain and the other for the structural part, respectively. These two solvers need to communicate and to transfer each other several information, i.e. stresses, velocities, displacements. In order to guarantee a continuous, effective, and mutual exchange of information, a coupling strategy, consisting of three different algorithms, has been developed and numerically tested. In particular, the effectiveness of the three algorithms is shown in terms of interface energy artificially produced by the approximate fulfilling of compatibility and equilibrium conditions at the fluid-structure interface. The proposed coupled approach is used in order to solve different fluid-structure interaction problems, i.e. cantilever beams immersed in a viscous fluid, the impact of the hull of the ship on the marine free-surface, blood flow in a deformable vessels, and even flapping wings simulating the take-off of a butterfly. The good results achieved in each application highlight the effectiveness of the proposed methodology and of the C++ developed software to successfully approach several two-dimensional fluid-structure interaction problems.

Finite element modeling of the cement-bone interface beneath the tibial tray of a total knee arthroplasty: Study of the stress shielding effect (modellazione agli elementi finiti dell'interfaccia cemento-osso sotto il piatto tibiale di protesi totale di ginocchio: Analisi dello stress shielding)

The goal of this thesis was the study of the cement-bone interface in the tibial component of a cemented total knee prosthesis. One of the things you can see in specimens after in vivo service is that resorption of bone occurs in the interdigitated region between bone and cement. A stress shielding effect was investigated as a cause to explain bone resorption. Stress shielding occurs when bone is loaded less than physiological and therefore it starts remodeling according to the new loading conditions. µCT images were used to obtain 3D models of the bone and cement structure and a Finite Element Analysis was used to simulate different kind of loads. Resorption was also simulated by performing erosion operations in the interdigitated bone region. Finally, 4 models were simulated: bone (trabecular), bone with cement, and two models of bone with cement after progressive erosions of the bone. Compression, tension and shear test were simulated for each model in displacement-control until 2% of strain. The results show how the principal strain and Von Mises stress decrease after adding the cement on the structure and after the erosion operations. These results show that a stress shielding effect does occur and rises after resorption starts.