Application of the finite element method to problems in fracture mechanics

Numerical techniques have been finding increasing use in all aspects of fracture mechanics, and often provide the only means for analyzing fracture problems. The work presented here, is concerned with the application of the finite element method to cracked structures. The present work was directed towards the establishment of a comprehensive two-dimensional finite element, linear elastic, fracture analysis package. Significant progress has been made to this end, and features which can now be studied include multi-crack tip mixed-mode problems, involving partial crack closure. The crack tip core element was refined and special local crack tip elements were employed to reduce the element density in the neighbourhood of the core region. The work builds upon experience gained by previous research workers and, as part of the general development, the program was modified to incorporate the eight-node isoparametric quadrilateral element. Also. a more flexible solving routine was developed, and provided a very compact method of solving large sets of simultaneous equations, stored in a segmented form. To complement the finite element analysis programs, an automatic mesh generation program has been developed, which enables complex problems. involving fine element detail, to be investigated with a minimum of input data. The scheme has proven to be versati Ie and reasonably easy to implement. Numerous examples are given to demonstrate the accuracy and flexibility of the finite element technique.

A critical assessment of the finite element method for calculating electric and magnetic fields

The present dissertation is concerned with the determination of the magnetic field distribution in ma[.rnetic electron lenses by means of the finite element method. In the differential form of this method a Poisson type equation is solved by numerical methods over a finite boundary. Previous methods of adapting this procedure to the requirements of digital computers have restricted its use to computers of extremely large core size. It is shown that by reformulating the boundary conditions, a considerable reduction in core store can be achieved for a given accuracy of field distribution. The magnetic field distribution of a lens may also be calculated by the integral form of the finite element rnethod. This eliminates boundary problems mentioned but introduces other difficulties. After a careful analysis of both methods it has proved possible to combine the advantages of both in a .new approach to the problem which may be called the 'differential-integral' finite element method. The application of this method to the determination of the magnetic field distribution of some new types of magnetic lenses is described. In the course of the work considerable re-programming of standard programs was necessary in order to reduce the core store requirements to a minimum.

Application of finite element method and photo-elasticity to an lap welded connection

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A finite-element method for the solution of turbine-generation end-zone fields

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Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem

We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].

A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling

Peer reviewed

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

SIMULATING LARGE DEFORMATION OF INTRANEURAL GANGLION CYST USING FINITE ELEMENT METHOD

Intraneural Ganglion Cyst is disorder observed in the nerve injury, it is still unknown and very difficult to predict its propagation in the human body so many times it is referred as an unsolved history. The treatments for this disorder are to remove the cystic substance from the nerve by a surgery. However these treatments may result in neuropathic pain and recurrence of the cyst. The articular theory proposed by Spinner et al., (Spinner et al. 2003) considers the neurological deficit in Common Peroneal Nerve (CPN) branch of the sciatic nerve and adds that in addition to the treatment, ligation of articular branch results into foolproof eradication of the deficit. Mechanical modeling of the affected nerve cross section will reinforce the articular theory (Spinner et al. 2003). As the cyst propagates, it compresses the neighboring fascicles and the nerve cross section appears like a signet ring. Hence, in order to mechanically model the affected nerve cross section; computational methods capable of modeling excessively large deformations are required. Traditional FEM produces distorted elements while modeling such deformations, resulting into inaccuracies and premature termination of the analysis. The methods described in research report have the capability to simulate large deformation. The results obtained from this research shows significant deformation as compared to the deformation observed in the conventional finite element models. The report elaborates the neurological deficit followed by detail explanation of the Smoothed Particle Hydrodynamic approach. Finally, the results show the large deformation in stages and also the successful implementation of the SPH method for the large deformation of the biological organ like the Intra-neural ganglion cyst.

Development of a Coupling Model for Fluid-Structure Interaction using the Mesh-free Finite Element Method and the Lattice Boltzmann Method

In the presented thesis work, the meshfree method with distance fields was coupled with the lattice Boltzmann method to obtain solutions of fluid-structure interaction problems. The thesis work involved development and implementation of numerical algorithms, data structure, and software. Numerical and computational properties of the coupling algorithm combining the meshfree method with distance fields and the lattice Boltzmann method were investigated. Convergence and accuracy of the methodology was validated by analytical solutions. The research was focused on fluid-structure interaction solutions in complex, mesh-resistant domains as both the lattice Boltzmann method and the meshfree method with distance fields are particularly adept in these situations. Furthermore, the fluid solution provided by the lattice Boltzmann method is massively scalable, allowing extensive use of cutting edge parallel computing resources to accelerate this phase of the solution process. The meshfree method with distance fields allows for exact satisfaction of boundary conditions making it possible to exactly capture the effects of the fluid field on the solid structure.

Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element

We propose a novel finite element formulation that significantly reduces the number of degrees of freedom necessary to obtain reasonably accurate approximations of the low-frequency component of the deformation in boundary-value problems. In contrast to the standard Ritz–Galerkin approach, the shape functions are defined on a Lie algebra—the logarithmic space—of the deformation function. We construct a deformation function based on an interpolation of transformations at the nodes of the finite element. In the case of the geometrically exact planar Bernoulli beam element presented in this work, these transformation functions at the nodes are given as rotations. However, due to an intrinsic coupling between rotational and translational components of the deformation function, the formulation provides for a good approximation of the deflection of the beam, as well as of the resultant forces and moments. As both the translational and the rotational components of the deformation function are defined on the logarithmic space, we propose to refer to the novel approach as the “Logarithmic finite element method”, or “LogFE” method.

Finite element analysis of anisotropic optical waveguide with arbitrary index profile

This work presents the application of a scalar finite element formulation for Ex (TE-like) modes in anisotropic planar and channel waveguides with diagonal permittivity tensor, diffused in both transversal directions. This extended formulation considers explicitly both the variations of the refractive index and their spatial derivates inside of each finite element. Dispersion curves for Ex modes in planar and channel waveguides are shown, and the results compared with solutions obtained by other formulations.

Crack mechanical failure in lithium niobate crystal under ion irradiation; novel simulation by extended finite elements

Swift heavy ion irradiation (ions with mass heavier than 15 and energy exceeding MeV/amu) transfer their energy mainly to the electronic system with small momentum transfer per collision. Therefore, they produce linear regions (columnar nano-tracks) around the straight ion trajectory, with marked modifications with respect to the virgin material, e.g., phase transition, amorphization, compaction, changes in physical or chemical properties. In the case of crystalline materials the most distinctive feature of swift heavy ion irradiation is the production of amorphous tracks embedded in the crystal. Lithium niobate is a relevant optical material that presents birefringence due to its anysotropic trigonal structure. The amorphous phase is certainly isotropic. In addition, its refractive index exhibits high contrast with those of the crystalline phase. This allows one to fabricate waveguides by swift ion irradiation with important technological relevance. From the mechanical point of view, the inclusion of an amorphous nano-track (with a density 15% lower than that of the crystal) leads to the generation of important stress/strain fields around the track. Eventually these fields are the origin of crack formation with fatal consequences for the integrity of the samples and the viability of the method for nano-track formation. For certain crystal cuts (X and Y), these fields are clearly anisotropic due to the crystal anisotropy. We have used finite element methods to calculate the stress/strain fields that appear around the ion-generated amorphous nano-tracks for a variety of ion energies and doses. A very remarkable feature for X cut-samples is that the maximum shear stress appears on preferential planes that form +/-45º with respect to the crystallographic planes. This leads to the generation of oriented surface cracks when the dose increases. The growth of the cracks along the anisotropic crystal has been studied by means of novel extended finite element methods, which include cracks as discontinuities. In this way we can study how the length and depth of a crack evolves as function of the ion dose. In this work we will show how the simulations compare with experiments and their application in materials modification by ion irradiation.

Effect Of Platform Connection And Abutment Material On Stress Distribution In Single Anterior Implant-supported Restorations: A Nonlinear 3-dimensional Finite Element Analysis.

Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections.