Numerical modelling of chemical effects of magma solidification problems in porous rocks

The solidification of intruded magma in porous rocks can result in the following two consequences: (1) the heat release due to the solidification of the interface between the rock and intruded magma and (2) the mass release of the volatile fluids in the region where the intruded magma is solidified into the rock. Traditionally, the intruded magma solidification problem is treated as a moving interface (i.e. the solidification interface between the rock and intruded magma) problem to consider these consequences in conventional numerical methods. This paper presents an alternative new approach to simulate thermal and chemical consequences/effects of magma intrusion in geological systems, which are composed of porous rocks. In the proposed new approach and algorithm, the original magma solidification problem with a moving boundary between the rock and intruded magma is transformed into a new problem without the moving boundary but with the proposed mass source and physically equivalent heat source. The major advantage in using the proposed equivalent algorithm is that a fixed mesh of finite elements with a variable integration time-step can be employed to simulate the consequences and effects of the intruded magma solidification using the conventional finite element method. The correctness and usefulness of the proposed equivalent algorithm have been demonstrated by a benchmark magma solidification problem. Copyright (c) 2005 John Wiley & Sons, Ltd.

The subcycled Newmark algorithm

The popular Newmark algorithm, used for implicit direct integration of structural dynamics, is extended by means of a nodal partition to permit use of different timesteps in different regions of a structural model. The algorithm developed has as a special case an explicit-explicit subcycling algorithm previously reported by Belytschko, Yen and Mullen. That algorithm has been shown, in the absence of damping or other energy dissipation, to exhibit instability over narrow timestep ranges that become narrower as the number of degrees of freedom increases, making them unlikely to be encountered in practice. The present algorithm avoids such instabilities in the case of a one to two timestep ratio (two subcycles), achieving unconditional stability in an exponential sense for a linear problem. However, with three or more subcycles, the trapezoidal rule exhibits stability that becomes conditional, falling towards that of the central difference method as the number of subcycles increases. Instabilities over narrow timestep ranges, that become narrower as the model size increases, also appear with three or more subcycles. However by moving the partition between timesteps one row of elements into the region suitable for integration with the larger timestep these the unstable timestep ranges become extremely narrow, even in simple systems with a few degrees of freedom. As well, accuracy is improved. Use of a version of the Newmark algorithm that dissipates high frequencies minimises or eliminates these narrow bands of instability. Viscous damping is also shown to remove these instabilities, at the expense of having more effect on the low frequency response.

Finite Element Modeling for Development and Optimization of a Bone Plate for Mandibular Fracture in Dogs

This study aimed to develop a plate to treat fractures of the mandibular body in dogs and to validate the project using finite elements and biomechanical essays. Mandible prototypes were produced with 10 oblique ventrorostral fractures (favorable) and 10 oblique ventrocaudal fractures (unfavorable). Three groups were established for each fracture type. Osteosynthesis with a pure titanium plate of double-arch geometry and blocked monocortical screws offree angulanon were used. The mechanical resistance of the prototype with unfavorable fracture was lower than that of the fcworable fracture. In both fractures, the deflection increased and the relative stiffness decreased proportionally to the diminishing screw number The finite element analysis validated this plate study, since the maximum tension concentration observed on the plate was lower than the resistance limit tension admitted by the titanium. In conclusion, the double-arch geometry plate fixed with blocked monocortical screws has sufficient resistance to stabilize oblique,fractures, without compromising mandibular dental or neurovascular structures. J Vet Dent 24 (7); 212 - 221, 2010

Finite Element Analysis of Shear Versus Torsion Adhesive Strength Tests for Dental Resin Composites

Stress distributions in torsion and wire-loop shear tests were compared using three-dimensional (3-D) linear-elastic finite element method, in an attempt to predict the ideal conditions for testing adhesive strength of dental resin composites to dentin. The torsion test presented lower variability in stress concentration at the adhesive interface with changes in the proportion adhesive thickness/resin composite diameter, as well as lower variability with changes in the resin composite elastic modulus. Moreover, the torsion test eliminated variability from changes in loading distance, and reduced the cohesive fracture tendency in the dentin. The torsion test seems to be more appropriate than wire-loop shear test for testing the resin composite-tooth interface strength. (c) Koninklijke Brill NV, Leiden, 2009

A monolithic smoothing-gap algorithm for contact-impact based on the signed distance function

A new algorithm has been developed for smoothing the surfaces in finite element formulations of contact-impact. A key feature of this method is that the smoothing is done implicitly by constructing smooth signed distance functions for the bodies. These functions are then employed for the computation of the gap and other variables needed for implementation of contact-impact. The smoothed signed distance functions are constructed by a moving least-squares approximation with a polynomial basis. Results show that when nodes are placed on a surface, the surface can be reproduced with an error of about one per cent or less with either a quadratic or a linear basis. With a quadratic basis, the method exactly reproduces a circle or a sphere even for coarse meshes. Results are presented for contact problems involving the contact of circular bodies. Copyright (C) 2002 John Wiley Sons, Ltd.

Comparação de desempenho entre a formulação direta do Método dos Elementos de Contorno com Funções Radiais e o Método dos Elementos Finitos em problemas de Poisson e Helmholtz

O presente trabalho objetiva avaliar o desempenho do MECID (Método dos Elementos de Contorno com Interpolação Direta) para resolver o termo integral referente à inércia na Equação de Helmholtz e, deste modo, permitir a modelagem do Problema de Autovalor assim como calcular as frequências naturais, comparando-o com os resultados obtidos pelo MEF (Método dos Elementos Finitos), gerado pela Formulação Clássica de Galerkin. Em primeira instância, serão abordados alguns problemas governados pela equação de Poisson, possibilitando iniciar a comparação de desempenho entre os métodos numéricos aqui abordados. Os problemas resolvidos se aplicam em diferentes e importantes áreas da engenharia, como na transmissão de calor, no eletromagnetismo e em problemas elásticos particulares. Em termos numéricos, sabe-se das dificuldades existentes na aproximação precisa de distribuições mais complexas de cargas, fontes ou sorvedouros no interior do domínio para qualquer técnica de contorno. No entanto, este trabalho mostra que, apesar de tais dificuldades, o desempenho do Método dos Elementos de Contorno é superior, tanto no cálculo da variável básica, quanto na sua derivada. Para tanto, são resolvidos problemas bidimensionais referentes a membranas elásticas, esforços em barras devido ao peso próprio e problemas de determinação de frequências naturais em problemas acústicos em domínios fechados, dentre outros apresentados, utilizando malhas com diferentes graus de refinamento, além de elementos lineares com funções de bases radiais para o MECID e funções base de interpolação polinomial de grau (um) para o MEF. São geradas curvas de desempenho através do cálculo do erro médio percentual para cada malha, demonstrando a convergência e a precisão de cada método. Os resultados também são comparados com as soluções analíticas, quando disponíveis, para cada exemplo resolvido neste trabalho.

Estimating Local Part Thickness in Midplane Meshes for Finite Element Analysis

Within the development of motor vehicles, crash safety (e.g. occupant protection, pedestrian protection, low speed damageability), is one of the most important attributes. In order to be able to fulfill the increased requirements in the framework of shorter cycle times and rising pressure to reduce costs, car manufacturers keep intensifying the use of virtual development tools such as those in the domain of Computer Aided Engineering (CAE). For crash simulations, the explicit finite element method (FEM) is applied. The accuracy of the simulation process is highly dependent on the accuracy of the simulation model, including the midplane mesh. One of the roughest approximations typically made is the actual part thickness which, in reality, can vary locally. However, almost always a constant thickness value is defined throughout the entire part due to complexity reasons. On the other hand, for precise fracture analysis within FEM, the correct thickness consideration is one key enabler. Thus, availability of per element thickness information, which does not exist explicitly in the FEM model, can significantly contribute to an improved crash simulation quality, especially regarding fracture prediction. Even though the thickness is not explicitly available from the FEM model, it can be inferred from the original CAD geometric model through geometric calculations. This paper proposes and compares two thickness estimation algorithms based on ray tracing and nearest neighbour 3D range searches. A systematic quantitative analysis of the accuracy of both algorithms is presented, as well as a thorough identification of particular geometric arrangements under which their accuracy can be compared. These results enable the identification of each technique’s weaknesses and hint towards a new, integrated, approach to the problem that linearly combines the estimates produced by each algorithm.

Surgical correction of scoliosis: Numerical analysis and optimization of the procedure

A previously developed model is used to numerically simulate real clinical cases of the surgical correction of scoliosis. This model consists of one-dimensional finite elements with spatial deformation in which (i) the column is represented by its axis; (ii) the vertebrae are assumed to be rigid; and (iii) the deformability of the column is concentrated in springs that connect the successive rigid elements. The metallic rods used for the surgical correction are modeled by beam elements with linear elastic behavior. To obtain the forces at the connections between the metallic rods and the vertebrae geometrically, non-linear finite element analyses are performed. The tightening sequence determines the magnitude of the forces applied to the patient column, and it is desirable to keep those forces as small as possible. In this study, a Genetic Algorithm optimization is applied to this model in order to determine the sequence that minimizes the corrective forces applied during the surgery. This amounts to find the optimal permutation of integers 1, ... , n, n being the number of vertebrae involved. As such, we are faced with a combinatorial optimization problem isomorph to the Traveling Salesman Problem. The fitness evaluation requires one computing intensive Finite Element Analysis per candidate solution and, thus, a parallel implementation of the Genetic Algorithm is developed.

Optimal design of piezolaminated structures using B-spline strip finite element models

A package of B-spline finite strip models is developed for the linear analysis of piezolaminated plates and shells. This package is associated to a global optimization technique in order to enhance the performance of these types of structures, subjected to various types of objective functions and/or constraints, with discrete and continuous design variables. The models considered are based on a higher-order displacement field and one can apply them to the static, free vibration and buckling analyses of laminated adaptive structures with arbitrary lay-ups, loading and boundary conditions. Genetic algorithms, with either binary or floating point encoding of design variables, were considered to find optimal locations of piezoelectric actuators as well as to determine the best voltages applied to them in order to obtain a desired structure shape. These models provide an overall economy of computing effort for static and vibration problems.

Comporta de vigas: dimensionamento e análise estrutural

As comportas de vigas de fundo, objecto de estudo no presente trabalho, são essenciais devido à sua capacidade de controlo do fluxo de água em casos de emergência. Assim este trabalho visou o dimensionamento e análise estrutural de uma comporta dessa natureza. Para o seu dimensionamento foi essencial a norma DIN19704-1:1998, que define todos os padrões que devem ser levados em conta numa construção hidráulica em aço. Deste modo, após uma breve descrição do enquadramento e do estado da arte relativamente a este assunto, foram apresentados ao longo do trabalho, os cálculos dos principais componentes mecânicos que fazem parte dum projecto de uma comporta de vigas. Para comprovar a validade do dimensionamento da comporta realizado através da norma, recorreu-se a um software de análise e simulação por elementos finitos, COSMOSWorks, no sentido de assim prever o comportamento mecânico em análise estática linear, que as solicitações mecânicas em presença têm sobre a comporta. Os resultados da comparação entre o dimensionamento teórico e a análise de tensões através do COSMOSWorks nos elementos mais críticos da estrutura, permitem concluir globalmente que a comporta está bem dimensionada tendo em conta os esforços que tem de suportar.

Finite element studies of the mechanical behaviour of the diaphragm in normal and pathological cases

The diaphragm is a muscular membrane separating the abdominal and thoracic cavities, and its motion is directly linked to respiration. In this study, using data from a 59-year-old female cadaver obtained from the Visible Human Project, the diaphragm is reconstructed and, from the corresponding solid object, a shell finite element mesh is generated and used in several analyses performed with the ABAQUS 6.7 software. These analyses consider the direction of the muscle fibres and the incompressibility of the tissue. The constitutive model for the isotropic strain energy as well as the passive and active strain energy stored in the fibres is adapted from Humphrey's model for cardiac muscles. Furthermore, numerical results for the diaphragmatic floor under pressure and active contraction in normal and pathological cases are presented.

Avaliação experimental do comportamento dinâmico de um edifício do século XIX: aplicação à calibração de modelos numéricos

Trabalho de Dissertação de natureza científica para obtenção do grau de Mestre em Engenharia Civil na Área de Especialização em Estruturas

Colloidal dipolar interactions in 2D smectic-C films

We use a two-dimensional (2D) elastic free energy to calculate the effective interaction between two circular disks immersed in smectic-C films. For strong homeotropic anchoring, the distortion of the director field caused by the disks generates topological defects that induce an effective interaction between the disks. We use finite elements, with adaptive meshing, to minimize the 2D elastic free energy. The method is shown to be accurate and efficient for inhomogeneities on the length scales set by the disks and the defects, that differ by up to 3 orders of magnitude. We compute the effective interaction between two disk-defect pairs in a simple (linear) configuration. For large disk separations, D, the elastic free energy scales as similar to D-2, confirming the dipolar character of the long-range effective interaction. For small D the energy exhibits a pronounced minimum. The lowest energy corresponds to a symmetrical configuration of the disk-defect pairs, with the inner defect at the mid-point between the disks. The disks are separated by a distance that, is twice the distance of the outer defect from the nearest disk. The latter is identical to the equilibrium distance of a defect nucleated by an isolated disk.

Modelação e monitorização do comportamento dinâmico de barragens abóbada: identificação modal automática

Trabalho Final de Mestrado elaborado no Laboratório de Engenharia Civil (LNEC) para obtenção do grau de Mestre em Engenharia Civil pelo Instituto Superior de Engenharia de Lisboa no âmbito do protocolo de cooperação entre o ISEL e o LNEC

Projeto de fundações e estrutura de colégio em Ponta Delgada utilizando os eurocódigos estruturais

Trabalho de Projeto para obtenção do grau de Mestre em Engenharia Civil na Área de Especialização em Estruturas