Dissertations / Theses on the topic 'The Newmark method'

Discontinuous deformation analysis (DDA) is a newly developed simulation method for discontinuous systems. It was designed to simulate systems with arbitrary shaped blocks with high efficiency while providing accurate solutions for energy dissipation. But DDA usually exhibits damping effects that are inconsistent with theoretical solutions. The deep reason for these artificial damping effects has been an open question, and it is hypothesized that these damping effects could result from the time integration scheme. In this thesis two time integration methods are investigated: the forward Euler method and the Newmark method. The work begins by combining the Newmark method and the DDA. An integrated Newmark method is also developed, where velocity and acceleration do not need to be updated. In simulations, two of the most widely used models are adopted to test the forward Euler method and the Newmark method. The first one is a sliding model, in which both the forward Euler method and the Newmark method give accurate solutions compared with analytical results. The second model is an impacting model, in which the Newmark method has much better accuracy than the forward Euler method, and there are minimal damping effects.
Master of Science

COMISSÃO NACIONAL DE ENERGIA NUCLEAR
Desenvolve –se um método de integração direta para solução temporal das equações de equilíbrio dinâmico resultantes de discretizações utilizando o método de elementos finitos. O algoritmo proposto consiste na generalização do método de Newmark com variação dos parâmetros de integração, permitindo uma redução do erro gerado no período da solução numérica e o aumento do passo temporal de integração. O método resultante é condicionalmente estável e uma análise detalhada do operador de aproximação temporal da solução, permite identificar a flexibilidade do método quanto ao erro introduzido na solução passo a passo. A Análise é desenvolvida considerando-se sistemas não dissipativos, porém conclusões da aplicação do método proposto são estendidas à sistemas amortecidos. O Algoritmo foi implementado em computador e alguns resultados são comparados com soluções analíticas e numéricas disponíveis que ilustram o desempenho e as possibilidades do método proposto.
A direct time integration method for the solution of dynamic equilibrium equations obtained from the finite element method is presented. The proposed algorithm is based on a generalization of the Newmark method for different integration parameters, which allows an error reduction in the integration time step. The method results in a conditionally stable technique, and a detailed analysis of the integration operator allows to identify its error response in the step-by-step solution. The analysis is presented for non-damping systems, however conclusion for applications of the proposed method to damping systems are also drawn. The algorithm has been implemented to analytical or other numerical solutions which illustrate its performance and applicability to engineering problems.

The meshless local Petrov-Galerkin (MLPG) method is used to numerically find an approximate solution of plane strain/stress linear elastostatic and elastodynamic problems. The MLPG method requires only a set of nodes both for the interpolation of the solution variables and the evaluation of various integrals appearing in the problem formulation. The monomial basis functions in the MLPG formulation have been enriched with those for the linear elastic fracture mechanics solutions near a crack tip. Also, the diffraction and the visibility criteria have been added to make the displacement field discontinuous across a crack. A computer code has been developed in Fortran and validated by comparing computed solutions of three static and one dynamic problem with their analytical solutions. The capabilities of the code have been extended to analyze contact problems in which a displacement component and the complementary traction component are prescribed at the same point of the boundary. The code has been used to analyze stress and deformation fields near a crack tip and to find the stress intensity factors by using contour integrals, the equivalent domain integrals and the J-integral and from the intercepts with the ordinate of the plots, on a logarithmic scale, of the stress components versus the distance ahead of the crack tip. We have also computed time histories of the stress intensity factors at the tips of a central crack in a rectangular plate with plate edges parallel to the crack loaded in tension. These are found to compare favorably with those available in the literature. The code has been used to compute time histories of the stress intensity factors in a double edge-notched plate with the smooth edge between the notches loaded in compression. It is found that the deformation fields near the notch tip are mode-II dominant. The mode mixity parameter can be changed in an orthotropic plate by adjusting the ratio of the Young's moduli in the axial and the transverse direction. The plane strain problem of compressing a linear elastic material confined in a rectangular cavity with rough horizontal walls and a smooth vertical wall has been studied with the developed code. Computed displacements and stresses are found to agree well with the analytical solution of the problem obtained by the Laplace transform technique. The Appendix describes the analysis with the finite element code ABAQUS of the dependence of the energy release rate upon the crack length in a polymeric disk enclosed in a steel ring and having a star shaped hole at its center. A starter crack is assumed to exist in one of the leaflets of the hole. The disk is loaded either by a pressure acting on the surfaces of the hole and the crack or by a temperature rise. Computed values of the energy release rate obtained by modeling the disk material as Hookean are found to be about 30% higher than those obtained when the disk material is modeled as Mooney-Rivlin. The latter set of results accounts for both material and geometric nonlinearities.
Ph. D.

In this study, the failure mechanism of the shore landslide which occured at Degirmendere coast region during 17 August 1999 Kocaeli (Izmit) - Turkey earthquake is analyzed. Geotechnical studies of the region are at hand, which reveal soil properties and geological formation of the region as well as the topography of the shore basin after deformations. The failure is analyzed as a landslide and permanent displacements are calculated by Newmark Method under 17 August 1999 Izmit record, scaled to a maximum acceleration of 0.4g. There are discussions on the main dominating mechanism of failure
landslide, liquefaction, fault rupture and lateral spreading. According to the studies, the failure mechanism is a seismically induced shore landslide also triggered by liquefaction and fault rupture, accompanied by the mechanism of lateral spreading by turbulence. A seismically induced landslide is discussed and modeled in this study. The finite element programs TELSTA and TELDYN are employed for static and dynamic analyses. Slope stability analyses are performed with the program SLOPE. The permanent displacements are calculated with Newmark Method, with the help of a MATLAB program, without considering the excess pore pressures.

Orientador: Aloisio Ernesto Assan
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo
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Resumo: Este estudo tem por objetivo implementar, em programa já existente para a análise de placas laminadas de compósitos, a análise dinâmica de placas laminadas sob ação de carregamento forçado com integração direta pelo algoritmo de Newmark. O programa inicial de elementos finitos, que realiza a análise estática, foi desenvolvido por Tápia (1998), usando o elemento finito de Kosmatka (1994), formulado com a teoria de deformação por cisalhamento de primeira ordem de Reissner-Mindlin. Cassiano (2002) implementou nesse programa o cálculo das freqüências naturais. Neste trabalho foi introduzida a análise dinâmica forçada, através da integração direta no tempo, empregando o método de Newmark. Exemplos comparativos com variações das espessuras das placas, do número de lâminas, das orientações das fibras e das vinculações das bordas, mostram o excelente comportamento do elemento finito aqui empregado
Abstract: : The aim of this study is the dynamic analysis of laminated composite plates under forced transverse vibration with time direct-integration method. The original program, with the static analysis, was developed by Tapia (1998) using the element proposed by Kosmatka (1994), formulated with first-order shear deformation theory of Reissner-Mindlin. Later Cassiano (2002) introduced into this finite element code the evaluation of the natural frequencies. In this thesis the dynamic analysis by means of a direct time integration method, which was formulated by Newmark, was performed. Comparative examples with several plates thicknesses, number of laminates, orientation of the fibers and boundary constraints, show the excellent performance of the finite element used herein
Mestrado
Estruturas
Mestre em Engenharia Civil

Orientador: Aloisio Ernesto Assan
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo
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Resumo: Neste trabalho estuda-se o comportamento de pórticos planos submetidos a ações dinâmicas. Apresenta-se, inicialmente, a Equação de Movimento de Lagrange através das variações das energias cinética, potencial mais o trabalho das forças não conservativas. Em seguida, pelo emprego do Método dos Elementos Finitos são desenvolvidas as matrizes de rigidez, massa e amortecimento para o elemento de pórtico plano. O amortecimento introduzido é o de Rayleigh. Estudam-se dois métodos para a realização da análise dinâmica: o método de Newmark e o Método da Superposição Modal, também sendo realizado um estudo do problema de autovalor e autovetor pelo emprego do Método das Potências e o Método da Deflação de Wielandt. Os autovalores e autovetores fornecerão as freqüências naturais e os modos de vibração da estrutura. Finalmente, são mostrados exemplos numéricos para a análise do comportamento dos pórticos planos
Abstract: In this work, it is studied the behavior of plane frames submitted to dynamic loads. First of all Lagrange¿s Equations of Motion is presented by the kinetic and potential energy variation plus the work of the nonconservative forces. Next, the stiffness, mass and damping matrices for the plane frame element are developed with the use of the Finite Element Method. Damping is introduced from the Rayleigh damping. Both Newmark Method and Modal Superposition Method are studied to carry out the dynamic analysis. It is also carried out a study of the eigenvalue problem by Power Method and Wielandt Deflation Method. Eigenvalues and eigenvectors will provide the natural frequencies and normal modes of the structure, respectively. Finally, numerical examples are related to the analysis of the plane frameworks behavior
Mestrado
Estruturas
Mestre em Engenharia Civil

The concept of using aluminum as the primary construction material for high speed ships and the hydroelastic behavior of the structure is widely gaining importance as a significant research topic in naval architecture. Aluminum is lighter than steel and hence can be predominantly used in high speed crafts which experiences significant slamming. This thesis work is focused on wedge shaped models. Free fall wedge impact is studied and a FORTRAN 90 computer program is developed to estimate the structural response of the wedge experiencing slamming by the use of matrix methods, finite element techniques and Newmark-Beta numerical time integration methods. The numerical solution is validated by comparison with the static solution. The theoretical hydrodynamic pressures which are used as input for this work was originally developed by using a flat cylinder theory [26]. The wedge drop at 0.6096 m (24 inch) drop height with an impact veloc- ity of v=3.05 m/s is based as the premise and the experimental pressure distributions measured by the pressure-transducers and the theoretical pressure predictions are used as inputs and the structural response is derived. Additionally, the response is compared for three different plate thicknesses and the results are compared against each other. The maximum deflection is comparable to the deflection evaluated from the experiment and tends to attain convergence as well. As the plate thickness reduces there tends to be a significant rise in the deflection values for the wedge plate, in the manner that when the plate thickness is halved there is a deviation of more than 75% in the deflection values as such.

The effects of a composite overwrapped gun barrel with viscoelastic damping layers are investigated. Interlaminar stresses and constrained layer damping effects are described. The Modal Strain Energy method is developed for measuring the extent to which the barrel is damped. The equations of motion used in the finite element analysis are derived. The transient solution process is outlined. Decisions for selected parameters are discussed. The results of the finite element analyses are presented using the program written in FORTRAN. The static solution is solved with a constant internal pressure resulting in a calculated loss factor from the Modal Strain Energy Method. The transient solution is solved using the Newmark-Beta method and a variable internal pressure. The analyses conclude that strategically placed viscoelastic layers dissipate strain energy more effectively than a thick single viscoelastic layer. The optimal angle for maximizing the coefficient of mutual influence in a composite cylinder is not necessarily the optimal angle when viscoelastic layers are introduced between layers.

Nel presente elaborato di tesi viene descritto un metodo di indagine che, mediante prove dinamiche e misure di accelerazione, si propone di identificare eventuali danneggiamenti in strutture reticolari spaziali. L’identificazione consiste, sulla base di dati sperimentali in termini di frequenze proprie del sistema, nel determinare, con la migliore precisione possibile l’area della sezione trasversale degli elementi. Il problema è formulato come un problema di ottimizzazione e l’identificazione è condotta mediante l’utilizzo di Algoritmi Genetici (brevemente GAs). In particolare, una funzione obiettivo misura la differenza tra le grandezze misurate sperimentalmente e le grandezze ottenute numericamente mediante un codice FEM della struttura in esame. Il principio cui sono ispirati gli algoritmi genetici fa sì che questi ricerchino il miglior individuo all’interno di una popolazione che rappresenta le possibili soluzioni del problema. Si riportano i dati ottenuti, mediante prove dinamiche, su una struttura reale, che permettono di ottenere informazioni sui parametri modali: frequenze proprie e smorzamento. Si confrontano, infine due differenti tipi di sensori di accelerazione, dimostrando la validità e i possibili benefici dell'utilizzo di sensori con tecnologia MEMS nell'ambito della misura delle vibrazioni.

Os Procedimentos de Comparações Múltiplas (PCM) podem ser utilizados para comparar médias de tratamentos. Há muitos testes de comparações múltiplas e, para escolher o melhor, devem ser levados em conta o controle do erro tipo I (testes exatos, conservadores ou liberais) e o poder desses testes. Para melhorar o seu desempenho, em relação ao erro tipo I e poder, métodos de reamostragem bootstrap têm sido utilizados em alguns estudos sobre PCM. O teste de Student-Newman-Keuls (SNK) possui boas qualidades estatísticas que poderiam ser melhoradas com o uso do bootstrap. Assim, os objetivos deste trabalho foram propor uma versão utilizando o bootstrap paramétrico do teste de comparações múltiplas SNK (SNKB), avaliar o desempenho do teste SNKB e compará-lo com o teste SNK. O desempenho foi avaliado pelas taxas de erro tipo I por experimento e pelo poder por meio de um estudo de simulação Monte Carlo em condições de normalidade e não normalidade dos resíduos. Foram realizadas N=1000 simulações de experimento com k tratamentos (k = 5, 10, 20 e 80) com r repetições (r = 4, 10 e 20). Diferentes hipóteses sobre as médias foram consideradas. Sob H0 completa, as médias foram consideradas todas iguais, sob H1, as médias foram todas diferentes, considerando a mesma variância, e, sob H0 parcial, foram considerados dois grupos cujas médias eram diferentes entre si. Ambos os testes apresentaram valores de taxas de erro tipo I próximos do nível nominal de 0,05 sob H0 completa e normalidade. Sob H0 completa e não normalidade, os testes SNK e SNKB controlaram as taxas de erro tipo I por experimento na maior parte dos casos simulados para k=5 e k=10, enquanto que, para k=20 e k=80, ambos os testes foram considerados liberais em alguns cenários. Sob H0 parcial, o teste SNKB foi liberal em todos os casos simulados, enquanto que o teste SNK foi, em geral, conservador para δ ≤ 2 e liberal para os demais valores de δ. O poder do teste proposto em geral superou o poder do teste original nas situações de normalidade e não normalidade. Assim, em situações práticas, se as diferenças entre as médias dos tratamentos forem pequenas (δ ≤ 2), o teste SNK é mais indicado por controlar o erro tipo I e apresentar valores de poder satisfatórios. Nos demais casos, o teste SNKB é mais recomendado, apesar de ambos serem liberais para δ ≥ 4, se a situação for de H0 parcial. Além disso, os testes SNK e SNKB foram aplicados em dados reais de um experimento delineado para avaliar os controles químico e mecânico de pragas da gravioleira com o objetivo de comparar os resultados obtidos pelos dois testes.
Multiple Comparisons Procedures (MCP) are used to compare treatment means. There are many tests with this purpose and to choose the best one, two features must be analysed: the control of type I error rate (exact, conservative or liberal tests) and the power. Bootstrap resampling methods have been used in some studies to improve the performance of MCP. The Student-Newman-Keuls (SNK) test shows good statistical qualities that can be improved with the use of bootstrap. Therefore, this study aimed to propose a SNK parametric bootstrap version (SNKB) and compare it with the original SNK test. The performance was evaluated by experimentwise error rates and power using a Monte Carlo simulation study considering normal and non-normal situations. We considered N = 1000 simulations of k treatments (k = 5, 10, 20 e 80) with r repetitions (r = 4, 10 and 20). Under null hypothesis, the means were considered all equal, under H1 the means were all different, but the variance was the same and, under partial H0, we considered two groups with different means. Both tests showed type I error rates values close to the nominal level of 0.05 under H0 and normality. Under H0 and non-normality, both tests controlled the experimentwise error rates in most simulated cases for k=5 and k=10, whereas, for k=20 and k=80, the tests were considered liberal in some scenarios. Under H0 partial, the SNKB test was liberal in all simulated cases, while SNK test was generally conservative for δ ≤ 2 and liberal to other δ values. In general, the power of the proposed test surpassed the power of original test under normality and non-normality. Thus, in practice, if the differences between the treatment means are small (δ ≤ 2), the SNK test works better given that it controls the type I error and the power is satisfactory. In the other cases, the SNKB test is recommended, although both are liberal for δ ≥ 4, if we are under partial H0. Furthermore, the tests were applied to a real experiment designed to evaluate the chemical and mechanical controls of pests soursop in order to compare the results of both tests.
Fundação de Amparo à Pesquisa do Estado de Minas Gerais - FAPEMIG

Nous étudions l’analyse asymptotique en relativité générale sous deux aspects: le peeling et le scattering (diffusion) conforme. Le peeling est construit pour les champs scalaires linéaire et non-linéaires et pour les champs de Dirac en espace-temps de Kerr (qui est non-stationnaire et à symétrie simplement axiale), généralisant les travaux de L. Mason et J-P. Nicolas (2009, 2012). La méthode des champs de vecteurs (estimations d’énergie géométriques) et la technique de compactification conforme sont développées. Elles nous permettent de formuler les définitions du peeling à tous ordres et d’obtenir les données initiales optimales qui assurent ces comportements. Une théorie de la diffusion conforme pour les équations de champs sans masse de spîn n/2 dans l’espace-temps de Minkowski est construite.En effectuant les compactifications conformes (complète et partielle), l’espace-temps est complété en ajoutant une frontière constituée de deux hypersurfaces isotropes représentant respectivement les points limites passés et futurs des géodésiques de type lumière. Le comportement asymptotique des champs s’obtient en résolvant le problème de Cauchy pour l’équation rééchelonnée et en considérant les traces des solutions sur ces bords. L’inversibilité des opérateurs de trace, qui associent le comportement asymptotique passé ou futur aux données initiales, s’obtient en résolvant le problème de Goursat sur le bord conforme. L’opérateur de diffusion conforme est alors obtenu par composition de l’opérateur de trace futur avec l’inverse de l’opérateur de trace passé
This work explores two aspects of asymptotic analysis in general relativity: peeling and conformal scattering.On the one hand, the peeling is constructed for linear and nonlinear scalar fields as well as Dirac fields on Kerr spacetime, which is non-stationary and merely axially symmetric. This generalizes the work of L. Mason and J-P. Nicolas (2009, 2012). The vector field method (geometric energy estimates) and the conformal technique are developed. They allow us to formulate the definition of the peeling at all orders and to obtain the optimal space of initial data which guarantees these behaviours. On the other hand, a conformal scattering theory for the spin-n/2 zero rest-mass equations on Minkowski spacetime is constructed. Using the conformal compactifications (full and partial), the spacetime is completed with two null hypersurfaces representing respectively the past and future end points of null geodesics. The asymptotic behaviour of fields is then obtained by solving the Cauchy problem for the rescaled equation and considering the traces of the solutions on these hypersurfaces. The invertibility of the trace operators, that to the initial data associate the future or past asymptotic behaviours, is obtained by solving the Goursat problem on the conformal boundary. The conformal scattering operator is then obtained by composing the future trace operator with the inverse of the past trace operator

The semi-classical black hole tunnelling method is a useful technique to calculate black hole temperature and understand black hole thermodynamics. I will investigate the black hole tunnelling method in detail. I will compare two different approaches used to calculate black hole tunnelling. The tunnelling method can be applied to a broad range of spacetimes and I will show this explicitly in order to demonstrate the robustness of the tunnelling technique. In particular, I will apply the tunnelling method to spacetimes including: Rindler (the method can recover the Unruh temperature), and more general spacetimes (such as Kerr-Newman and Taub-NUT). I will also discuss the 5d Kerr-Gödel spacetimes in detail (while showing a previous unobserved property of these spaces). Once the parameter space of Kerr-Gödel is understood in detail, I will show how the tunnelling method can also be successfully applied to the Kerr-Gödel black hole. Finally, the key result of my thesis involves extending the tunnelling method to model fermion emission. The previous tunnelling calculations all involved the emission of scalar particles. I will model the emission of spin-1/2 fermions from various spacetimes including the Rindler spacetime and general non-rotating black holes. I will also model the emission of charged spin-1/2 fermions from the Kerr-Newman spacetime to show that the method is also applicable to rotating spacetimes. In all these cases I show that the correct Hawking temperature (Unruh temperature in the case of Rindler) is recovered for spin-1/2 fermion emission. Although this final result is not surprising, it is an important result because it confirms that Dirac particles will radiate from the black hole at the same temperature as scalar particles. It has always been assumed that this is the case but there is very little literature involving fermion radiation of black holes. So the results of my calculations are twofold, I demonstrate that Dirac particles are emitted at the same temperature as scalar particles from a black hole and it shows how robust the semi-classical tunnelling technique is.