Academic literature 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.<br>Master of Science

COMISSÃO NACIONAL DE ENERGIA NUCLEAR<br>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.<br>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.<br>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<br>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<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo<br>Made available in DSpace on 2018-08-07T16:33:50Z (GMT). No. of bitstreams: 1 Volpini_EstevaoXavier_M.pdf: 3994255 bytes, checksum: 682eea9ccb0ec139a6d062e4466cd140 (MD5) Previous issue date: 2006<br>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<br>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<br>Mestrado<br>Estruturas<br>Mestre em Engenharia Civil

Orientador: Aloisio Ernesto Assan<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo<br>Made available in DSpace on 2018-08-07T10:17:54Z (GMT). No. of bitstreams: 1 Gatti_AndersonCarlos_M.pdf: 1799347 bytes, checksum: c5db751be8130693e5a2966d279bc22e (MD5) Previous issue date: 2006<br>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<br>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<br>Mestrado<br>Estruturas<br>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.