Explicit methods are widely used in finite element analysis as efficient ways to solve differential equations. The efficiency of explicit methods relies on the economical evaluation of internal forces at each time step. The greatest efficiency can be provided by one-point quadrature. However, instability arises because of the shortcomings in the use of one-point quadrature. The instability is called hourglass mode, or spurious singular mode. An effective method to control the instability is to add “hourglass stiffness” to an element integrated by one-point quadrature. Explicit methods often require a very small time step to ensure stability. Thus, for complex problem with refined meshes, a very large number of timesteps will be required to complete the analysis. Minimizing the number of operations per time step can provide significant improvement on efficiency of the methods. Since hourglass terms typically require more computational operations than one-point quadrature terms, we are very interested in reducing the number of operations on hourglass control. In addition, considerable approximation is involved with hourglass control, and hence overall accuracy may not be seriously affected by relaxing the precision of the temporal integration of the hourglass force. Consequently, there is a possibility of trading some accuracy of the hourglass control for computational efficiency. A subcycling approach is applied to the hourglass portion of explicit methods. Namely, instead of updating hourglass forces every time step, we update hourglass forces every two steps. The proposed approach is examined with the use of mass-spring models. The applicability to more complex models is demonstrated on a 3-D model with the subcycling approach implemented into an explicit finite element code. Efficiency, stability and accuracy are discussed as important issues of the proposed approach. The mass-spring models and finite element implementation show that a beating instability can be introduced by the subcycling approach, and additional restriction is placed on the stable time step for the central difference operator. However, sufficient damping can restore the usual stability conditions. Thus, the proposed subcycling approach is seen to be highly advantageous where damping can be used, and it can cut computation time by 30% or more without significantly affecting the overall accuracy of the solution. / Thesis / Master of Applied Science (MASc)

[pt] O custo computacional requerido nas simulações de problemas em dinâmica estrutural em geral é muito alto. Em determinadas situações é necessária a obtenção de respostas imediatas a fim de que sejam tomadas decisões importantes com base nessas respostas. Em outras situações existe a necessidade de se fazer várias simulações de um mesmo problema variando alguns poucos parâmetros entre elas. Estas situações são muito comuns em problemas envolvendo a análise dinâmica de linhas de ancoragem que é objeto de estudo deste trabalho. Este trabalho apresenta um sistema para análise dinâmica de linhas de ancoragem que utiliza recursos de adaptação no tempo e de subciclagem com o objetivo de melhorar a precisão e a eficiência das simulações. Este sistema consiste de um ambiente gráfico através do qual são disponibilizados recursos de pré- processamento, análise e pós-processamento. Durante o processo de análise numérica estão disponíveis para o usuário as facilidades de pré- e pós-processamento caracterizando o paradigma de análise interativa-adaptativa. São apresentados neste trabalho a metodologia utilizada no desenvolvimento deste sistema e os resultados obtidos com a utilização do mesmo, mostrando que com a utilização de recursos como a subciclagem e adaptação no tempo é possível a obtenção de respostas precisas num tempo muito menor do que o tempo que seria requerido numa análise convencional. / [en] In general, the computational cost required for dynamic simulations of structural problems is very high. In certain situations, the system must provide immediate answers so that important decisions can be made based on them. In other cases, several simulations of the same problem, varying only a few parameters, must be performed. Such contexts are very common in problems involving the dynamic analysis of mooring lines.This work presents a computational system for the dynamic analysis of mooring lines using a time-step adaptivity scheme and a subcycling technique with the objective of improving the precision and efficiency of the simulations. The system is an integrated graphical environment and consists of three modules: preprocessor, analysis, and postprocessor. It also allows interactive-adaptive analysis, in which the user can interrupt the analysis at any time, change parameters and restart the simulation.The methodology used in the development of this system is discussed in detail. The results obtained using the time-step adaptivity and subcycling techniques demonstrate that the computational cost can be substantially reduced by using the proposed methodology when compared to conventional formulations presented in the technical literature.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-01-04T11:17:29Z No. of bitstreams: 1 daniellerosanydemedeirosleal.pdf: 19032116 bytes, checksum: 03bebf3d76cd23f21fc6a647e7c00d77 (MD5) / Approved for entry into archive by Diamantino Mayra (mayra.diamantino@ufjf.edu.br) on 2017-01-31T10:32:59Z (GMT) No. of bitstreams: 1 daniellerosanydemedeirosleal.pdf: 19032116 bytes, checksum: 03bebf3d76cd23f21fc6a647e7c00d77 (MD5) / Made available in DSpace on 2017-01-31T10:32:59Z (GMT). No. of bitstreams: 1 daniellerosanydemedeirosleal.pdf: 19032116 bytes, checksum: 03bebf3d76cd23f21fc6a647e7c00d77 (MD5) Previous issue date: 2016-08-29 / Este trabalho apresenta um novo esquema explícito de marcha no tempo para a análise problemas de propagação de ondas compatível com qualquer método de discretização espacial que seja baseado em elementos (e.g., Método dos Elementos Finitos, etc.). Por ser explícito, isto é, sem necessidade da solução de um sistema de equações, o método é de fácil implementação. Baseado em integradores de tempo adaptativos, a técnica aqui proposta contempla dissipação numérica local e otimizada, permitindo a minimização de oscilações espúrias e aumento da precisão. Também, com o emprego de discretização temporal local (subciclagem), acrescenta-se robustez ao algoritmo do método, flexibilizando a estabilidade e aumentando a eficiência da análise em foco. / This work presents a new explicit time marching procedure for wave propagation problems, which is compatible with any spatial discretization method based on elements (e.g. Finite Element Method - FEM, etc.). Because it does not require any system of equations to be solved, its implementation is very simple. Based on adaptive time integrators, it provides local and optimized numerical damping, allowing the influence of spurious oscillations to be minimized, improving accuracy. In addition, by employing local time discretization, considering a subclycing technique, the performance to the method is improved, enhancing the flexibility of the method regarding stability and increasing the efficiency of the proposed approach.