[pt] Otimização estrutural sujeita a carregamentos dinâmicos é um problema desafiador em vários aspectos, a começar pelo grande número de restrições que devem ser atendidas em todos os instantes de tempo. Além disso, o custo computacional para avaliar os gradientes destas restrições é bastante elevado e requer um grande espaço de armazenamento. Na literatura, alguns métodos reduzem o número de restrições avaliando em instantes de tempo selecionados, como o pior caso por exemplo, ou ainda constroem um funcional equivalente, integrando as restrições violadas ao longo do tempo, assim eliminando essa dependência. Nesta dissertação, o método do Carregamento Estático Equivalente (ESL) é utilizado, no qual o problema dinâmico original é transformado em uma sequência de subproblemas de otimização linear estática com múltiplos casos de carga. Um atrativo deste método é a possibilidade da solução de problemas não lineares, evitando o alto custo devido às repetidas análises estruturais e cálculos das restrições. Problemas clássicos de treliças planas submetidas a carregamentos dinâmicos são resolvidos utilizando o método ESL. A função a ser minimizada é a massa da treliça, que está sob restrições de tensão e deslocamento, onde as variáveis de projeto são as áreas da seção transversal dos membros. Além disso, uma interface utilizando ANSYS e MATLAB é desenvolvida para uma abordagem modular, na qual a análise via elementos finitos e a otimização possam ser realizadas separadamente. Este processo viabiliza a otimização de estruturas que apresentam comportamentos não lineares a partir da utilização de diversos softwares comerciais disponíveis no mercado. / [en] Structural optimization subject to dynamic loading is a challenging problem in many aspects, starting with the large number of constraints that must be respected at all instants of time. Furthermore, the computational cost to evaluate the gradients of these constraints is significantly high and requires a large storage space. In the literature, some methods reduce the number of constraints evaluating at selected instants of time, such as the worst case. Alternatively, a single equivalent functional is constructed to eliminate the time dependence by integrating the violated constraints over time. In this work, the Equivalent Static Load (ESL) method is used, in which the original dynamic problem is reduced into a number of static linear optimization problems with multiple load cases. An attractive feature of this method is the possibility of solving non-linear problems, avoiding the high cost due to repeated structural analyzes and constraint calculations. Classical problems of plane trusses subjected to dynamic loads are solved using the ESL method. The function to be minimized is the truss mass, which is subjected to stress and displacement constraints, where the design variables are the cross-sectional areas of the members. In addition, an interface using ANSYS and MATLAB was developed for a modular approach, in which finite element analysis and optimization can be performed separately. This process makes possible the optimization of structures that present non-linear behavior from the use of most structural analysis software packages available on the market.

Three progressively larger statnamic lateral load tests were performed on a 2.59 m diameter drilled shaft foundation after the surrounding soil was liquefied using down-hole explosive charges. An attempt to develop p-y curves from strain data along the pile was made. Due to low quality and lack of strain data, p-y curves along the test shaft could not be reliably determined. Therefore, the statnamic load tests were analyzed using a ten degree-of-freedom model of the pile-soil system to determine the equivalent static load-deflection curve for each test. The equivalent static load-deflection curves had shapes very similar to that obtained from static load tests performed previously at the site. The computed damping ratio was 30%, which is within the range of values derived from the log decrement method. The computer program LPILE was then used to compute the load-deflection curves in comparison with the response from the field load tests. Analyses were performed using a variety of p-y curve shapes proposed for liquefied sand. The best agreement was obtained using the concave upward curve shapes proposed by Rollins et al. (2005) with a p-multiplier of approximately 8 to account for the increased pile diameter. P-y curves based on the undrained strength approach and the p-multiplier approach with values of 0.1 to 0.3 did not match the measured load-deflection curve over the full range of deflections. These approaches typically overestimated resistance at small deflections and underestimated the resistance at large deflections indicating that the p-y curve shapes were inappropriate. When the liquefied sand was assumed to have no resistance, the computed deflection significantly overestimated the deflections from the field tests.

[pt] A otimização topológica de estruturas sujeitas a carregamentos que variam ao longo do tempo, costuma ter custos computacionais bastante elevados. Isso acontece devido ao grande número de análises dinâmicas que são necessárias. ALém disso, avaliar os gradientes da resposta, que fazem parte da análise de sensibilidade, também resulta em alto custo de computação e requer um grande espaço de armazenamento. Nesta dissertação, em vez de resolver o problema dinâmico original diretamente, é resolvida uma sequência de problemas de otimização de resposta estática com múltiplos casos de carga. Essa abordagem, chamada de método do carregamento estático equivalente, gera cargas estáticas que produzem uma resposta equivalente à obtida na análise dinâmica. Para avaliar as abordagens presentes na literatura, desenvolveu-se um código MATLAB, e diversos exemplos representativos são apresentados. / [en] Topology optimization in the time domain of structures subjected to time-dependent loads is usually computationally expensive, starting with the large number of time-dependent analyses that are required. Futhermore, the computational cost to evaluate the gradients of the response is significantly high and requires a large storage space. In this paper, instead of solving the original dynamical problem directly, we solve a sequence of static response optimization problems with many load cases. This approach, called the equivalent static loads method, generates static loads that produce a similar response in comparison to the same response that the dynamic analysis does. In order to verify the approaches present in the literature, a MATLAB code was developed, and several representatives examples are presented.

Kongsberg Automotive is developing a brand-new actuator for engaging and disengaging a clutch for different driveline applications. This master thesis research improves the concept design of the shift fork for the new Dog-Clutch Actuator using Design for Manufacturability (DFM). Initially, the knowledge about the mechanism of the product is gained with the aid of the design team and the proper boundary conditions for the boundary value problem are obtained. The conventional die-cast materials are investigated, and appropriate material is selected to create the material model. Most of the traditional HPDC aluminum alloys are aluminum-silicon system; therefore, a detailed study on the nucleation of Silicon in the melt and how it influences the mechanical properties of the alloy is conducted. During gear engagement, the two rotating gears of the dog-clutch collide and synchronize the angular velocity of the hub and the input gear. The synchronization force is dynamic; therefore, explicit time integration is used to capture the system's response with the assistance of FEM software. As the shift fork undergoes cyclic load during the gear shift, the fatigue analysis is performed to evaluate the life (Nf) of the component using Wohler's curve. The value of the maximum principal stress at the critical spots like notch and its direction are determined using the 3D Mohr's circle. In this analysis, the endurance limit correction factors and notch factor (Kf) are used for the S-N curve correction, and Goodman's criteria are used to incorporate the mean stress effect. Fatigue analysis requires a very fine mesh to estimate the precise stress magnitude at the critical locations and, the structural optimization algorithm requires many iterations to determine the optimal layout of the shift fork. Therefore, the explicit integration scheme is not efficient as it will be computationally expensive and time-consuming to solve the problem. Hence, the equivalent static load is determined for the gear shift force at the peak load and used for calculations and product development. As the initial concept design of the shift fork is asymmetrical, it requires varying stiffness in its structure to transfer the force efficiently to the shift sleeve. The FEA results state that one prong of the shift fork experience up to 75% of the total load, which increases the overall stress of the component (up to 0.9Sy). The shift fork also doesn't have adequate torsional stiffness, and as a result, stress concentration has occurred in one of the fillets in the shift fork. The iterative design is set up to improve the design of the shift fork by optimizing the stiffness of the two prongs which provided the key observations that describe the design changes which improved the design. In this phase, the overall stress of the component is reduced by 20% and minimizes the difference in the load between the two prongs by 27.5% compared to the initial design. The shift fork needs to be light to achieve the necessary acceleration during the gear shift. Therefore, topology optimization using the projected subgradient method is implemented to optimize the mass and compliance of the improved design in the iterative design phase. Then the design realization phase is set up to implement the results obtained from the topology optimization to conceptualize the viable product. The optimized result decreased the overall stress and maximum deflection by 20%. It also reduced the load difference in the two prongs of the shift fork by 35% by maintaining the same mass as the initial concept design.