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The Finite Element Method (FEM) is a technique for finding the approximate solution of differential equations. It is commonly used in structural analysis to evaluate the deformation and internal stresses of a structure that is subject to outer loads. This thesis investigates the Finite Element Analysis (FEA) workflow that is used at Andritz Hydro AB, with the objective to find solutions that make the workflow more time effective. The current workflow utilises Siemens NX and Salomé for pre- and post-processing, and Code Aster as the FEM solver. Two different approaches that improve the workflow are presented. The first suggest that the entire FEA workflow is migrated to NX using the built-in FEM package of NX called Advanced Simulation. The second approach utilises the Salomé API (Application Programming Interface) to create a customised toolbox (a script containing several functions) that automate several repetitive and cumbersome steps of the workflow, therefore effectively reducing the time that is required by the analyst to perform FEA. Due to the positive results and ease-of-use, the Salomé toolbox is preferred over the license cost and steep learning curve that is related to NX and Advanced Simulation.

The introduction of creases into thin sheets has a dramatic effect on their global mechanical properties. This can be observed by manipulating a crumpled piece of paper which has been unfolded; it no longer deforms in the same way as the original sheet. Creases have typically been modelled as singular hinge lines, often accompanied by a torsional spring to provide some opening resistance; however, the appropriate stiffness of these springs is unclear. In reality, creases have a discrete geometry based on the method they were formed. This dissertation investigates the flexural behaviour of a creased thin metallic strip and the influence of the crease geometry. When a strip is bent perpendicular to the crease, putting the crease region in tension and the strip edges in compression, initially torsional deformations occur which ultimately coalesce into a central localised flattened region. An analytical model of this flexural behaviour is developed, which idealises the crease as an initially circular segment. Predictions show the bending resistance increases as the crease decreases in size. The model predictions are compared to finite element analysis and experimental results showing excellent agreement. When a strip is bent in the opposite direction, with the crease region in compression and the strip edges in tension, a bistable snap-through occurs. The deformed shape is characterised by a sharp vertex on the crease line. An analytical model is developed by generalising a Gauss mapping approach, and used to predict the deformed shape. These predictions match experimental results well. This dissertation provides an understanding of the mechanics of creased thin strips, where the crease is given a discrete geometry, and explores the nature of localisation. It also provides the foundation to explore the mechanics of thin sheets featuring a network of creases. This offers the opportunity to improve the efficiency of thin shell structures by using creasing to optimise the mechanics, leading to reduced material use, more sustainable construction, and fuel savings from lighter vehicles.

Although instabilities and large oscillations are traditionally considered as conditions to be avoided in structures, a new design philosophy based on their exploitation towards the achievement of innovative mechanical features has been initiated in the last decade. In this spirit, instabilities are exploited towards the development of systems that can yield designed responses in the post-critical state. Further, the presence of oscillating constraints may allow for a stabilization of the dynamic response. These subjects entail a rich number of phenomena due to the non-linearity, so that the study of such mechanical systems becomes particularly complex, from both points of view of the mechanical modeling and of the computational tools. Two elastic structures are studied. The first consists of a flexible and extensible rod that is clamped at one end and constrained to slide along a given profile at the other. This feature allows one to study the effect of the axial stiffness of the rod on the tensile buckling of the system and on the compressive restabilization. A very interesting effect is that in a region of parameters double restabilization is found to occur, involving four critical compressive loads. Also, the mechanical system is shown to work as a novel force limiter that does not depend on sacrificial mechanical elements. Further, it is shown that the system can be designed to be multi-stable and suitable for integration in metamaterials. The second analyzed structure is a flexible but inextensible rod that is partially inserted into a movable rigid sliding sleeve which is kept vertical in a gravitational field. The system is analytically solved and numerically and experimentally investigated, when a horizontal sinusoidal input is prescribed at the sliding sleeve. In order to model the system, novel computational tools are developed, implementing the fully nonlinear inextensibility and kinematic constraints. It is shown that the mathematical model of the system agrees with the experimental data. Further, a study of the inclusion of dissipative terms is developed, to show that a steady motion of the rod can be accomplished by tuning the amplitude or the frequency of the sliding sleeve motion, in contrast with the situation in which a complete injection of the rod inside the sleeve occurs. A special discovery is that by slowly decreasing the frequency of the sleeve motion, the length of the rod outside the sleeve can be increased significantly, paving the way to control the rod’s end trajectory through frequency modulation.

No description available.

No description available.

No description available.

<p>The numerical simulation of physical systems plays a key role in different fields of science and engineering. The popularity of numerical methods stems from their ability to simulate complex physical phenomena for which analytical solutions are only possible for limited combinations of geometry, boundary, and initial conditions. Despite their flexibility, the computational demand of classical numerical methods quickly escalates as the size and complexity of the model increase. To address this limitation, and motivated by the unprecedented success of Deep Learning (DL) in computer vision, researchers started exploring the possibility of developing computationally efficient DL-based algorithms to simulate the response of complex systems. To date, DL techniques have been shown to be effective in simulating certain physical systems. However, their practical application faces an important common constraint: trained DL models are limited to a predefined set of configurations. Any change to the system configuration (e.g., changes to the domain size or boundary conditions) entails updating the underlying architecture and retraining the model. It follows that existing DL-based simulation approaches lack the flexibility offered by classical numerical methods. An important constraint that severely hinders the widespread application of these approaches to the simulation of physical systems.</p> <p><br></p> <p>In an effort to address this limitation, this dissertation explores DL models capable of combining the conceptual flexibility typical of a numerical approach for structural analysis, the finite element method, with the remarkable computational efficiency of trained neural networks. Specifically, this dissertation introduces the novel concept of <em>“Finite Element Network Analysis”</em> (FENA), a physics-informed, DL-based computational framework for the simulation of physical systems. FENA leverages the unique transfer knowledge property of bidirectional recurrent neural networks to provide a uniquely powerful and flexible computing platform. In FENA, each class of physical systems (for example, structural elements such as beams and plates) is represented by a set of surrogate DL-based models. All classes of surrogate models are pre-trained and available in a library, analogous to the finite element method, alleviating the need for repeated retraining. Another remarkable characteristic of FENA is the ability to simulate assemblies built by combining pre-trained networks that serve as surrogate models of different components of physical systems, a functionality that is key to modeling multicomponent physical systems. The ability to assemble pre-trained network models, dubbed <em>network concatenation</em>, places FENA in a new category of DL-based computational platforms because, unlike existing DL-based techniques, FENA does not require <em>ad hoc</em> training for problem-specific conditions.</p> <p><br></p> <p>While FENA is highly general in nature, this work focuses primarily on the development of linear and nonlinear static simulation capabilities of a variety of fundamental structural elements as a benchmark to demonstrate FENA's capabilities. Specifically, FENA is applied to linear elastic rods, slender beams, and thin plates. Then, the concept of concatenation is utilized to simulate multicomponent structures composed of beams and plate assemblies (stiffened panels). The capacity of FENA to model nonlinear systems is also shown by further applying it to nonlinear problems consisting in the simulation of geometrically nonlinear elastic beams and plastic deformation of aluminum beams, an extension that became possible thanks to the flexibility of FENA and the intrinsic nonlinearity of neural networks. The application of FENA to time-transient simulations is also presented, providing the foundation for linear time-transient simulations of homogeneous and inhomogeneous systems. Specifically, the concepts of Super Finite Network Element (SFNE) and network concatenation in time are introduced. The proposed concepts enable training SFNEs based on data available in a limited time frame and then using the trained SFNEs to simulate the system evolution beyond the initial time window characteristic of the training dataset. To showcase the effectiveness and versatility of the introduced concepts, they are applied to the transient simulation of homogeneous rods and inhomogeneous beams. In each case, the framework is validated by direct comparison against the solutions available from analytical methods or traditional finite element analysis. Results indicate that FENA can provide highly accurate solutions, with relative errors below 2 % for the cases presented in this work and a clear computational advantage over traditional numerical solution methods. </p> <p><br></p> <p>The consistency of the performance across diverse problem settings substantiates the adaptability and versatility of FENA. It is expected that, although the framework is illustrated and numerically validated only for selected classes of structures, the framework could potentially be extended to a broad spectrum of structural and multiphysics applications relevant to computational science.</p>

The performance of some polymeric materials is profoundly affected by long-term exposure to moisture during service. This poses problems for high precision and/or load bearing components in engineering applications where moisture-induced changes in mechanical properties and dimensional stability could compromise the reliability of the device or structure. In addition to external factors such as moisture, the material properties are also evolving due to inherent structural relaxation within the polymeric material through a process known as physical aging. Based on the current knowledge of both mechanisms, they have opposite effects on material properties. The common approach to studying the effects of moisture is to expose the polymeric material to combined moisture and heat, also referred to as hygrothermal conditions. The application of heat not only increases the rate of moisture diffusion but also accelerates physical aging processes which would otherwise be very slow. In spite of this coupled response, nearly all hygrothermal studies ignore physical aging in their investigations due to the complexity of the coupled problem. The goal of this work is to develop a numerical model for simulating the interactive effects of moisture diffusion and physical aging in a glassy polymer. The intent is to develop a capability that would also allow one to model these effects under various mechanical loading and heat transfer conditions. The study has chosen to model the response of polycarbonate/acrylonitrile-butadiene-styrene (PC/ABS), which is a glassy polymer blend that has very similar behaviour to polycarbonate. In this study, a comprehensive approach which considers four physical mechanisms – structural mechanics, moisture diffusion, heat conduction, and physical aging – has been applied. The most current analytical models in the literature usually attempt to model two or three coupled physical phenomena. To develop the four coupled phenomena model, the current work has undertaken an extensive scope of work involving experimental characterization and finite element modeling. In the experimental part of this work, seven sets of different tests were conducted to characterize the behaviour of PC/ABS exposed to moisture diffusion and accelerated physical aging. These experiments provided a comparative study between the effects of physical aging and moisture diffusion on the material’s behaviour; and at the same time, provided data for the numerical modeling. The dual glass transition temperatures (Tg) of the material were determined using two techniques: dynamic mechanical analysis (DMA) and thermo-mechanical analysis (TMA). The DMA tests provided data for studying the effects of hygrothermal aging on the Tg’s of the material and were also useful for mechanical tests such as creep and stress relaxation performed using the DMA. The Tg’s obtained using the TMA were also required for physical aging experiments using the dilatometry mode of TMA. Structural relaxation of the blend was studied by aging the material at 80 °C for 7 aging times in the TMA. These experiments gave an insight into the volume relaxation behaviour of the blend at a constant temperature. Specific heat capacity of the PC/ABS blend was also measured using another thermal analysis technique; i.e., differential scanning calorimeter (DSC), before and after test specimens were exposed to hygrothermal aging for 168 hours. The interactive effects of physical aging and moisture diffusion on the moisture uptake of the material were studied using gravimetric experiments performed at 5 different hygrothermal conditions. The experimental results were used to determine the coefficient of diffusion as well as the equilibrium moisture uptake of the samples. Furthermore, the effects of both moisture diffusion and physical aging on the mechanical behaviour of the polymer blend were investigated using stress relaxation tests. The comparison of the results of the tests performed on un-aged specimens with those of thermally and hygrothermally aged samples showed how physical aging effects competed with moisture diffusion. Also, the coefficient of hygroscopic expansion of the PC/ABS blend was determined using a so-called TMA/TGA technique. The numerical modeling of the four-coupled physics was achieved using the governing equations in the form of partial differential equations. Modeling was performed using the commercial finite element software package, COMSOL Multiphysics®. First, the uncoupled physical mechanisms of structural mechanics, moisture diffusion, and heat conduction were modeled separately to investigate the validity of the PDEs for each individual phenomenon. The modeling of the coupled physics was undertaken in two parts. The three coupled physics of structural mechanics, moisture diffusion, and heat conduction was first simulated for a gas pipe having a linear elastic behaviour. The comparison of the results with similar analysis available in the literature showed the capability of the developed model for the analysis of the triple coupled mechanisms. The second part modeled the four coupled phenomena by incorporating the experimentally determined coupling coefficients. In the developed numerical model, the material behaviour was considered to be linear viscoelastic, which complicated the model further but provided more realistic results for the behaviour of the polymer blend. Moreover, an approximation method was proposed for estimating the coupling coefficients that exist between different coupled physics in this study. It was also suggested that the anomalous moisture diffusion in the material can be modeled using a time varying boundary condition. Finally, the model was successfully verified and demonstrated using test case studies with thin thermoplastic plates. The proposed four-coupled physics model was able to predict with good accuracy the deflection of thin thermoplastic plates under bending for a set of hygorthermal test condition.