Smart passive adaptive control of laminated composite plates (through optimisation of fibre orientation)

In the classical laminate plate theory for composite materials, it is assumed that the laminate is thin compared to its lateral dimensions and straight lines normal to the middle surface remain straight and normal to the surface after deformation. As a result, the induced twist which is due to the transverse shear stresses and strains are neglected. Also, this induced twist was considered as an unwanted displacement and hence was ignored. However, in certain cases this induced twist would not be redundant and can be a useful displacement to control the behaviour of the composite structure passively. In order to use this induced twist, there is a need for a modified model to predict the behaviour of laminated composites. A composite normally consists of two materials; matrix and fibres. Fibres can be embedded in different orientations in composite lay-ups. In this research, laminated composite models subject to transfer shear effect are studied. A semi analytical model based on Newton-Kantorovich-Quadrature Method is proposed. The presented model can estimate the induced twist displacement accurately. Unlike other semi analytical model, the new model is able to solve out of plane loads as well as in plane loads. It is important to mention that the constitutive equations of the composite materials (and as a result the induced twist) are determined by the orientation of fibres in laminae. The orientation of composite fibres can be optimised for specific load cases, such as longitudinal and in-plane loading. However, the methodologies utilised in these studies cannot be used for general analysis such as out of plane loading problems. This research presents a model whereby the thickness of laminated composite plates is minimised (for a desirable twist angle) by optimising the fibre orientations for different load cases. In the proposed model, the effect of transverse shear is considered. Simulated annealing (SA), which is a type of stochastic optimisation method, is used to search for the optimal design. This optimisation algorithm is not based on the starting point and it can escape from the local optimum points. In accordance with the annealing process where temperature decreases gradually, this algorithm converges to the global minimum. In this research, the Tsai-Wu failure criterion for composite laminate is chosen which is operationally simple and readily amenable to computational procedures. In addition, this criterion shows the difference between tensile and compressive strengths, through its linear terms. The numerical results are obtained and compared to the experimental data to validate the methodology. It is shown that there is a good agreement between finite element and experimental results. Also, results of the proposed simulated annealing optimisation model are compared to the outcomes from previous research with specific loading where the validity of the model is investigated

Hierarchical component-wise models for enhanced stress analysis and health monitoring of composites structures

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Advances in Structural Mechanics Modeled with FEM

It is well known that many structural and physical problems cannot be solved by analytical approaches. These problems require the development of numerical methods to get approximate but accurate solutions. The minite element method (FEM) represents one of the most typical methodologies that can be used to achieve this aim, due to its simple implementation, easy adaptability, and very good accuracy. For these reasons, the FEM is a widespread technique which is employed in many engineering fields, such as civil, mechanical, and aerospace engineering. The large-scale deployment of powerful computers and the consequent recent improvement of the computational resources have provided the tools to develop numerical approaches that are able to solve more complex structural systems characterized by peculiar mechanical configurations. Laminated or multi-phase composites, structures made of innovative materials, and nanostructures are just some examples of applications that are commonly and accurately solved by the FEM. Analogously, the same numerical approaches can be employed to validate the results of experimental tests. The main aim of this Special Issue is to collect numerical investigations focused on the use of the finite element metho

General δ\delta-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation

In this work we consider the two-dimensional Dirac operator with general local singular interactions supported on a closed curve. A systematic study of the interaction is performed by decomposing it into a linear combination of four elementary interactions: electrostatic, Lorentz scalar, magnetic, and a fourth one which can be absorbed by using unitary transformations. We address the self-adjointness and the spectral description of the underlying Dirac operator, and moreover we describe its approximation by Dirac operators with regular potentials

Algorithmic Modelling of Folded Surfaces. Analysis and Design of Folded Surfaces in Architecture and Manufacturing.

Both in the field of design and architecture origami is often taken as a reference for its kinetic proprieties and its elegant appearance. Dynamic facades, fast deployment structures, temporary shelters, portable furniture, retractile roofs, are some examples which can take advantage of the kinetic properties of the origami. While designing with origami, the designer needs to control shape and motion at the same time, which increases the complexity of the design process. This complexity of the design process may lead the designers to choose a solution where the patterns are mere copies of well-known patterns or to reference to the origami only for ornamental purposes. The origami-inspired projects that we gathered and studied in the fields of architecture, manufacturing and fashion, confirmed this trend. We observed that the cause of this lack of variety could also be attributed to insufficient knowledge, or to inefficiency of the design tools. Many researchers studied the mathematical implications of origami, to be able to design specific patterns for precise applications. However, this theoretical knowledge is hard to apply directly to different practical projects without a deep understanding of these theorems. Thus, in this thesis, we aim to narrow the gap between potentialities of this discipline and limits of the available designing tools, by proposing a simplified synthetic constructive approach, applied with a parametric modeller, which allows the designers to bypass scripting and algebraic formulations and, at the same time, it increases the design freedom. Among the cases studies, we propose some fabrication-aimed examples, which introduce the subjects of thick-origami, distribution of stresses and analysis of deformations of the folded models.Nei campi dell’architettura e dell’industrial design, l’origami è spesso preso come riferimento per le sue proprietà cinetiche e le sue forme eleganti. Facciate dinamiche, strutture pieghevoli, rifugi temporanei, arredi portatili, tetti retrattili, sono alcuni esempi di progetti che potrebbero beneficiare delle proprietà cinetiche dell’origami. Progettare con l’origami richiede di controllare forma e movimento contemporaneamente; ciò aumenta la complessità del processo progettuale. Questa difficoltà progettuale può portare i progettisti a scegliere soluzioni che non sono altro che mere copie di pattern noti o a considerare l’origami come riferimento solo per ragioni ornamentali. I progetti ispirati all’origami che abbiamo raccolto ed analizzato nei campi di architettura, industria manifatturiera, e moda, confermano questo trend. Abbiamo osservato che la causa di questo mero utilizzo potrebbe essere attribuibile a preparazione insufficiente del progettista o a inefficienza degli strumenti progettuali. Diversi ricercatori hanno studiato le implicazioni matematiche dell’origami, per poter progettare specifici pattern per precise applicazioni. Nonostante ciò, questa conoscenza teorica è difficile da applicare direttamente ad altri progetti pratici senza una profonda comprensione di questi teoremi. Questa tesi punta quindi a ridurre il divario tra potenzialità di questa disciplina e limiti imposti dagli strumenti progettuali disponibili, proponendo un approccio sintetico e costruttivo semplificato, che permetta ai progettisti di evitare scripting e formulazioni algebriche, aumentando allo stesso tempo la libertà progettuale. Tra i casi studio, proponiamo anche alcuni esempi mirati alla fabbricazione che introducono il tema dell’origami a spessore non nullo, della distribuzione delle forze e dell’analisi delle deformazioni sui modelli piegati

Topological finiteness properties of monoids. Part 1: Foundations

We initiate the study of higher dimensional topological finiteness properties of monoids. This is done by developing the theory of monoids acting on CW complexes. For this we establish the foundations of $M$-equivariant homotopy theory where $M$ is a discrete monoid. For projective $M$-CW complexes we prove several fundamental results such as the homotopy extension and lifting property, which we use to prove the $M$-equivariant Whitehead theorems. We define a left equivariant classifying space as a contractible projective $M$-CW complex. We prove that such a space is unique up to $M$-homotopy equivalence and give a canonical model for such a space via the nerve of the right Cayley graph category of the monoid. The topological finiteness conditions left-$\mathrm{F}_n$ and left geometric dimension are then defined for monoids in terms of existence of a left equivariant classifying space satisfying appropriate finiteness properties. We also introduce the bilateral notion of $M$-equivariant classifying space, proving uniqueness and giving a canonical model via the nerve of the two-sided Cayley graph category, and we define the associated finiteness properties bi-$\mathrm{F}_n$ and geometric dimension. We explore the connections between all of the these topological finiteness properties and several well-studied homological finiteness properties of monoids which are important in the theory of string rewriting systems, including $\mathrm{FP}_n$, cohomological dimension, and Hochschild cohomological dimension. We also develop the corresponding theory of $M$-equivariant collapsing schemes (that is, $M$-equivariant discrete Morse theory), and among other things apply it to give topological proofs of results of Anick, Squier and Kobayashi that monoids which admit presentations by complete rewriting systems are left-, right- and bi-$\mathrm{FP}_\infty$.Comment: 59 pages, 1 figur

Higher-order Strong and Weak Formulations for Arbitrarily Shaped Doubly-Curved Shells Made of Advanced Materials

The well-known three-dimensional elasticity theory represents the most comprehensive approach to analyze the structural behavior of doubly-curved shells. However, this approach could be extremely burdensome in terms of calculation. Consequently, two-dimensional models are introduced to reduce the computations to obtain the solution. Among them, the Classical Shell Theory (CST) and the First-order Shear Deformation Theory (FSDT) are the most exploited approaches due to their simplicity. Nevertheless, their inadequacy could be evident if innovative and advanced mechanical constituents are considered. For this purpose, more refined approaches are developed. These models are known as Higher-order Structural Theories (HSDTs). This thesis aims to present a higher-order formulation able to model accurately the mechanical behavior of doubly-curved shells made of innovative and advanced materials. It is known that a closed-form solution cannot be obtained for these mathematical models. In other words, the governing equations cannot be solved analytically. Thus, a numerical method must be used to get an approximate solution. In general, two formulations of the same system of governing equations can be developed, which are the strong and weak formulations, respectively. If the strong formulation is solved, a numerical tool capable to approximate derivatives is required, since these equations are directly changed into a discrete system. On the other hand, a numerical approximation of integrals is needed when an equivalent integral formulation of lower order is solved, as in the case of the weak form. Therefore, two different numerical methods can be used to obtain the solution of these formulations. The Differential Quadrature (DQ) and Integral Quadrature (IQ) methods are discussed in this thesis. The accuracy, stability and reliability of the present formulations, as well as their superiority with respect to commercial Finite Element codes, are proven by a set of numerical analyses. An excellent agreement with the exact solutions is observed

On Undecidable Dynamical Properties of Reversible One-Dimensional Cellular Automata

Cellular automata are models for massively parallel computation. A cellular automaton consists of cells which are arranged in some kind of regular lattice and a local update rule which updates the state of each cell according to the states of the cell's neighbors on each step of the computation. This work focuses on reversible one-dimensional cellular automata in which the cells are arranged in a two-way in_nite line and the computation is reversible, that is, the previous states of the cells can be derived from the current ones. In this work it is shown that several properties of reversible one-dimensional cellular automata are algorithmically undecidable, that is, there exists no algorithm that would tell whether a given cellular automaton has the property or not. It is shown that the tiling problem of Wang tiles remains undecidable even in some very restricted special cases. It follows that it is undecidable whether some given states will always appear in computations by the given cellular automaton. It also follows that a weaker form of expansivity, which is a concept of dynamical systems, is an undecidable property for reversible one-dimensional cellular automata. It is shown that several properties of dynamical systems are undecidable for reversible one-dimensional cellular automata. It shown that sensitivity to initial conditions and topological mixing are undecidable properties. Furthermore, non-sensitive and mixing cellular automata are recursively inseparable. It follows that also chaotic behavior is an undecidable property for reversible one-dimensional cellular automata.Siirretty Doriast