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Metastructures are engineered systems composed of periodic arrays of identical components, called resonators, designed to achieve specific dynamic effects, such as creating a band gap-a frequency range where waves cannot propagate through the structure. When equipped with patches of piezoelectric material, these metastructures exhibit an additional capability: they can harvest energy effectively even from frequencies much lower than the fundamental frequency of an individual resonator. This energy harvesting capability is particularly valuable for applications where low-frequency vibrations dominate. To support the design of metastructures for dual purposes, such as energy harvesting and vibration suppression (reducing unwanted oscillations in the structure), we develop a multi-patch isogeometric model of a piezoelectric energy harvester. This model is based on a piezoelectric Kirchhoff-Love plate-a thin, flexible structure with embedded piezoelectric patches-and uses Nitsche's method to enforce compatibility conditions in terms of displacement, rotations, shear force, and bending moments across the boundaries of different patches. The model is validated against experimental and numerical data from the literature. We then present a novel, parameterized metastructure plate design and conduct a parametric study to explore how resonator geometries affect key performance metrics, including the location and width of the band gap and the position of the first peak in the voltage frequency response function. This model can be integrated with optimization algorithms to maximize outcomes such as energy harvesting efficiency or vibration reduction, depending on application needs.

The thermal conductivity of Functionally Graded Materials (FGMs) can be efficiently designed through topology optimization to obtain thermal meta-structures that actively steer the heat flow. Compared to conventional analytical design methods, topology optimization allows handling arbitrary geometries, boundary conditions and design requirements; and producing alternate designs for non-unique problems. Additionally, as far as the design of meta-structures is concerned, topology optimization does not need intuition-based coordinate transformation or the form invariance of governing equations, as in the case of transformation thermotics. We explore isogeometric density-based topology optimization in the continuous setting, which perfectly aligns with FGMs. In this formulation, the density field, geometry and solution of the governing equations are parameterized using non-uniform rational basis spline entities. Accordingly, the heat conduction problem is solved using Isogeometric Analysis. We design various 2D & 3D thermal meta-structures under different design scenarios to showcase the effectiveness and versatility of our approach. We also design thermal meta-structures based on architected cellular materials, a special class of FGMs, using their empirical material laws calculated via numerical homogenization.

The current battery-powered fault detection system for vibration monitoring has a rather limited lifetime. This is because the high-frequency sampling (typically tens of kilo-Hertz) required for vibration monitoring results in high energy consumption in both the analog-to-digital (ADC) converter and wireless transmissions. This paper proposes a new fault detection architecture that can significantly reduce the energy consumption of the ADC and wireless transmission. Our inspiration for the new architecture is based on the observation that the many tens of thousand of data samples collected for fault detection are ultimately transformed into a small number of features. If we can generate these features directly without high frequency sampling, then we can avoid the the energy cost for ADC and wireless transmissions. We propose to use piezoelectric energy harvesters (which can be designed to have different frequency responses) and integrators to obtain these features in an energy-efficient manner. By using a publicly available data set for ball bearing fault detection (which was originally sampled at 51.2kHz) and piezoelectric energy harvester models, we can produce features, which when sampled at 0.33Hz, give a fault detection accuracy of 89% while reducing the sampling requirement by 4 orders-of-magnitude., Comment: 8 pages, 8 figures

Piezoelectric energy harvesters (PEHs) can be used as an additional power supply for a Structural Health Monitoring (SHM) system. Its design can be optimised for the best performance; however, the optimal design depends on the input vibration, e.g. acceleration of a bridge due to wind loads and passing traffic. In previous studies, we have shown that optimal design tunes to some predominant frequency of the signal spectrum. However, our previous study was limited to a single location of a PEH on a bridge. In this work, we extend the rigorous optimisation framework to include the effect of the PEH's location. The optimisation framework uses the PEH plate model discretised by IsoGeometric Analysis (IGA) and coupled with the Particle Swarm Optimisation algorithm to find the designs with maximum energy outputs for many acceleration histories, extracted from the recorded dynamic response data of a real cable-stayed bridge in Australia. Then, clustering is performed to find several best candidates for the entire bridge. An additional study is performed to quantify the effect of traffic intensity on the produced energy. It is shown that variation in traffic volume throughout the 24hr time window leads to variation in optimal PEH designs. The study concludes the impact of location and traffic on energy harvesting by identifying the optimal PEH design and placement throughout the bridge structure. The results indicate that the key factors of maximising energy harvesting efficiency are related to the input excitation and the mode of vibration being excited. The position of maximum displacement in the vibration mode corresponds to the best location for energy harvesting. Also, the change in traffic intensity affects the amount of convertible mechanical energy and also directs the fundamental frequency of a PEH to shift within a specific range of frequencies to achieve the highest energy conversion.

We exploit level set topology optimization to find the optimal material distribution for metamaterial-based heat manipulators. The level set function, geometry, and solution field are parameterized using the non-uniform rational B-spline (NURBS) basis functions in order to take advantage of easy control of smoothness and continuity. In addition, NURBS approximations can produce conic geometries exactly and provide higher efficiency for higher-order elements. The values of the level set function at the control points (called expansion coefficients) are utilized as design variables. For optimization, we use an advanced mathematical programming technique, Sequential Quadratic Programming (SQP). Taking into account a large number of design variables and the small number of constraints associated with our optimization problem, the adjoint method is utilized to calculate the required sensitivities with respect to the design variables. The efficiency and robustness of the proposed method are demonstrated by solving three numerical examples. We have also shown that the current method can handle different geometries and types of objective functions. In addition, regularization techniques such as Tikhonov regularization and volume regularization have been explored to reduce unnecessary complexity and increase the manufacturability of optimized topologies.

Geometry Independent Field approximaTion (GIFT) was proposed as a generalization of Isogeometric analysis (IGA), where different types of splines are used for the parameterization of the computational domain and approximation of the unknown solution. GIFT with Non-Uniform Rational B-Splines (NUBRS) for the geometry and PHT-splines for the solution approximation were successfully applied to problems of time-harmonic acoustics, where it was shown that in some cases, adaptive PHT-spline mesh yields highly accurate solutions at lower computational cost than methods with uniform refinement. Therefore, it is of interest to investigate performance of GIFT for shape optimization problems, where NURBS are used to model the boundary with their control points being the design variables and PHT-splines are used to approximate the solution adaptively to the boundary changes during the optimization process. In this work we demonstrate the application of GIFT for 2D acoustic shape optimization problems and, using three benchmark examples, we show that the method yields accurate solutions with significant computational savings in terms of the number of degrees of freedom and computational time.

There has been a growing interest in controlled heat flux manipulation to increase the efficiency of thermal apparatus. Heat manipulators control and manipulate heat flow. A key to the effective performance of these heat manipulators is their thermal design. Such designs can be achieved by a periodic assembly of unit cells (known as metamaterials or meta-structure), whose geometry and material properties can be optimized for a specific objective. In this work, we focus on thermal metamaterial-based heat manipulators such as thermal concentrator (which concentrates the heat flux in a specified region of the domain). The main scope of the current work is to optimize the shape of the heat manipulators using Particle Swarm Optimization (PSO) method. The geometry is defined using NURBS basis functions due to the higher smoothness and continuity and the thermal boundary value problem is solved using Isogeometric Analysis (IGA). Often, nodes as design variables (as in Lagrange finite element method) generate the serrate shapes of boundaries which need to be smoothened later. For the NURBS-based boundary with the control points as design variables, the required smoothness can be predefined through knot vectors and smoothening in the post-processing can be avoided. The optimized shape generated by PSO is compared with the other shape exploited in the literature. The effects of the number of design variables, the thermal conductivity of the materials used, as well as some of the geometry parameters on the optimum shapes are also demonstrated.

Piezoelectric Energy Harvesters (PEHs) are typically employed to provide additional source of energy for a sensing system. However, studies show that a PEH can be also used as a sensor to acquire information about the source of vibration by analysing the produced voltage signal. This opens a possibility to create Simultaneous Energy Harvesting and Sensing (SEHS) system, where a single piece of hardware, a PEH, acts as both, a harvester and as a sensor. This raises a question if it is possible to design a bi-functional PEH device with optimal harvesting and sensing performance. In this work, we propose a bi-objective PEH design optimisation framework and show that there is a trade-off between energy harvesting efficiency and sensing accuracy within a PEH design space. The proposed framework is based on an extensive vibration (strain and acceleration) dataset collected from a real-world operational cable-stayed bridge in New South Wales, Australia. The bridge acceleration data is used as an input for a PEH numerical model to simulate a voltage signal and estimate the amount of produced energy. The numerical PEH model is based on the Kirchhoff-Love plate and isogeometric analysis. For sensing, convolutional neural network AlexNet is trained to identify traffic speed labels from voltage CWT (Continuous Wavelet Transform) images. In order to improve computational efficiency of the approach, a kriging metamodel is built and genetic algorithm is used as an optimisation method. The results are presented in the form of Pareto fronts in three design spaces.

Vibrational energy harvested from the bridge excitation due to the traffic flow or the wind load can be supplied to sensors in a Structural Health Monitoring (SHM) system and help prolong its service life, reduce chemical battery waste and enable its use in remote locations. A common approach to designing a Piezoelectric Energy Harvester (PEH) consists in tuning its fundamental frequency to some target value (e.g., the fundamental frequency of a bridge). However, such approach does not answer the question if the chosen target frequency is optimal, and does not take into account the possibility to have multiple design configurations with the same fundamental frequency. In this work, we approach the problem of a PEH design optimisation in a rigorous way, using a PEH model based on the Kirchhoff-Love plate theory and Isogeometric Analysis (IGA), coupled with the Modal Order Reduction (MOR) approach and Runge-Kutta time integration method. The model is further equipped with the Particle Swarm Optimisation (PSO) algorithm that allows finding geometry which maximises energy output from a given base acceleration signal. A comprehensive study is conducted to infer the impact of a PEH geometry on its energy harvesting performance in a real-world setting by considering field health monitoring data of a large-scale cable-stayed bridge in NSW, Australia. A shape optimisation framework is developed based on acceleration events, i.e., where the level of response exceeds a certain threshold. Designs obtained in the event-based optimisation are then clustered to propose several best candidates for continuous energy generation. This work represents the first study on PEH design optimisation for real operational conditions.

The Linear Smoothing (LS) scheme \cite{francisa.ortiz-bernardin2017} ameliorates linear and quadratic approximations over convex polytopes by employing a three-point integration scheme. In this work, we propose a linearly consistent one point integration scheme which possesses the properties of the LS scheme with three integration points but requires one third of the integration computational time. The essence of the proposed technique is to approximate the strain by the smoothed nodal derivatives that are determined by the discrete form of the divergence theorem. This is done by the Taylor's expansion of the weak form which facilitates the evaluation of the smoothed nodal derivatives acting as stabilization terms. The smoothed nodal derivatives are evaluated only at the centroid of each integration cell. These integration cells are the simplex subcells (triangle/tetrahedron in two and three dimensions) obtained by subdividing the polytope. The salient feature of the proposed technique is that it requires only $n$ integrations for an $n-$ sided polytope as opposed to $3n$ in~\cite{francisa.ortiz-bernardin2017} and $13n$ integration points in the conventional approach. The convergence properties, the accuracy, and the efficacy of the LS with one point integration scheme are discussed by solving few benchmark problems in elastostatics., Comment: 19 pages, 15 figures, 6 Tables

This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main advantage of isogeometric analysis, i.e. preserves the original, exact CAD geometry (for example, given by NURBS), but allows pairing it with an approximation space which is more suitable/flexible for analysis, for example, T-splines, LR-splines, (truncated) hierarchical B-splines, and PHT-splines. This generalization offers the advantage of adaptive local refinement without the need to re-parameterize the domain, and therefore without weakening the link with the CAD model. We demonstrate the use of the method with different choices of the geometry and field splines, and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for non-nested spaces., Comment: 39 pages, 24 figures, 10 tables, 2 algorithms