Structures Of Arbitrary Shape Research Articles

Influence of cyclic loading on physical and mechanical properties of thin-film membrane structures

The principle of modification of mechanical properties of thin-film membrane structures of arbitrary shape by non-contact method was proposed, realized and explained for the first time. The idea was tested on an aluminum thin-film membrane formed by magnetron method on a silicon substrate. The external influence was realized by means of cyclic loading in the form of discharge and supply of excess air pressure to the membrane. As a result of repeated impacts, physical properties of materials (grain size and roughness) and mechanical properties (internal mechanical stresses and critical overpressure) are changed. Changing the magnitude of residual mechanical stresses in the membrane material allows the formation of a surface with a desired curvature value. In this work, after cyclic loading with pressure equal to half of the critical pressure, the following effects were revealed: the deflection of the membrane in the absence of external influence increased by more than an order of magnitude, the structure shifted to the plastic type of deformation, the critical rupture pressure decreased by several tens of percent. Application of this methodology allows to create new materials with unique mechanical properties.

MODVORTEx: computer vision-driven automation for magnetic domain wall velocity analysis

Abstract This paper presents Magneto Optic Domain Velocity Observation and Real-Time Extraction (MODVORTEx), a comprehensive software solution for automating domain wall (DW) velocity measurements in magnetic materials using magneto-optic Kerr effect microscopy. Building upon our previous work on bubble domain structures, we introduce a versatile graphical user interface (GUI) that accommodates arbitrary domain shapes and employs advanced computer vision techniques. The software provides different methods for DW detection and velocity calculation, catering to various domain structures of arbitrary shape. Our approach significantly reduces the time and effort required for data extraction, transforming a process that previously took days of manual work into a task completable within minutes. We provide the details of the algorithmic implementation which is organized into pre-processing, DW detection, displacement measurement, and velocity extraction. This tool is applicable to a wide range of scenarios, including bubble domain dynamics, Dzyaloshinskii–Moriya interaction studies in perpendicular magnetic anisotropy systems, current-driven DW motion in patterned strips etc. By providing both GUI and Application Programing Interface, our software offers flexibility for integration into existing measurement systems and adaptability for specific research needs. This automation promises to accelerate research in spintronics and magnetic materials, enabling more comprehensive and accurate studies of DW dynamics.

On the dynamics of 3D nonlocal solids

The stress-driven nonlocal continuum theory is a well-established integral elasticity formulation. Modelling the elastic strain via a convolution integral between stress and an averaging kernel, the theory leads to an integro-differential structural problem for arbitrary 3D nonlocal solids. Integral elasticity solutions are mainly available for 1D solids by adopting a bi-exponential kernel and reverting the boundary-value integro-differential problem to an equivalent differential formulation involving both classical and constitutive boundary conditions. A general computational framework to implement the stress-driven theory for 3D nonlocal solids is still missing. This paper tackles this issue, solving the relevant integro-differential problem by a two-field finite-element approach involving displacements and stresses. The approach can handle the dynamics of complex small-size structures of arbitrary shape. Focusing on free vibration responses, two examples are presented: a 2D rectangular plate, serving as benchmark to demonstrate size effects captured by stress-driven nonlocal elasticity, and a 3D solid modelling a typical dual microcantilever resonator with overhang.

Numerical aspects of a Godunov-type stabilization scheme for the Boltzmann transport equation

We discuss the numerical aspects of the Boltzmann transport equation (BE) for electrons in semiconductor devices, which is stabilized by Godunov’s scheme. The k-space is discretized with a grid based on the total energy to suppress spurious diffusion in the stationary case. Band structures of arbitrary shape can be handled. In the stationary case, the discrete BE yields always nonnegative distribution functions and the corresponding system matrix has only eigenvalues with positive real parts (diagonally dominant matrix) resulting in an excellent numerical stability. In the transient case, this property yields an upper limit for the time step ensuring the stability of the CPU-efficient forward Euler scheme and a positive distribution function. Similar to the Monte-Carlo (MC) method, the discrete BE can be solved in time together with the Poisson equation (PE), where the time steps for the PE are split into shorter time steps for the BE, which can be performed at minor additional computational cost. Thus, similar to the MC method, the transient approach is matrix-free and the solution of memory and CPU intensive large systems of linear equations is avoided. The numerical properties of the approach are demonstrated for a silicon nanowire NMOSFET, for which the stationary I–V characteristics, small-signal admittance parameters and the switching behavior are simulated with and without strong scattering. The spurious damping introduced by Godunov’s (upwind) scheme is found to be negligible in the technically relevant frequency range. The inherent asymmetry of the upwind scheme results in an error for very strong scattering that can be alleviated by a finer grid in transport direction.

Few pulses femtosecond laser exposure for high efficiency 3D glass micromachining.

Advanced three-dimensional manufacturing techniques are triggering new paradigms in the way we design and produce sophisticated parts on demand. Yet, to fully unravel its potential, a few limitations have to be overcome, one of them being the realization of high-aspect-ratio structures of arbitrary shapes at sufficiently high resolution and scalability. Among the most promising advanced manufacturing methods that emerged recently is the use of optical non-linear absorption effects, and in particular, its implementation in 3D printing of glass based on femtosecond laser exposure combined with chemical etching. Here, we optimize both laser and chemical processes to achieve unprecedented aspect ratio levels. We further show how the formation of pre-cursor laser-induced defects in the glass matrix plays a key role in etching selectivity. In particular, we demonstrate that there is an optimal energy dose, an order of magnitude smaller than the currently used ones, yielding to higher process efficiency and lower processing time. This research, in addition to a conspicuous technological advancement, unravels key mechanisms in laser-matter interactions essential in chemically-based glass manufacturing and offers an environmentally-friendly pathway through the use of less-dangerous etchants, replacing the commonly used hydrofluoric acid.

The cellular automata model of sound propagations and its application in structural noise calculations

Based on the cellular automata (CA) method and the principle of wave superposition, this study examines a computational technique to analyze the sound radiation characteristics of arbitrary shape structures. The local evolution rule of the one-dimensional (1D) CA model of Y-function was derived from the acoustic wave equation in spherical coordinate, and the relationship between Y-function and sound pressure was used to calculate the sound pressure value. On this basis, the 1D CA model of sound propagation for pulsating sphere source was established, and the superimposed sound field of multiple sphere sources in two-dimensional (2D) space was analyzed. Furthermore, combined with the principle of the wave superposition, the acoustic radiation characteristics of a rectangular piston in three-dimensional (3D) space were discussed, and the feasibility of the proposed method was verified by experiments. Finally, by introducing the finite element method, the calculation method of noise radiated by the 3D structure under external loads was presented, and the radiated sound field of a simply supported beam under loads was analyzed. The results shown that the proposed method could avoid anisotropic updating of cell state variables in the traditional 2D CA model. Moreover, the modeling was simpler, the calculation accuracy and efficiency were also higher. The results calculated by the proposed method matched well with the analytical solutions, experimental results, and numerical results, which indicated the veracity of the calculation method. The proposed method can provide a novel way for noise calculation of engineering structures.

Qualification of 3-D Printed Mortar With Electrical Conductivity Measurements

Additive manufacturing (AM) or 3-D printing of concrete allows for construction of arbitrary shape structures without a mold. Since reproducibility of 3-D printed concrete is lower than that of conventional fabrication, each 3-D printed structure should be monitored for proper curing. Conventional qualification of concrete is based on several tests, including destructive compressive strength measurements. Because a structure is 3-D printed layer-by-layer, the surfaces of AM concrete structures have significant surface roughness. This limits the applicability of conventional nondestructive testing methods. We investigated qualification of 3-D printed mortar by monitoring curing with nondestructive electrical conductivity measurements. Bulk resistance of concrete was extracted from electrochemical impedance spectroscopy (EIS) measurements made using custom flexible self-adhesive electrodes, which contour to rough surfaces. We show that bulk resistivity of concrete increases linearly with time. This allows for developing a calibration curve for compressive strength lookup from nondestructive electrical conductivity measurements. Conductivity measurements also allow for estimation of formation factor, which is an indicator of mortar permeability.

Solution of Maxwell’s Equations for Nonrectangular Electromagnetic Applications

The use of a fourth-order modified Runge–Kutta (MRK) scheme on a transformed coordinate system with Maxwell’s equations for nonrectangular domains and applications is presented. Maxwell’s equations are the governing equations for modeling electromagnetic wave propagation involving scattering, radiating structures, transmission lines, radar, biomedical applications, and nondestructive testing. Because of complex geometries in most problems where the material boundaries are not parallel to the grid axis, the application of finite differencing schemes in physical coordinates becomes nonviable. Therefore, by transforming the arbitrary-shaped structures to a uniform rectangular grid, numerical schemes and boundary conditions can be easily implemented. Numerical results for four cases are presented in this paper. Accuracy of the scheme has been established by comparing numerical results with the exact solution and error distribution plots. In the third case, scattering from the lossless and the lossy square cylindrical dielectric device where the plane wave source is injected using the total-field–scattered-field technique has been investigated. The results are compared with the results obtained from the benchmark finite difference time domain scheme. Lastly, the application of the numerical model to simulate scattering from curved boundaries has been presented in the fourth example.

Intra-well and cross-well chaos in membranes and shells liable to buckling

This work presents the mathematical modeling for the nonlinear vibration analysis of membrane and shell structures of arbitrary shape. These structures are usually the optimal form in many engineering applications. However, they may buckle under specific loading conditions and, in most cases, are sensitive to geometric imperfections. These structures when liable to unstable buckling present for load levels lower than the static critical load a multiwell potential functions, which has an underlying influence on the nonlinear dynamic behavior and stability of the structure in a dynamic environment. The energy barrier of each well is a key factor, and depending on the force control parameters and initial conditions, intra-well and cross-well motions may occur. Also coexisting attractors are the norm, influencing the structure's dynamic integrity. In these structures, escape from a potential well is preceded by global and local bifurcations, usually leading to chaos, which influence the number of coexisting attractor, their period and the topology of the basins of attraction. In the present work, three problems are addressed: an axially loaded cylindrical shell, a pressure-loaded spherical cap and a spherical membrane under internal pressure. These problems illustrate the possible multiwell functions observed in several membrane and shell problems, namely potential functions with one, two and three (symmetric or asymmetric) potential wells. A detailed parametric analysis is conducted through bifurcation diagrams of the Poincare map, time responses and Floquet stability criterion to clarify the influence of the multiwell potential function on the bifurcation scenario, basins of attraction and system safety.

Poynting Localized Energy: Method and Applications to Gain Enhancement in Coupled Antenna Systems

We present a general and comprehensive approach to evaluate spatio-temporal localized energy around radiating structures of arbitrary shapes and excitation signals. The method utilizes the finite-difference time-domain (FDTD) algorithm to calculate the Poynting localized energy for any antenna by working directly with computed fields, rather than source currents. It is established that this localized energy is fundamentally different from the classical antenna reactive energy associated with frequency-domain Q-factors of electrically small antennas. The proposed localized energy theory leads to the formulation of new performance evaluation measures, effectively going beyond traditional S-parameters and far-field patterns, which are then applied in several design examples involving strongly coupled arrays and weakly coupled antenna systems. It was found that gain enhancement caused by strong mutual coupling in the near zone (directors in Yagi-Uda systems or split-ring resonator arrays) is closely correlated with localized energy enhancement (but such correlation does not hold in weak mutual coupling scenarios). The new performance metrics are also used to generate spatial distributions for energy localization in MIMO printed dipoles. We propose that this proposed localized energy concept and the apparatus developed to investigate its relevant new data can assist in implementation of ultrahigh gain closely spaced antenna elements needed for the upcoming sub-6 GHz/mmWave 5G MIMO systems.

Harnessing transition waves to realize deployable structures

Transition waves that sequentially switch bistable elements from one stable configuration to another have received significant interest in recent years not only because of their rich physics but also, for their potential applications, including unidirectional propagation, energy harvesting, and mechanical computation. Here, we exploit the propagation of transition waves in a bistable one-dimensional (1D) linkage as a robust mechanism to realize structures that can be quickly deployed. We first use a combination of experiments and analyses to show that, if the bistable joints are properly designed, transition waves can propagate throughout the entire structure and transform the initial straight configuration into a curved one. We then demonstrate that such bistable linkages can be used as building blocks to realize deployable three-dimensional (3D) structures of arbitrary shape.

Efficient computation of 2D point-spread functions for diffractive lenses.

Diffractive lenses, such as Fresnel zone plates, photon sieves, and their modified versions, have been of significant recent interest in high-resolution imaging applications. As the advent of diffractive lens systems with different configurations expands, the fast and accurate simulation of these systems becomes crucial for both the design and image reconstruction tasks. Here we present a fast and accurate method for computing the 2D point-spread function (PSF) of an arbitrary diffractive lens. The method is based on the recently derived closed-form mathematical formula for the PSF and the transfer function of a diffractive lens. In the method, first, the samples of the transfer function are computed using the transmittance function of the diffractive lens, and then the inverse Fourier transform of this transfer function is computed to obtain the PSF. For accurate computation, the selection of the sampling parameters is handled with care, and simple selection rules are provided for this purpose. The developed method requires a single fast Fourier transform, and, therefore, has little computational complexity. Moreover, it is also applicable to any diffractive lens configuration with arbitrary-shaped structures and modulation. As a result, this fast and accurate PSF computation method enables efficient simulation, analysis, and development of diffractive lens systems under both focused and defocused settings.

Nonlinear Strength Calculation of Shell Structure of Arbitrary Shape Based on FEM

This article discusses the algorithm for calculating the shell structure of arbitrary shape, taking into account the physical nonlinearity of the material used. In determining the parameters of the stress-strain state, a step loading procedure was used. Algorithm for calculating the shell structure of arbitrary shape, taking into account the physical nonlinearity of the used material is discussed in this article. In determining the parameters of the stress-strain state, a step loading procedure was used.

Elastic–slip interface effect on the diffraction of plane waves around a saturated lining structure in saturated soil

By combining Biot's dynamic wave theory with the elastic and slip interface theory, the scattering of plane waves around a saturated lining structure embedded in saturated soil is studied. The lining structure is assumed to be arbitrary shape. Separating variable method of Helmholtz equations leads to the semi-analytical solutions of the potentials. By using the conformal mapping method, the lining structures of arbitrary shape can be mapped to the cirque at the same centre with different radii. The elastic and slip material constants of interface are introduced to analyze the effect of interfacial properties. The dynamic stress and pore pressure are solved by applying the displacement and stress boundary conditions with interface effect. In numerical examples, the dynamic stress and pore pressure under different interface coefficients (normal and circumferential spring coefficients and slip coefficient) are analyzed. It is found that the effect of normal spring coefficient is larger than that of circumferential spring coefficients. The imperfect interface effect on the dynamic stress and pore pressure is also related with the wave frequencies.

Computation of Magnetic Anomalies Caused by Two‐Dimensional Structures of Arbitrary Shape: Derivation and Matlab Implementation

AbstractThe very first computational and most referred in the literature algorithm of Talwani and Heirtzler (1964) for calculating of the magnetic anomaly caused by two‐dimensional irregular shape subsurface structure has particular fundamental and educational significance in geophysics theory. We re‐derive this algorithm from first principles and discuss previous derivation omissions. Our resulting solution differs from the original publication. Based on our new solution we present the two‐dimensional forward magnetic modeling software and associated tutorials which are available for download from the website www.ualberta.ca/~vadim/software.htm. Additionally, we include the computation of the remnant magnetization which can be found using already published apparent polar wonder paths.

Automatic three-dimensional acoustic-structure interaction analysis using the scaled boundary finite element method

An automatic approach for 3D analysis of acoustic-structure interaction problems is proposed based on the scaled boundary finite element method (SBFEM). The acoustic domain studied in this paper is assumed to be infinite. The infinite acoustic domain is divided into a near field (bounded domain) and a far field (unbounded domain). The acoustic near field contains structures of arbitrary shape, while the far field represents the unbounded acoustic domain. For modeling the wave propagation accurately and efficiently, continued fractions are employed to evaluate the dynamic stiffness and impedance of subdomains in both structural and acoustic domains. The time-domain equations for both structural and acoustic domains can be obtained by introducing auxiliary variables. Via satisfying the boundary conditions on the acoustic-structure interface, the global system of equations for acoustic-structure interaction system can be constructed. Symmetric formulations can also be obtained for this coupled system. Since the SBFEM requires the discretization of only the boundary, the mesh transition on the acoustic-structure interface is easily addressed by the subdivisions of 2D surface elements. Automatic meshing techniques can be incorporated in the proposed approach to generate meshes directly from the input geometrical models. Numerical examples are presented to demonstrate the accuracy, efficiency and potential of the proposed approach for modeling complex 3D acoustic-structure interaction problems.

Parametric Stochastic Analysis of a Piezoelectric Vibration Absorber Applied to Automotive Body Structure

This paper presents a systematic approach to quantify the uncertainties that influences directly the design of a Piezoelectric Vibration Absorber applied to shell structures with arbitrary shape, normally employed in automotive body structures. Sensitivity and spectral analyses are performed to study the impact of randomness in the optimal piezoelectric patch implementation in automotive structures. The randomness arising from the manufacturing process of the mechanical structure, such as stamping spring back effects, as well as in the boundary conditions, is considered in the analyses, likewise the effects of variability during the positioning process for piezoelectric patches. The effects of the inherent uncertainties in the dynamic behavior of the mechanical structure, the optimal electromechanical coupling coefficient and the piezoelectric vibration absorber attenuation are presented. The present paper has the advantage of indicating the loss in the vibration attenuation when Piezoelectric Vibration Absorbers are used in arbitrary shape structures, such as automotive hoods, fenders and doors. The Dynamic Vibration Absorber deterministically optimized provides an attenuation of approximately 18 dB in the theoretical model. However, losses of 5 dB in the attenuation can be obtained when the uncertainties are taken into account, and can reach up to 10 dB when the temperature effects are involved, representing more than 50% loss in attenuation for real applications, such as automotive body structures.

Thrust network analysis of masonry helical staircases

ABSTRACTWe exploit a recent generalization of the Thrust Network Analysis (TNA) to analyse masonry structures of extremely complicated and audacious geometry such as helicoidal staircases. Actually, differently from available methods, based on ad-hoc solutions holding for each particular structure, the TNA allows for studying the equilibrium of structures of arbitrary shape by invoking the principles of limit analysis of masonry structures dictated by Heyman. Four paradigmatic monumental staircases, with increased degree of complexity, have been selected as case studies in order to show the versatility and accuracy of the proposed approach. The results entailed from the generalized TNA are also successfully compared, for the first time in the literature, with those related to the adoption of available analytical methods for the analysis of no-tension membranes.

Supplements to “A Time-Domain Macromodel Based on the Frequency-Domain Moment Method for the Field-to-Wire Coupling”

A macromodel method based on the method of moments was proposed in a previous paper to efficiently and statistically analyze the field coupling to thin-wire structures of arbitrary shape in free space or above the perfectly conducting ground. Through numerical tests and physical insights, it was shown that the extracted macromodel is irrelevant to the port impedances. In this correspondence, a rigorous mathematical derivation is given to prove the irrelevance. The work completes the macromodel method and constitutes its theoretical foundation.

Spectral element computation of high-frequency leaky modes in three-dimensional solid waveguides

A numerical method is proposed to compute high-frequency low-leakage modes in structural waveguides surrounded by infinite solid media. In order to model arbitrary shape structures, a waveguide formulation is used, which consists of applying to the elastodynamic equilibrium equations a space Fourier transform along the waveguide axis and then a discretization method to the cross-section coordinates. However several numerical issues must be faced related to the unbounded nature of the cross-section, the number of degrees of freedom required to achieve an acceptable error in the high-frequency regime as well as the number of modes to compute. In this paper, these issues are circumvented by applying perfectly matched layers (PML) along the cross-section directions, a high-order spectral element method for the discretization of the cross-section, and an eigensolver shift suited for the computation of low-leakage modes. First, computations are performed for an embedded cylindrical bar, for which literature results are available. The proposed PML waveguide formulation yields good agreement with literature results, even in the case of weak impedance contrast. Its performance with high-order spectral elements is assessed in terms of convergence and accuracy and compared to traditional low-order finite elements. Then, computations are performed for an embedded square bar. Dispersion curves exhibit strong similarities with cylinders. These results show that the properties of low-leakage modes observed in cylindrical bars can also occur in other types of geometry.