Finite Boundary Conditions Research Articles

Benchmark between N-body, PIC, and semi-Lagrangian simulations of Landau-damped Langmuir wave

This work presents a benchmark study comparing three distinct numerical methods—Particle-In-Cell (PIC), semi-Lagrangian, and N-body simulations—for analyzing the damping of Langmuir waves in a one-dimensional Vlasov–Poisson plasma system. Each approach has unique advantages in terms of accuracy, resolution, and computational cost. The comparison aims to discriminate between numerical artifacts and physical phenomena, identifying the contribution of finite particle numbers and boundary conditions in both linear and nonlinear regimes. The study demonstrates strong agreement between the PIC and semi-Lagrangian methods in both regimes. N-body simulations, while requiring a specific method to overcome statistical noise, agree in the limit of many bodies (>500). Crucial subtleties regarding initial and boundary conditions are discussed throughout.

Numerical analysis of circular hollow section bar with stiffened flattened ends

Circular hollow sections are usually used in long-span roof truss systems due to the advantages they offer. One of the typology for connecting elements in such structures involves the flattening of bar ends, in order to provide a simpler and more economical connection. A new flattening typology called stiffened flattening is proposed, characterized by a non-flat geometry, with the creation of stiffeners in the lateral edges of the bar flattened ends. A theoretical, numerical and experimental study was carried out on the behavior of a plane truss composed of circular hollow sections, in which diagonal bars have stiffened flattening ends. The diagonal connecting system with the chord members uses connecting plates. The plates are welded to the chords and the diagonals are connected to latter through a single bolt. This work presents the numerical analysis of a circular hollow section bar with stiffened flattening ends subjected to compression. This is a study of the behavior of an isolated bar compressed from the truss, which corresponds to the most requested diagonal composed by circular hollow sections with stiffened flattening ends. The numerical analysis using finite elements method was developed through ANSYS software with the Parametric Design Language (APDL), in which parameters such as geometry, material, element type, definition of the finite element mesh, boundary conditions and application of compression loads are specified. A non-linear analysis was performed using shell element on the bar with stiffened flattened ends. The numerical analysis result satisfactorily represented the structural behavior of the isolated circular hollow section bar with stiffened flattening ends. It was possible to observe the buckling effect of the compressed circular hollow section bar and the effect of the axial load eccentricity due to the stiffened flattening of bar ends.

Metaharvesting: emergent energy harvesting by piezoelectric metamaterials

Vibration energy harvesting is a technology that enables electric power generation by augmenting vibrating materials or structures with piezoelectric elements. In a recent work, we quantified the intrinsic energy-harvesting availability (EHA) of a piezoelectric phononic crystal (Piezo-PnC) by calculating its damping ratio across the Brillouin zone and subtracting off the damping ratio of the corresponding non-piezoelectric version of the phononic crystal. It was highlighted that the resulting quantity indicates the amount of useful energy available for harvesting and is independent of the finite structure size and boundary conditions and of any forcing conditions. Here, we investigate the intrinsic EHA of two other material systems chosen to be statically equivalent to a given Piezo-PnC: a piezoelectric locally resonant metamaterial (Piezo-LRM) and a piezoelectric inertially amplified metamaterial (Piezo-IAM). Upon comparing with the intrinsic EHA of the Piezo-PnC, we observe an emergence of energy-harvesting capacity, a phenomenon we refer to as metaharvesting. This is analogous to the concept of metadamping, except the quantity evaluated is associated with piezoelectric energy harvesting rather than raw dissipation. Our results show that the intrinsic EHA is enhanced by local resonances and enhanced further by inertial amplification. These findings offer a new paradigm for the design—at the fundamental level—of architectured piezoelectric materials with superior energy-harvesting capacity.

Development of a numerical and analytical methodology for analyzing hybrid laminates with multi-oriented piezoelectric and structural layers

Piezoelectric materials can generate an electrical response under mechanical stress, functioning as sensors. Conversely, applying an electrical field to these materials enables precise motion control, making them effective as actuators. Using a proposed methodology, this work focuses on evaluating the effective properties of hybrid multi-oriented composite laminates consisting of structural and piezoelectric layers driven by monoclinic constitutive equations. Square unit cell model was used to calculate all coefficients of the material tensor. The finite element (FE) homogenization method and periodic boundary conditions implemented by node-to-node constraint equations are used to study a representative volume element (RVE) modeled as three-layer unit cell in the mesoscale. The pre-processing, FE analysis, and post-processing are conducted in the FE package ABAQUSⓇ through Python scripts. The computational approach yields results that align closely with the analytical effective coefficients derived from the Asymptotic Homogenization Method (AHM), demonstrating the robustness and accuracy of the proposed methodology.

Modified 3ω conductivity technique for measurements of thermal conductivity in cryogenic fluids

An instrument based on a modification to the 3-omega thermal conductivity technique that allows precise measurement of thermal properties in fluids is presented. Existing hot-wire techniques have difficulty measuring thermal conductivity because of the effects of natural convection distorting the measurement, however the standard 3-omega technique has been used extensively in the measurement of the properties of solids with great success. To address the challenge posed by natural convection in fluids, we modify the boundary condition of the 3-omega device configuration to be finite in extent, thereby restricting fluid motion and enabling a direct high-precision measurement of a fluid’s thermal conductivity. This modified scenario also presents an opportunity for a simultaneous measurement of the thermal diffusivity of the fluid. The behavior of the device is described with the reformed boundary conditions to show how a simultaneous measurement is made. By applying a constant temperature finite boundary condition, the solution characteristic in the frequency domain gains features that allow for simultaneous measurements of the fluid thermal conductivity and diffusivity. Given the density of the fluid, measured separately, the specific heat of the fluid can be calculated. The effects of the thermal properties of the measurement wire influence the measurement characteristic, and only when the wire thermal properties are sufficiently small compared to those of the fluid can a simultaneous measurement be made. Due to limitations in the dynamic reserve of the measurement devices, a setup is described that allows the signal of interest to be extracted and a precise measurement to be made with minimal distortion. Initial data on the thermal conductivity of helium is presented in the 4-300K temperature range. Preliminary specific heat data is also presented. Limitations on the device’s thermal properties prevent a specific heat measurement above 70K. This data is compared with reference fluid properties databases to validate the device performance.

The Hilbert problem in a half-plane for generalized analytic functions with a singular point on the real axis

This article analyzes the inhomogeneous Hilbert boundary value problem for an upper half-plane with the finite index and boundary condition on the real axis for one generalized Cauchy–Riemann equation with a singular point on the real axis. A structural formula was obtained for the general solution of this equation under restrictions leading to an infinite index of the logarithmic order of the accompanying Hilbert boundary value problem for analytic functions. This formula and the solvability results of the Hilbert problem in the theory of analytic functions were applied to solve the set boundary value problem.

Finite size effects and optimization of the calculation of the surface tension in surfactant mixtures at liquid/vapour interfaces

The surface tension of monolayers with mixtures of anionic and nonionic surfactant at the liquid/vapour interface is studied. Previous works have observed that calculations of the surface tension of simple fluids show artificial oscillations for small interfacial areas, indicating that the surface tension data fluctuate due to the finite size effects and periodic boundary conditions. In the case of simulations of monolayers composed of surfactant mixtures, the surface tension not only oscillates for small areas but can also give non-physical data, such as negative values. Analysis of the monolayers with different surfactant mixtures, ionic (DTAB, CTAB, SDS) and nonionic (SB3-12), was done for density profiles, parameters of order and pair correlation functions for small and large box areas and all of them present similar behaviour. The fluctuations and the non-physical values of the surface tension are corrected when boxes with large interfacial areas are considered. The results indicate that in order to obtain reliable values of the surface tension, in computer simulations, it is important to choose not only the correct force field but also the appropriate size of the simulation box.

On the validity of periodic boundary conditions for modelling finite plate-type acoustic metamaterials.

Plate-type acoustic metamaterials (PAMs) are thin structures that exhibit antiresonances with high sound transmission loss (STL) values, making PAMs a promising new technology for controlling tonal noise in the challenging low-frequency regime. A PAM consists of rigid masses periodically attached to a thin baseplate. The periodicity of PAM can be exploited in simulations, allowing to model only a single unit cell using periodic boundary conditions. This approach essentially represents the PAM as an infinite structure, but real PAM implementations will always be finite and influenced by boundary conditions. In this paper, extensive numerical simulations of different PAM configurations have been performed to study the performance of finite PAM compared to infinite PAM. The results indicate that as the number of unit cells in a finite PAM increase, the STL converges toward that of an infinite PAM. The impact of the finite PAM edge boundary conditions becomes negligible at some point. Based on the numerical results, a simple criterion is proposed to determine a priori how many unit cells are required in a finite PAM design to consider it quasi-infinite. This criterion aids in justifying unit cell models with periodic boundary conditions for efficient design optimizations in practical PAM applications.

Numerical simulation of ultrasonic impact treatment (UIT) assisted laser directed energy deposition (DED) CrCoNi medium entropy alloy process

In order to enhance the microstructure and mechanical properties of additively manufactured metal parts, the application of ultrasonic impact treatment (UIT) after the additive manufacturing process is introduced as a means to modulate and optimize the material's microstructure and properties. This study systematically investigates the effect of UIT on the distribution of residual stresses in CrCoNi medium entropy alloy (CrCoNi-MEA) through numerical simulation. A suitable finite element model and boundary conditions are established to simulate the UIT assisted laser DED process. The reliability of the finite element model is verified by XRD residual test results and EBSD observation results. The numerical simulation results shows that the specimen's surface exhibited predominantly compressive stress within a specific depth range, with the maximum compressive stress in the vertical direction. Furthermore, it is observed that UIT amplitude, frequency, and impact needle diameter also significantly influenced the residual stresses. By appropriately adjusting the UIT parameters, the magnitude and distribution of residual stresses could be further controlled and regulated. In addition, it is found that multiple UITs at different surface locations exhibited no significant mutual influence between each other.

Finite element modeling of assembling rivet-fastened rectangular hollow flange beams in bending

The assembling rivet-fastened rectangular hollow flange beam (ARHFB) is a new type of cold-formed steel beam. The ARHFB section has two rectangular hollow flanges formed by U-shaped and C-shaped components that connected by self-locking rivets. A finite element model is developed to simulate 16 four-point bending experiments. Details of the modeling including finite element meshing, loading and boundary conditions, contact and analysis methods are presented. The accuracy of the developed finite element model is verified by comparing the ultimate moment capacity, applied load versus deflection curves, bending moment versus deflection curves, strain versus deflection curves and failure modes obtained from the tests and the finite element analysis. Based on the validated finite element model, a parametric analysis is carried out to discuss the effects of rivet spacing, section depth, flange thickness, and web thickness on the bending performance of ARHFB. The moment capacities of these sections obtained from the parametric study are compared with predictions from Australia and New Zealand, Chinese design standards for cold-rolled sections and the DSM (Direct Strength Method). It is found that GB50018 can conservatively predict the bearing capacity of ARHFB with a large error, while AS / NZS 4600 and DSM (Direct Strength Method) cannot provide reliable prediction results.

Peridynamic analysis of curved elastic beams

Peridynamics is an extended continuum theory which operates with non-local deformation measures as well as long range internal force/moment interactions. The aim of this paper is to present and to analyze peridynamic governing equations for elastic curved beams. To this end the strain energy density is formulated as a function of two non-local deformation measures including the axial deformation and curvature. Applying the Lagrangian formalism, peridynamic equations of motion are derived. To analyze curved beams of finite length peridynamic boundary conditions are required. Examples of boundary conditions including simple support and clamped edge are presented by introducing a fictitious domain. Solutions to PD equations of motion are presented for various problems including static analysis of simply supported and clamped arc beams as well as modal analysis of a slender ring and a simply supported arc beam. To validate peridynamic formulations, solutions for displacements, natural frequencies and vibration modes are compared with those by the classical beam theory. A very good agreement between the non-local and the classical theories is observed for the case of the small horizon sizes which shows the capability of the derived equations of motion and proposed boundary conditions.

Evaluating the importance of Raman and Brillouin side scattering at ignition conditions

A complete linear model for Raman and Brillouin side scattering is analyzed with infinite and finite boundary conditions. Analytic formulas of absolute thresholds and convective gains for side scatterings are derived when infinite boundary is assumed. Finite beam width introduces finite boundary conditions to the side scattering, which could influence both absolute thresholds and convective gains. Using these formulas and models, we have evaluated the importance of stimulated Raman side scattering and stimulated Brillouin side scattering at ignition conditions, including both direct drive and indirect drive. It shows that side scattering could be a possible way of scattering other than backscattering in several ignition situations.

Spectral properties of the finite system of Klein-Gordon S-wave equations with general boundary condition

The spectral characteristics of the operator L is studied where L is defined within the Hilbert space L2(R+, CV) given by a finite system of Klein-Gordon type differential equations and boundary condition at general form. The research of the Klein-Gordon type operator continues to be an important topic for researchers due to the range of applicability of them in numerous branches of mathematics and quantum physics. Contrary to the previous works, we take the potential as complex valued and generalize the problem to the matrix Klein-Gordon operator case. The spectrum is derived by determining the Jost function and resolvent operator of the prescribed operator. Further, we provide the conditions that must be met for the certain quantitative properties of the spectrum.

Inhomogeneous chiral condensation under rotation in the holographic QCD

We investigate inhomogeneous chiral condensation under rotation considering finite size effects and boundary conditions in the holographic QCD model. The rotational suppression effect determined by $\Omega r$ is confirmed in the holographic model which is not influenced by the boundary conditions. For chiral condensation at the center, it is found that under Neumann boundary condition the finite size exhibits two opposite effects, i.e., catalysis at high temperatures and inverse catalysis at low temperatures. In contrast, under Dirichlet boundary condition, the effect of finite size on condensation is inverse catalysis, and small size induces a phase transition from inhomogeneous to homogeneous phase. The temperature-angular velocity phase diagrams of QCD are obtained for different boundary conditions and sizes, and it is found that the critical temperature decreases with angular velocity.

Estimation of the Effective Magnetic Properties of Two-Phase Steels

We investigate the predictive performance of specific analytical and numerical methods to determine the effective magnetic properties of two-phase steels at the macroscale. We utilize various mixture rules reported in the literature for the former, some of which correspond to rigorous bounds, e.g., Voigt (arithmetic) and Reuss (harmonic) averages. For the latter, we employ asymptotic homogenization together with the finite element method (FEM) and periodic boundary conditions (PBC). The voxel-based discretization of the representative volume element is conducted with digital image processing on the existing micrographs of DP600-grade steel. We show that unlike the considered isotropic mixture rules, which use only the phase volume fraction as the statistical microstructural descriptor, finite element method-based first-order asymptotic homogenization allows prediction of both phase content and directional dependence in the magnetic permeability by permitting an accurate consideration of the underlying phase geometry.

Enhanced ultrasonic wave generation using energy-localized behaviors of phononic crystals

This paper aims to bridge the energy-localized behaviors of a phononic crystal (PnC) and an ultrasonic-wave-generation (UWG) system. A defective PnC manifests an intriguing phenomenon in which input ultrasonic-wave energy is confined near the defect in several defect-band frequencies that appear in the phononic band-gap range. Using the inverse of this energy localization, remarkably amplified ultrasonic waves can be generated compared to a UWG system without the PnC. This work proposes an analytical model that predicts the UWG system's sensitivities and electrical admittance. The mechanical equation of motions and the electrical circuit equation of the piezoelectric-patch-bonded defect are derived using the Rayleigh-Love rod theory and the extended Hamilton's principle. Through the use of Green's functions, these electroelastically coupled equations are solved. With two assumptions, specifically, (i) continuity conditions throughout the PnC and (ii) no incident waves toward the UWG system, the S-parameter-method-based analytical approach presents the system performances explicitly. Furthermore, the modified analytical model for application to engineering situations with finite boundary conditions is also proposed. The predicted results of the proposed analytical model match well with those of the finite element model and show that the UWG performances are amplified to several times their prior value. The main contributions of this work are as follows: (i) this is the first attempt to utilize a defective PnC as UWG systems, (ii) the analytical model is newly proposed and dramatically shortens the computational time compared to the finite-element-method, and (iii) the proposed defective-PnC-incorporated UWG system and its analytical model are effective, regardless of the boundary conditions.

Finite Boundary Conditions Due to the Bar Presence in the Model of Chloride Penetration.

The chloride penetration is usually modelled through the application of a solution of Fick’s second law of diffusion, based on the assumption of semi-infinite boundary conditions. However, the presence of the bars, on whose surface the chlorides accumulate, makes this assumption incorrect. As the time progresses, the chlorides in the steel/concrete interface increase in concentration more than the chlorides overpassing the bar position without obstacles. This circumstance, although previously studied, has not been introduced in common practice, in spite of it supposes early reaching of the chloride threshold. The study in this paper shows a deterministic analysis of the chloride diffusion process by the finite element method (FEM) which numerically solves Fick’s second law, taking into account the accumulation of the chlorides on the bar surface. Several examples are calculated and factors between the finite/semi-infinite solutions are given. These factors depend on the cover depth and the diffusion coefficient, and with less importance, on the diameter of the bar, which make it unfeasible to propose a general trend.

Finite impedance boundary conditions determined in situ for modeling underwater acoustical measurement in laboratory tanks

In underwater acoustics, laboratory tank sound propagation models may be improved using in situ characterization of water tank boundaries. An underwater acoustic tank model is developed with finite impedance boundaries determined in situ from impulse response measurements calculated from the frequency deconvolution of swept-sine signals following techniques commonly used in room acoustics. Impulse responses were used to obtain the acoustic absorption of the acrylic tank walls through reverse Schroeder integration determining the reverberation time and solving the Eyring equation for absorptive effects. This approach improves modeling of sound propagation in water tanks and is validated with numerical test cases and measurements. An improved tank model considering measured finite impedance boundaries will further develop the ability for more realistic data simulation in water tanks which will be used to design machine learning refinement.

Approximate analytical solution for Richards’ equation with finite constant water head Dirichlet boundary conditions

Approximate analytical solution for Richards’ equation with finite constant water head Dirichlet boundary conditions

Multi-objective optimal design of periodically stiffened panels for vibration control using data-driven optimization method

Vibration reduction properties of the periodically stiffened panels are studied using the data-driven optimization method and are verified using the 3D printing techniques. The dynamic responses and band gaps of periodically stiffened panels are calculated using the finite element method and periodic boundary conditions. To further develop the potential in vibration mitigation, a data-driven method is used to study the multi-objective structural optimization problem for minimizing the weight and mean square velocity simultaneously. The layout, thickness, and height of the stiffeners are taken as design variables. Numerical results show that the data-driven method is efficient in the optimal design of stiffened panels, and the optimized panels have targeted band gaps for different engineering demands. Moreover, two 3D printed panels are fabricated to study band gap properties of periodically stiffened panels experimentally.