Multi-domain Technique Research Articles

An adaptive Ritz formulation for progressive damage modelling in variable angle tow composite plates

In this work, an adaptive Ritz model for the analysis of variable angle tow composite plates featuring damage initiation and evolution under progressive loading is proposed, developed, implemented and tested. The plate kinematics is represented employing a first-order shear deformation theory, while the plate equilibrium equations at a given load step are obtained by minimizing the structure potential energy. The constitutive behaviour is modelled within the framework of continuum damage mechanics. In particular the initiation and evolution of damage, up to failure, are tracked by defining irreversible damage indices related to both fibres and matrix, both in tensile or compression loading. The discrete equations are then obtained by assuming a polynomial Ritz approximation of the primary kinematic variables in the energy minimization. Preliminary tests show how the application of the method as a single-domain approach induces the emergence of problematic spurious effects, related to Gibbs artefacts due to the inability of the selected polynomial basis to represent damage localization. An adaptive multi-domain technique is thus proposed to circumvent such issues, which has been successfully validated by benchmark tests. Eventually, original results about variable angle tow plates featuring damage evolution under progressive loading are presented.

An efficient meshless method for bimaterial interface cracks in 2D thin-layered coating structures

The interface crack problems in thin-layered coating/substrate structures are analyzed by using the generalized finite difference method, a recently developed meshless collocation method. Since the method is meshless, no element connectivity is needed and the burdensome remeshing of the domain similar to the finite element method is avoided. The multi-domain technique is employed to handle the non-homogeneity of the composite materials. The complex stress intensity factors of the bimaterial interface cracks are computed by using the displacement extrapolation method. Accurate and reliable numerical results with only a small number of degrees of freedom can be obtained for relatively small layer-to-substrate thicknesses. Numerical results calculated by using the boundary element method are also given for the purpose of comparison.

A numerical study of MHD heat and mass transfer of a reactive Casson–Williamson nanofluid past a vertical moving cylinder

The numerical investigation of a Casson–Williamson reactive nanofluid species in a moving vertical medium is the subject of this study. The complete exothermic reaction of viscoplastic nanofluid material in a cylindrical system is considered using a generalized Arrhenius kinetic. Casson and Williamson fluids are combined to give the fluid its viscoelastic property. In collaboration with the bivariate overlapping multi-domain technique, the spectral quasi-linearization scheme is used to find solutions to dimensionless mathematical nonlinear formulated flow equations. The findings are displayed in tabular and graphical form, demonstrating the sensitivity of the thermofluid parameters. The study indicates that the flow motion is not caused by the activation energy or the material reaction. It was obtained that the magnetic field increased the viscosity of the material and the thermal conductivity of the nanoparticles. Also, Lewis number enhanced the fluid viscoplastic property. Thermal and chemical engineering, as well as nanotechnology development, will benefit from the findings of this investigation.

Stress analysis of elastic bi-materials by using the localized method of fundamental solutions

<abstract> <p>The localized method of fundamental solutions belongs to the family of meshless collocation methods and now has been successfully tried for many kinds of engineering problems. In the method, the whole computational domain is divided into a set of overlapping local subdomains where the classical method of fundamental solutions and the moving least square method are applied. The method produces sparse and banded stiffness matrix which makes it possible to perform large-scale simulations on a desktop computer. In this paper, we document the first attempt to apply the method for the stress analysis of two-dimensional elastic bi-materials. The multi-domain technique is employed to handle the non-homogeneity of the bi-materials. Along the interface of the bi-material, the displacement continuity and traction equilibrium conditions are applied. Several representative numerical examples are presented and discussed to illustrate the accuracy and efficiency of the present approach.</p> </abstract>

Emerging Tools for Link Adaptation on 5G NR and Beyond: Challenges and Opportunities

With the speeding up of the fifth generation (5G) new radio (NR) worldwide commercialization, one of the paramount questions for operators and vendors is how to optimize the radio links, considering the widely diverse scenarios envisioned. One of the key pillars of 5G has been an unprecedented flexibility on the configuration of the radio access network (RAN) on scenarios that include cellular, vehicular, and industrial networks among others. This flexibility has its main exponent on link adaptation (LA), which has evolved into a multi-domain technique where a plethora of parameters, like numerology, bandwidth part, radio frequency beam, power, modulation and coding scheme (MCS) or multiple antenna precoding can be adapted to the instantaneous link conditions. Although such enhancements open the door to a significant performance improvement, they also pose many challenges to LA optimization. In this article, we first present the signaling aspects of NR technology for multi-domain LA and the challenges that need to be faced. Then, we explore the latest advances on LA for wireless networks. We envision a combination of machine learning (ML) tools with multi-domain LA as a key enabler for 5G and beyond networks. Finally, we investigate emerging ML approaches for LA and present a promising application of ML for LA that is assessed with simulations. With this scheme, the training is performed at the network side to relieve the user equipment (UE) to do such a complex task. It is shown with simulations that our ML approach outperforms the well known outer loop link adaptation (OLLA) algorithm in terms of instantaneous block error rate (BLER), while reaching the same average spectral efficiency (SE). Interestingly, it is shown that the proposed scheme only requires 4 bits to represent the features used to train the model, which makes it suitable for implementation in real systems with limited feedback.

Numerical solution of time-dependent Emden-Fowler equations using bivariate spectral collocation method on overlapping grids

AbstractIn this work, we present a new modification to the bivariate spectral collocation method in solving Emden-Fowler equations. The novelty of the modified approach is the use of overlapping grids when applying the Chebyshev spectral collocation method. In the case of nonlinear partial differential equations, the quasilinearisation method is used to linearize the equation. The multi-domain technique is applied in both space and time intervals, which are both decomposed into overlapping subintervals. The spectral collocation method is then employed in the discretization of the iterative scheme to give a matrix system to be solved simultaneously across the overlapping subintervals. Several test examples are considered to demonstrate the general performance of the numerical technique in terms of efficiency and accuracy. The numerical solutions are matched against exact solutions to confirm the accuracy and convergence of the method. The error bound theorems and proofs have been considered to emphasize on the benefits of the method. The use of an overlapping grid gives a matrix system with less dense matrices that can be inverted in a computationally efficient manner. Thus, implementing the spectral collocation method on overlapping grids improves the computational time and accuracy. Furthermore, few grid points in each subinterval are required to achieve stable and accurate results. The approximate solutions are established to be in excellent agreement with the exact analytical solutions.

Dynamic Wave Propagation in Fiber Reinforced Piezoelectric Composites with Cracks

This paper presents the transient dynamic analysis of micro-cracks of arbitrary shape in two-dimensional, linear piezoelectric fiber reinforced composite materials. Interface cracks between fiber and matrix as well as cracks inside the matrix and fibers are investigated. For this purpose, a symmetric Galerkin time-domain boundary element method in conjunction with a multi-domain technique is developed. The time-domain fundamental solutions for linear piezoelectric materials are applied. The time discretization is performed by a collocation method. An explicit time-stepping scheme is obtained to compute the discrete boundary data including the generalized crack-opening-displacements (CODs). Iterative solution algorithms are implemented to solve the nonlinear semi-permeable electrical crack-face boundary conditions and for a crack-face contact analysis at time-steps when a physically unacceptable crack-face intersection occurs. Several numerical examples are presented to reveal the influences of the micro-cracks, the material combinations and the transient dynamic loading on the intensity factors and the scattered wave fields.

Analysis of multi-crack problems by the spline fictitious boundary element method based on Erdogan fundamental solutions

The Erdogan fundamental solutions are derived from an infinite plane containing a crack. When they are used in the formulation of the boundary element method (BEM), the stress boundary conditions on the crack surface are automatically satisfied and the singular behavior at the crack tip can be naturally reflected. Using the multi-domain technique, the multi-crack problem can be transformed into a series of single-crack problems involving displacement continuity conditions along common boundaries. In this paper, the displacements which are expressed in terms of the integral of a complex function in the Erdogan fundamental solutions are derived in closed-form expressions. Then, the multi-domain spline fictitious boundary element method (SFBEM) based on the above fundamental solutions is proposed and formulated for analyzing multi-crack problems. The computational accuracy and stability of the proposed method are verified by comparing the stress intensity factor (SIF) results of a double-inner crack problem with different inclined angles and crack lengths against those calculated by the finite element method. Also, the SIF results of a double-edge crack problem with different crack lengths are compared with those obtained from studies. Finally, the proposed method is applied to the analysis of the triple-crack problem, in which the shielding effects of multi-crack and stress contours are studied with different crack lengths and locations.

Multidomain-staggered coupling technique for Darcy–Navier Stokes multiphase flow: An application to CO2 geosequestration

This paper introduces a multidomain-staggered technique for coupling multiphase flow in a porous medium, dominated by the Darcy laminar flow, with multiphase flow in a wellbore, dominated by the Navier Stokes viscous, compressible flow. The Darcy flow in the porous medium is formulated using the averaging theory, and the Navier Stokes flow in the wellbore is formulated using the drift-flux model. The governing equations are discretized using a mixed discretization finite element scheme, in which the partition of unity finite element method, the level set method and the standard Galerkin finite element method are combined in an integrated numerical scheme. A multidomain technique is utilized to uncouple the physical system into two subdomains, coupled back by enforcing flow constraints at their interaction boundaries. The resulting system of equations is solved using an iterative staggered technique and a multiple time-stepping scheme. This combination between the multidomain technique and the staggered-multiple time-stepping technique enables the use of different mathematical and numerical formulations for the two subdomains, and facilitates the implementation of a standard finite element computer code. The proposed model is tailored to simulate sequestered CO2 leakage through heterogeneous geological formation layers and abandoned wellbores. A numerical example describing different leakage scenarios is given to demonstrate the computational capability of the model. The numerical results are compared to those obtained from a commercial simulator.

Multi-domain simulations of shock wave interaction with aerodynamic obstacles in cylindrical implosions

A multi-domain finite-volume approach is presented to simulate the interaction of converging shock waves and aerodynamic obstacles for dilute gases. The so-called reshaping process, in which the cylindrical shock is reshaped into a polygonal shock due to the presence of obstacles along the shock path, is studied. To accurately capture the diverse spatial scales of the problem, the computational domain is divided into three sub-domains, namely, the far-field region, the obstacle region and the focus region. Shock propagation in the far-field region is simulated under the axisymmetric, namely, one-dimensional approximation. The obstacle region is described by a fully two-dimensional model, in which initial conditions are interpolated from the far-field. The solution in the obstacle region is then interpolated into the focus region surrounding the center of the imploding shock. These two regions partially overlap to allow for linear interpolation. Numerical results are presented for air in dilute conditions and for four, eight, sixteen and twenty four aerodynamic obstacles. The proposed multi-domain solution technique is found to be capable of describing the complex gas dynamics of the shock propagation and reshaping, while reducing the computational burden for a large number of obstacles of one order of magnitude with respect to fully two-dimensional simulations.

BEM Analysis of a Piezoelectric Structural Health Monitoring System for Delamination Detection

In the present work a piezoelectric based structural health monitoring (SHM) system is analyzed with the aim of assessing the ability of the piezoelectric patch to detect both edge and embedded delaminations proper of flange-skin composite laminated structures. The boundary element model is developed for piezoelectric solids and is implemented by taking advantage of the multidomain technique to model laminated and cracked configurations. A non-linear spring model interface is then implemented in conjunction with an iterative procedure allowing for the simulation of the finite stiffness of the bonding layers as well as of the non-penetration condition of the delamination surfaces. The dynamic behavior of the damaged structures and of the bonded piezoelectric patch is modeled by means of the dual reciprocity approach. To fully characterize the structure response the fracture mechanics behavior is studied in terms of energy release rate G and mode-mix phase angle Y. Finally, a damage index based on the electrical current output of the SHM system is introduced as an effective identification parameter of the flange-skin delamination occurrence.

On the analysis of aerostatic thrust bearings with the differential quadrature method

This paper presents a numerical approach to analyze the performance of aerostatic thrust bearings based on the differential quadrature method. The Reynolds equation of aerostatic thrust bearings is firstly discretized as a series of algebraic equations by the differential quadrature method and the pressure distribution is calculated with the discretized equations invoking the boundary conditions. Analytical approximation of Heaviside step function and a multi-domain technique are then introduced to resolve the discontinuous problem of grooved aerostatic bearings. Numerical solutions are obtained for two types of aerostatic thrust bearings. The mass flow rate, load capacity, and stiffness predicted by these solutions are further compared with corresponding analytical, finite difference method and computational fluid dynamics solutions. It is demonstrated that the differential quadrature method has high efficiency and accuracy for the solution of aerostatic thrust bearings.

A pseudo‐spectral method that uses an overlapping multidomain technique for the numerical solution of sine‐Gordon equation in one and two spatial dimensions

In this article, we study an explicit scheme for the solution of sine‐Gordon equation when the space discretization is carried out by an overlapping multidomain pseudo‐spectral technique. By using differentiation matrices, the equation is reduced to a nonlinear system of ordinary differential equations in time that can be discretized with the explicit fourth‐order Runge–Kutta method. To achieve approximation with high accuracy in large domains, the number of space grid points must be large enough. This yields very large and full matrices in the pseudo‐spectral method that causes large memory requirements. The domain decomposition approach provides sparsity in the matrices obtained after the discretization, and this property reduces storage for large matrices and provides economical ways of performing matrix–vector multiplications. Therefore, we propose a multidomain pseudo‐spectral method for the numerical simulation of the sine‐Gordon equation in large domains. Test examples are given to demonstrate the accuracy and capability of the proposed method. Numerical experiments show that the multidomain scheme has an excellent long‐time numerical behavior for the sine‐Gordon equation in one and two dimensions. Copyright © 2013 John Wiley & Sons, Ltd.

Application of the 3-D boundary element method to delaminated composite structures

A three-dimensional boundary element model for anisotropic solids is presented to study the fracture mechanics behavior of delaminated composite structures. The multi-domain technique is implemented to model the layered configurations and the cracks occurring at bi-material interface. The Modified Crack Closure Integral technique is implemented to characterize the fracture mechanics behavior of delaminations in terms of the total energy release rate and mode mix phase angles. Validating analyses, performed on different delaminated configurations, have shown the effectiveness of the proposed approach. Moreover, some original results are presented to investigate the effects of the stacking sequence on the fracture parameters.

Numerical Analysis of Piezoelectric Active Repair in the Presence of Frictional Contact Conditions

The increasing development of smart materials, such as piezoelectric and shape memory alloys, has opened new opportunities for improving repair techniques. Particularly, active repairs, based on the converse piezoelectric effect, can increase the life of a structure by reducing the crack opening. A deep characterization of the electromechanical behavior of delaminated composite structures, actively repaired by piezoelectric patches, can be achieved by considering the adhesive layer between the host structure and the repair and by taking into account the frictional contact between the crack surfaces. In this paper, Boundary Element (BE) analyses performed on delaminated composite structures repaired by active piezoelectric patches are presented. A two-dimensional boundary integral formulation for piezoelectric solids based on the multi-domain technique to model the composite host damaged structures and the bonded piezoelectric patches is employed. An interface spring model is also implemented to take into account the finite stiffness of the bonding layers and to model the frictional contact between the delamination surfaces, by means of an iterative procedure. The effect of the adhesive between the plies of piezoelectric bimorph devices on the electromechanical response is first pointed out for both sensing and actuating behavior. Then, the effect of the frictional contact condition on the fracture mechanics behavior of actively repaired delaminated composite structures is investigated.

Numerical analysis of a piezoelectric structural health monitoring system for composite flange-skin delamination detection

In this paper, a piezoelectric based Structural Health Monitoring (SHM) system is proposed to detect skin/stiffener debonding and delamination cracks proper of laminated composite structures. The SHM system is analyzed by means of a boundary element code implemented in the framework of piezoelectricity. The multidomain technique, coupled with an interface spring model, is used to model laminated composite structures as well as the bonding between the host delaminated structure and the piezoelectric sensor. Static sensitivity analyses are firstly performed on a drop-ply delaminated structure in order to identify a suitable configuration for the sensor. Then, the dynamic electromechanical response of the damaged structure with the bonded piezoelectric sensor is investigated. The definition of a damage index allows an effective identification of the skin/stiffener debonding occurrence. In order to fully characterize the host structure SHM system assembly, the fracture mechanics behavior of the structure is also studied in terms of the total energy release rate G and of the phase angle Ψ.

Blood Clot Simulation Model by Using the Bond‐Graph Technique

The World Health Organization estimates that 17 million people die of cardiovascular disease, particularly heart attacks and strokes, every year. Most strokes are caused by a blood clot that occludes an artery in the cerebral circulation and the process concerning the removal of this obstruction involves catheterisation. The fundamental object of the presented study consists in determining and optimizing the necessary simulation model corresponding with the blood clot zone to be implemented jointly with other Mechanical Thrombectomy Device simulation models, which have become more widely used during the last decade. To do so, a multidomain technique is used to better explain the different aspects of the attachment to the artery wall and between the existing platelets, it being possible to obtain the mathematical equations that define the full model. For a better understanding, a consecutive approximation to the definitive model will be presented, analyzing the different problems found during the study. The final presented model considers an elastic characterization of the blood clot composition and the possibility of obtaining a consecutive detachment process from the artery wall. In conclusion, the presented model contains the necessary behaviour laws to be implemented in future blood clot simulation models.

Magic Cube Approach for Crashworthiness Design with Lightweight Considerations

This paper presents the basic theories and methodologies of the Magic Cube (MQ) approach, an advanced design approach which provides a systematic way to examine general crashworthiness and blast protection designs in terms of both structural and material aspects. The MQ approach is developed to assist the design process for improved structural crashworthiness: by applying time (process) decomposition, the original difficult nonlinear dynamic crashworthiness design problem is converted into a sequence of simplified linear design problems; by applying multi-domain topology optimization technique to the simplified linear design problems, the optimal configuration of the designed structure is obtained. A design of reinforced thin-walled rail under oblique impact is used to demonstrate the MQ approach. Numerical simulation results show that, compared with the original rail of the same weight, the MQ approach leads to a design with significantly higher energy absorption performance and lower initial crushing force under oblique impact.

Multi-Domain Topology Optimization of Pulsed Magnetic Field Generator Sourced by Harmonic Current Excitation

This paper presents multi-domain topology optimization using a current-carrying coil and a ferromagnetic material in order to focus the pulsed magnetic field (PMF) onto a target area. The multi-domain design sensitivities in the harmonic magnetic field are calculated using the adjoint variable method (AVM). In numerical examples, the multi-domain topology optimization technique is applied to the designs of a C-core actuator in the magnetostatic field and a PMF generator in the time-harmonic magnetic field. The magnetic saturation effect is considered in the optimization, and optimization results using linear steel and nonlinear steel are compared.

Crashworthiness Design for Reinforced Thin-Walled Column under Oblique Impact Using a Magic Cube Approach

This paper is concerned with crashworthiness design of a reinforced thin-walled column under oblique impact. To transform the failure mode of the column under oblique loads from low energy-absorption global bending to high energy-absorption progressive collapse, Magic Cube (MQ) approach, a systematic design approach, is employed to assist the design process: by applying time (process) decomposition, the original difficult nonlinear dynamic crashworthiness design problem is converted into a sequence of simplified linear design problems; by applying multi-domain topology optimization technique to the simplified linear design problems, the optimal configuration of the reinforcement is obtained. Numerical simulation results show that, compared with the original column with same weight, the optimal reinforced thin-walled column has higher energy absorption performance and lower initial crushing force under oblique impact.