Equivalent Material Properties Research Articles

Wave dispersion characteristics of agglomerated multi-scale hybrid nanocomposite beams

Herein, the agglomeration effect of nanoparticles on the wave dispersion of multi-scale hybrid nanocomposite beams is investigated. The constituent material consists of both macro- and nano-reinforcements which are dispersed in the polymer matrix. Homogenization is conducted according to the well-known micromechanical methods. Herein, the combination of the Eshelby–Mori–Tanaka model and the rule of the mixture is implemented in order to estimate the equivalent material properties of the nanocomposite beam. Also, a refined higher-order beam theory is used in order to calculate the kinetic relations free from utilizing an additional factor to account for the shear deformation. Furthermore, the governing equations are achieved by applying Hamilton’s principle. Then, the governing equations are solved analytically to enrich the wave frequency. The effects of various parameters on the variation in wave frequency and phase velocity of the multi-scale hybrid nanocomposite beam are studied. The results of this study reveal that the mechanical responses of the system decrease whenever the nanotubes are inside the clusters.

Application of the nonlocal strain gradient elasticity on the wave dispersion behaviors of inhomogeneous nanosize beams

In this article, the wave dispersion analysis of heterogeneous functionally graded (FG) nanosize beams is undertaken in the framework of a nonlocal strain gradient higher-order beam theory. Shear deformation effects are completely included free from any additional shear correction coefficient by the means of a refined sinusoidal beam theorem. Furthermore, the small scale effects are covered based on the nonlocal strain gradient elasticity theory. This is proven that the aforementioned theory is powerful enough to guesstimate the behavior of the nanostructures better than formerly presented ones. In fact, both stiffness-softening and -hardening characteristics of nanosize elements are coupled together in this theory. On the other hand, the equivalent material properties are achieved utilizing the rule of mixture. The motion equations are derived extending the dynamic version of the principle of virtual work. Thereafter, the size-dependent partial differential equations of the problem are solved based on an exponential solution function to reach the circular wave frequency. Next, some graphical examples are presented to investigate the influences of various parameters on the wave propagation behaviors of FG nanobeams.

Concurrent multi-scale and multi-material topological optimization of vibro-acoustic structures

Most of the presented works in the field of vibro-acoustic topology optimization are focused on single-scale design of the structure or material so far, which cannot exert the potential of the material to the largest extent. Even though multi-scale topology optimization has been investigated increasingly in recent years, few works concern the topological design with respect to the vibro-acoustic criteria. In this paper, a concurrent multi-scale multi-material topology optimization method is presented for minimizing sound radiation power of the vibrating structure subjected to harmonic loading. The metamaterial consisting of different periodic microstructures and its distribution over the macrostructural domain are designable to reduce the sound radiation power. A general multi-scale multi-material interpolation model based on SIMP and PAMP is developed and applied to the concurrent topological design. The optimum distribution of the base materials at micro-scale and metamaterial associated with the optimized microstructures at macro-scale will be obtained concurrently. The homogenization method is employed to calculate the equivalent macro-scale material properties of the periodic microstructures. A high-frequency approximation formulation is introduced to simplify calculation of the sound power from the vibrating structure to its surrounding acoustic medium. The sensitivities of the sound power with respect to macro-scale and micro-scale topological densities are calculated by the adjoint method. The MMA method is employed to find the solution of the concurrent multi-scale vibro-acoustic topology optimization problem. Numerical examples are given to validate the accuracy of the established model and show the advantages of the multi-scale topology optimization in specific cases of vibro-acoustic design. Many interesting features of the concurrent vibro-acoustic multi-scale topological design have been revealed and discussed. In comparison with the single-scale microstructural design, the importance of simultaneous macro-structural level design to improve overall vibro-acoustic characteristics of the structure is proved by the examples.

Development of Bead Modelling for Distortion Analysis Induced by Wire Arc Additive Manufacturing using FEM and Experiment

In this research, Wire Arc Additive Manufacturing is modelled and simulated to determine the most suitable bead modelling strategy. This analysis is aimed to predict distortion by means of thermomechanical Finite Element Method (FEM). The product model with wire as feedstock on plate as substrate and process simulation are designed in form of multi-layered beads and single string using MSC Marc/Mentat. This research begins with finding suitable WAAM parameters which takes into account the bead quality. This is done by using robotic welding system with 01.2mm filler wire (AWS A5.28 : ER80SNi1), shielding gas (80% Ar/ 20% CO2) and 6mm-thick low carbon steel as base plate. Further, modelling as well as simulation are to be conducted with regards to bead spreading of each layers. Two different geometrical modelling regarding the weld bead are modelled which are arc and rectangular shape. Equivalent material properties from database and previous researches are implemented into simulation to ensure a realistic resemblance. It is shown that bead modelling with rectangular shape exhibits faster computational time with less error percentage on distortion result compared to arc shape. Moreover, by using the rectangular shape, the element and meshing are much easier to be designed rather than arc shape bead.

Research on Equivalent Material Properties and Modal Analysis Method of Stator System of Permanent Magnet Motor With Concentrated Winding

Establishing an accurate stator system modal analysis model is of great significance for the vibration and noise analysis of the motor, scholars still have some controversy about how to set the material properties of the stator core and winding in modal analysis. First, the equivalent models of the stator core and winding was analyzed, the initial value of equivalent material parameters was determined. Second, the finite element models were used to analyze the influence of the equivalent material parameters on the natural frequency, a correction method of equivalent material parameters was proposed. Third, the modal of the stator core and the stator core with winding were tested by the moving force method. The finite element analysis results are consistent with the modal test results. Some influence laws of equivalent material parameters on natural frequency are obtained. The proposed correction method of equivalent material parameters helps to quickly determine the equivalent material properties of the stator core and windings. Setting the properties of the stator core and the winding material to the orthotropic materials can ensure the accuracy of the modal analysis.

Identification of Three‐Dimensional Equivalent Material Properties for Laminated Disks Pack of Electric Machine Stators: Application in Reciprocal Compressors

Laminated structures can be represented computationally by the finite element method (FEM) using the homogenization procedure, which consists of the adjustment of equivalent orthotropic properties to a homogeneous structure. The application occurs in stators of electric machines composed of stacked laminated disks connected to each other through windings and other fastening components. This paper describes a method to the dynamic characterization of a typical laminated stator through the application of the homogenization technique to the magnetic core and consideration of the effect of winding contour conditions and screw joints. Two simplified three‐dimensional models for the stator were compared. The first considers the application of a typical tightening of the fastening screws and the presence of a homogeneous isotropic volume representing the winding. The second considers the effect of the boundary condition of the winding on the region of the teeth of the nucleus in order to reduce the degrees of freedom of the complete model. The coupling between the components is accomplished through the application of modal synthesis methods, which require the definition of the surfaces and the type of connection between the components. The obtainment of the set of equivalent orthotropic properties is based on the minimization of residues related to the difference between the natural and experimental frequencies in the range of 0 to 10 kHz. This was carried out using the multiobjective genetic algorithm (MOGA) method used in conjunction with commercial Ansys® software. Both models presented satisfactory experimental correlation. The simplified model demonstrated limitations of representativeness emphasized in specific frequency bands.

Representative volume element analysis for wafer-level warpage using Finite Element methods

Wafer warpage of semiconductors in the manufacturing process is severe problem that decreases the quality and productivity. As the 3D NAND flash was developed, warpage became more important because the stack height increased. Some researches were carried out to expect the warpage using simulation. However, most studies have focused on the wafer-level regardless of the 3D NAND structures. It is very difficult to study the warpage with 3D NAND structures due to the inherent complexity. This paper presents simulation techniques to analyze warpage of the wafer-level. Equivalent material properties were obtained by using Representative Volume Element (RVE) model in this simulation. Wafer-level warpage predictions were analyzed and verified by comparing to experiment results. Finally, a sensitivity analysis was conducted to find the dominant factors affecting warpage. From this analysis, Young's modulus and thermal expansion coefficient were determined as dominant parameters of wafer warpage

Preliminary structural assessment of the HELIAS 5-B breeding blanket

The European Roadmap to the realisation of fusion energy, carried out by the EUROfusion consortium, considers the stellarator concept as a possible long-term alternative to a tokamak fusion power plant. To this purpose a pivotal issue is the design of a HELIcal-axis Advanced Stellarator (HELIAS) machine equipped with a tritium Breeding Blanket (BB), considering the achievements and the design experience acquired in the pre-conceptual design phase of the tokamak DEMO BB. Therefore, within the framework of EUROfusion Work Package S2 R&D activity, a research campaign has been launched at KIT.The scope of the research has been the determination of a preliminary BB segmentation scheme able to ensure, under the assumed loading conditions, that no overlapping may occur among the BB neighbouring regions. To this purpose, the Helium-Cooled Pebble Bed (HCPB) and the Water-Cooled Lithium Lead (WCLL) BB concepts, listed as starter blanket among those presently considered for the design of the DEMO tokamak fusion reactor, have been taken into account. A 3D CAD model of a HELIAS 5-B torus sector has been adopted, focussing attention on its central region. Due to the early stage of the HELIAS 5-B BB R&D activities, the considered CAD model includes homogenized blanket modules without internal details. Hence, in order to simulate the features of the HCPB and WCLL BB concepts, equivalent material properties have been purposely calculated and assumed. Moreover, a proper nominal steady state loading scenario, based on the DEMO HCPB and WCLL thermomechanical analyses, has been taken into account.A theoretical-numerical approach, based on the Finite Element Method (FEM), has been followed and the qualified ANSYS commercial FEM code has been adopted. The obtained results are herewith presented and critically discussed.

Orthotropic Analysis of Steel Deck–Girder–Rib Systems Subjected to Transverse Load

As one of the advanced modern techniques, orthotropic steel decks are widely used in bridge engineering. Because of its structural complexity, theoretical analysis of mechanical performances of the orthotropic steel bridge deck is very difficult. Therefore, in the past 50 years, a series of experiments and finite element analysis have been used to obtain the information. A steel deck–girder–rib bridge system subjected to the transverse load is investigated in this paper. The bridge deck is laid on four simply-supported girders at the four edges and is reinforced by ribs in longitudinal direction. The longitudinally stiffened deck is idealized as an orthotropic plate. The equivalent material properties in the longitudinal and breadth directions of the orthotropic plate are evaluated using micro-mechanics of composite material by treating the ribs as reinforcing fiber-beams. Governing equations for the deck–girder–rib bridge systems are established and are solved using Ritz method. The analytical solutions are substantiated by comparing with the classic solutions of an isotropic deck with fixed ends and with the finite element predictions. The analytical approach presented in this paper eliminates the very intricate and arduous kinematics study among deck–girder–rib and allows the bridge engineer to fast and convenient estimate the deformation in an orthotropic bridge deck.

Size-dependent forced vibration response of embedded micro cylindrical shells reinforced with agglomerated CNTs using strain gradient theory

This article presents an analysis into the nonlinear forced vibration of a micro cylindrical shell reinforced by carbon nanotubes (CNTs) with considering agglomeration effects. The structure is subjected to magnetic field and transverse harmonic mechanical load. Mindlin theory is employed to model the structure and the strain gradient theory (SGT) is also used to capture the size effect. Mori-Tanaka approach is used to estimate the equivalent material properties of the nanocomposite cylindrical shell and consider the CNTs agglomeration effect. The motion equations are derived using Hamilton\'s principle and the differential quadrature method (DQM) is employed to solve them for obtaining nonlinear frequency response of the cylindrical shells. The effect of different parameters including magnetic field, CNTs volume percent and agglomeration effect, boundary conditions, size effect and length to thickness ratio on the nonlinear forced vibrational characteristic of the of the system is studied. Numerical results indicate that by enhancing the CNTs volume percent, the amplitude of system decreases while considering the CNTs agglomeration effect has an inverse effect.

A new numerical approach and visco-refined zigzag theory for blast analysis of auxetic honeycomb plates integrated by multiphase nanocomposite facesheets in hygrothermal environment

The current work suggests a mathematical model for the dynamic response of sandwich plates subjected to a blast load using a numerical method. The sandwich structure is made from an auxetic honeycomb core layer integrated by multiphase nanocomposite facesheets. The facesheets are composed of polymer–carbon nanotube (CNT)–fiber where the equivalent material properties of the multiphase nanocomposite layers are obtained using fiber micromechanics and Halpin–Tsai equations in hierarchy. The top and bottom layers are subjected to magnetic field and the material properties of them are assumed temperature and moisture dependent. The Kelvin–Voigt model is employed to consider the viscoelastic properties of the structure. The sandwich structure is rested on a viscoelastic foundation which is modeled by orthotropic visco-Pasternak medium. Based on refined zigzag theory (RZT), energy method and Hamilton’s principle, the motion equations are derived. A new numerical method, namely differential cubature method (DCM) in conjunction with Newmark method is utilized for obtaining the dynamic deflection of the structure for different boundary conditions. The effects of various parameters such as blast load, viscoelastic foundation, structural damping, magnetic field, volume fraction of CNTs, temperature and moisture changes, geometrical parameters of honeycomb layer and sandwich plate are considered on the dynamic deflection of the structure. The results show that the magnetic field to the facesheets can be considered as effective parameters to control the dynamic deflection. In addition, hygrothermal condition leads to increase of 24% in the dynamic displacement of system.

Streamline stiffener path optimization (SSPO) for embedded stiffener layout design of non-uniform curved grid-stiffened composite (NCGC) structures

A bio-inspired concept of non-uniform curved grid-stiffened composite structures with embedded stiffeners (embedded NCGCs) is proposed in the paper. Shallow curved stiffeners are embedded in the laminate skin to form an integrated structure to improve the skin–stiffener deformation compatibility. A method named streamline stiffener path optimization (SSPO) based on multiscale modeling is proposed for curved stiffener layout design of embedded NCGCs. Firstly, the homogenization-based global/local analysis is used to calculate structural responses on a global unstiffened model with the equivalent material properties obtained from local representative cell configurations (RCCs). Secondly, the discrete distribution of 2D curved stiffener paths is transformed into a continuous distribution of the streamline function values (SFVs) on a 3D level set surface. The stiffener path description using the streamline function is similar as the level set method with specific constraints. Projections of points with the same integral SFVs will form one stiffener path. Thirdly, optimal curved stiffener layout is achieved using shape design of local parallelogram representative cell configurations with analytical sensitivities calculated using the affine mapping from the square master domain to the parallelogram RCCs. Fourthly, stiffener spacing and angle constraints are added for manufacturing considerations and local buckling resistance, and optimization design is implemented to maximize the buckling load within a given weight. Finally, numerical examples of a square laminated panel under uniaxial and biaxial compressions validate the effectiveness of the proposed SSPO method and indicate the significant improvement of the buckling loads by steering the stiffener paths.

Effect of Porosity on Flexural Vibration of CNT-Reinforced Cylindrical Shells in Thermal Environment Using GDQM

This article investigates the flexural vibration of temperature-dependent and carbon nanotube-reinforced (CNTR) cylindrical shells made of functionally graded (FG) porous materials under various kinds of thermal loadings. The equivalent material properties of the cylindrical shell of concern are estimated using the rule of mixture. Both the cases of uniform distribution (UD) and FG distribution patterns of reinforcements are considered. Thermo-mechanical properties of the cylindrical shell are supposed to vary through the thickness and are estimated using the modified power-law rule, by which the porosities with even and uneven types are approximated. As the porosities occur inside the FG materials during the manufacturing process, it is necessary to consider their impact on the vibration behavior of shells. The present study is featured by consideration of different types of porosities in various CNT reinforcements under various boundary conditions in a single model. The governing equations and boundary conditions are developed using Hamilton's principle and solved by the generalized differential quadrature method. The accuracy of the present results is verified by comparison with existing ones and those by Navier's method. The results show that the length to radius ratio and temperature, as well as CNT reinforcement, porosity, thermal loading, and boundary conditions, play an important role on the natural frequency of the cylindrical shell of concern in thermal environment.

Simplification of finite element modeling for plates structures with constrained layer damping by using single-layer equivalent material properties

As an effective approach of suppressing vibrations, the constrained layer damping (CLD) has drawn wide attention from the automotive and aerospace industries. However, most of the existing investigations focus on the beam structures with CLD and few studies have been done on the plate structures with CLD. Considering the practical applications, this work studies the finite element (FE) modeling of plate structures with CLD by considering the shear and extension strains in all of three layers. To reduce the computational cost and ensure the accuracy, a simplified single-layer equivalent method is originally proposed to model the plate structure with CLD based on the equivalent material properties. In this method, the equivalent material properties are obtained by defining a new equation which includes the equivalent bending stiffness. By nonlinear regression of these responses at resonance frequencies, the equivalent bending stiffness can be obtained, and the plate structure with CLD can be regarded as a regular single-layer plate for modeling. The simulation result shows that the proposed simplified single-layer equivalent method using single-layer equivalent material properties is efficient and accurate for modeling plate structures with CLD.

Nondestructive characterization of bone tissue scaffolds for clinical scenarios

ObjectivesThis study aimed to develop a simple and efficient numerical modeling approach for characterizing strain and total strain energy in bone scaffolds implanted in patient-specific anatomical sites. Materials and methodsA simplified homogenization technique was developed to substitute a detailed scaffold model with the same size and equivalent orthotropic material properties. The effectiveness of the proposed modeling approach was compared with two other common homogenization methods based on periodic boundary conditions and the Hills-energy theorem. Moreover, experimental digital image correlation (DIC) measurements of full-field surface strain were conducted to validate the numerical results. ResultsThe newly proposed simplified homogenization approach allowed for fairly accurate prediction of strain and total strain energy in tissue scaffolds implanted in a large femur mid-shaft bone defect subjected to a simulated in-vivo loading condition. The maximum discrepancy between the total strain energy obtained from the simplified homogenization approach and the one obtained from detailed porous scaffolds was 8.8%. Moreover, the proposed modeling technique could significantly reduce the computational cost (by about 300 times) required for simulating an in-vivo bone scaffolding scenario as the required degrees of freedom (DoF) was reduced from about 26 million for a detailed porous scaffold to only 90,000 for the homogenized solid counterpart in the analysis. ConclusionsThe simplified homogenization approach has been validated by correlation with the experimental DIC measurements. It is fairly efficient and comparable with some other common homogenization techniques in terms of accuracy. The proposed method is implicating to different clinical applications, such as the optimal selection of patient-specific fixation plates and screw system.

Creep-fatigue strength design of plate-fin heat exchanger by a homogeneous method

Creep-fatigue life prediction is essential to plate-fin heat exchangers (PFHE) work at high temperatures and pressures in addition to thermal cycles. As the core of PFHE, the plate-fin structure is a complex pore structure and it is pretty difficult to carry out the stress analysis by conventional finite element method. Thus in this paper, a homogeneous method is proposed to do the strength design for plate-fin structure. This method treats the pore structure as an equivalent solid structure, and the key is to calculate the equivalent material properties and the equivalent stress. The equivalent mechanical properties have been obtained in our previous work [1], and in this paper the equivalent thermophysical properties including thermal conductivity, coefficient of thermal expansion, specific heat and density have been derived. This equivalent method is also verified by the three-dimensional finite element method. Besides, creep and fatigue tests of plate-fin structure are applied to calculate the stress and strain magnification factors. Basing on the equivalent material properties, a full scale stress analysis of PFHE by the equivalent finite element model has been carried out successfully to calculate the equivalent stress. After that, we multiply the equivalent stress-strain by the stress and strain magnification factors to calculate the local stress and strain. Then the creep and fatigue damages are predicted according to design curves of base metal. The result of equivalent model agrees well with that of the classical model, which concludes that this homogeneous method is effective to predict the macroscopic performance of plate-fin structure.

Technical and economical assessment of applying silica nanoparticles for construction of concrete structures

The use of nanotechnology materials and applications in the construction industry should be considered for enhancing material properties. However, in this paper, the technical and economical assessment of applying silica nanoparticles for construction of concrete structure is studied. In order to obtain the equivalent material properties of the structure, the Mori-Tanaka model is used considering agglomeration of nanoparticles. The effect of using these nanoparticles on mechanical properties of concrete, such as the modulus of elasticity, compressive strength, as well as its indirect effect on armature percentage is investigated. Finally, the price of silica nanoparticles and its effect on the price increase of concrete structure is investigated. The results show that increasing the volume percent of silica nanoparticles up to 10% improves elastic modulus 111% and reduces amateur percentage up to 72%.

Dynamic buckling of magnetorheological fluid integrated by visco-piezo-GPL reinforced plates

This paper deals with the dynamic buckling analysis of sandwich plates with magnetorheological (MR) fluid core and piezoelectric nanocomposite facesheets. The core is subjected to magnetic field and the facesheets are exposed to 3D electric field. Due to the piezoelectric properties of the facesheets, the top and bottom layers can be used as actuator and sensor, respectively. Hence, a proportional-derivative (PD) controller is employed to control the dynamic buckling and vibration responses of the structure. In addition, the facesheets are reinforced by with non-uniform graphene platelets (GPLs) which their equivalent material properties are obtained using Halpin-Tsai micromechanics model. The structural damping of the piezoelectric layers is considered according to Kelvin-Voigt theory. The sandwich structure is rested on orthotropic viscoelastic model with normal, shear and damping forces. Based on the sinusoidal shear deformation theory (SSDT) and piezoelasticity theory, the motion equations are derived utilizing Hamilton's principle. Applying differential cubature method (DCM), the motion equations are solved for calculating the dynamic instability region (DIR) of the structure. The influences of various parameters such as magnetic field, applied voltage, structural damping, viscoelastic medium, volume fraction and distribution of GPLs, boundary conditions and geometric parameters of the structure are shown on the dynamic buckling behavior of the system. The results are validated with other published work for indication the accuracy of the obtained results. The results reveal that by applying the magnetic field to the MR fluid core, the DIR with be happened at higher excitation frequencies.

A comprehensive study on composite risers: Material solution, local end fitting design and global response

Two up-to-date composite riser solutions, specifically, the thermoset and thermoplastic based ones are studied in a global-local framework to examine their technical feasibility for offshore applications. At the local scale, the riser pipe body with multi-layered structure is homogenized through an analytical approach, obtaining equivalent material properties of the riser string model for the global analysis. The metal-composite interface (MCI) end fittings between the riser body and standard connector are examined using finite element (FE) simulations to understand their load-transfer mechanisms for both solutions. At the global scale, an in-house analysis code is performed to study the risers' static and dynamic response in a certain sea condition due to top-tension, current drag and vortex induced vibration (VIV). The analyzed parameters include the resulting riser deflection, axial stress, tension and bending moment distributions. Following that, an integrated analysis utilizing the global results and the local failure envelopes is performed to determine if the maximum stress states of the riser exceed the equivalent structural strength boundary. It is concluded that composite risers exhibit a larger safety margin than traditional steel riser under the same sea condition.

Analysis for deformation behavior of multilayer ceramic capacitor based on multiscale homogenization approach

Given the rapid improvements in the miniaturization, functionality, and efficiency of electronic products in recent years, the dielectric layers and electrodes of multilayer ceramic capacitors have become thinner, with the number of stacked layers also increasing. As a result, the deformation defects induced during manufacturing of the capacitors have increased. In this study, the deformation behavior of a multilayer ceramic capacitor composed of ceramic dielectric layers and Ni electrode layers during the compression process was analyzed numerically using the FEM. To analyze the deformation behavior of the capacitor, which consisted of several hundred laminated ceramic and Ni layers, in the plane direction, the material properties were represented by equivalent material properties based on the multiscale homogenization approach. Then, the deformation of the capacitor in the plane direction owing to the residual stress arising during the compression process was analyzed based on the calculated equivalent material properties. Finally, the possibility of a product defect with the size of the ceramic dielectric and electrode layers during the cutting process was predicted.