Flexible Matrix Research Articles

Analytical solution for forced vibration of multilayer structures composed of plates with different geometric dimensions

Multilayer system composed of parallel plate components with different geometric dimensions is frequently used to describe engineering objects, such as electronic assembly. In this work, an analytical method was proposed for forced vibration of this type of multilayer system. The proposed method overcomes the limitation that the traditional wave method is only applicable to all plate components must have the same in-plane dimensions. The proposed analytical method has an efficiency advantages in parameter analysis than element-based methods such as finite element method (FEM). The connection joints between two adjacent plate components, such as ball grid array (BGA) solder interconnect, are represented by elastic springs. The vibration of each component are described in terms of general and physical analytical waves, respectively, and the dynamic coupling between them are established by an equivalent dynamic flexibility matrix. The forced responses of the multilayer system are analytically calculated by solving the system equation in wave space. In the numerical examples, the effectiveness of the proposed method is validated by comparing the present results with the FEM results. The influence of number of the defective solder joints on vibration response is also investigated.

Flexible PVDF/BST nanocomposites for mechanical energy harvesting application

The development of a piezoelectric generator (PEG) that exhibits improved durability, stability, and enhanced output performance continues to be a crucial objective for self-powered and wearable electronic devices. In this study, a PEG was constructed using nanocomposite films composed of sol-gel derived Barium Strontium Titanate (BST) filler embedded within a Polyvinylidene fluoride (PVDF) matrix. This flexible polymer matrix structure is selected for its exceptional performance, flexibility, and cost-efficiency, making it ideal for advanced piezoelectric applications. Homogeneous nanocomposite films of PVDF-BST with different proportions of BST were fabricated using the solution casting method. Integrating BST filler into the PVDF matrix significantly enhances the nucleation of the electroactive β-phase, thereby improving the dielectric and ferroelectric properties, which vary according to the volume fraction of BST used. Specifically, the PVDF-BST composite containing 10 % BST (PB10) exhibited the highest electroactive β-phase content at 41.8 %, and demonstrated an energy storage density of 0.8 J/cm³ with an efficiency of 73.9 %. The dielectric constant at room temperature is seen to rise from 23 in pure PVDF to 132 in the PB20 composition at 1 kHz. The open-circuit voltage (Voc) of the PEG was recorded by exerting a periodic force on its surface. Notably, the PB10 variant achieved the highest peak-to-peak open-circuit voltage, reaching 28 V. Additionally, PB10 produced an open-circuit voltage of 22 V in response to finger tapping, highlighting its suitability for applications in touch and pressure sensing.

Ultra-fast light repair, ultrasensitive, large strain detection range PDA@RGO/EVA composites fiber flexible strain sensor

The sensor fabricated from high-molecular polymer is soft, lightweight, and biocompatible; however, traditional high-molecular polymers suffer from viscoelasticity and poor cycle stability. To address these issues, it is essential to develop flexible matrix materials that can overcome viscoelasticity, ensuring high sensitivity and long-term use under large strains for next-generation wearable intelligent devices. In this study, ethylene-vinyl acetate (EVA) with a shape memory effect was utilized as the substrate for a flexible sensor，the shape memory effect of EVA can eliminate the residual strain generated by each long time of use to improve its service life. A polydopamine@reduced graphene oxide (PDA@RGO)/EVA fiber flexible strain sensor was fabricated through melt extrusion, swelling ultrasound, and in-situ polymerization techniques. The resulting sensor exhibits high sensitivity (gauge factor=1801.21), a wide strain detection range (strain = 193 %), and excellent stability and durability (2000 cycles). Notably, the PDA@RGO/EVA fiber flexible strain sensor demonstrates exceptional dual thermal and light repair functions, with light repair achieving a repair speed of 5 seconds, 100 % electrical performance repair efficiency, and perfect consistency in relative resistance response before and after repair. Furthermore, the PDA@RGO/EVA strain sensor can monitor finger and wrist movements in real-time with high accuracy, highlighting its significant potential application in the wearable technology field.

An algorithm based on B-differentiable equations method for solving problems involving frictional contact coupled with concrete plastic damage

In this paper, an algorithm is proposed to solve the frictional contact problems while considering elasto-plastic material properties. The static and dynamic solution procedures are derived in incremental form, respectively. The proposed method employs a two-layer iteration strategy. In the outer iteration layer, the equilibrium equations are solved, with the stress and stiffness matrix updated at each iteration. Within the inner iteration layer, the contact force is calculated, where the contact equations, expressed as B-differentiable equations, incorporate only contact conditions in normal and tangential directions, and the contact flexibility matrix, obtained by applying unit force pair to all contact node pairs in turn, is introduced. Consequently, the solution for nonlinear equilibrium equations and contact equations is decoupled, requiring only one decomposition of the stiffness matrix for each calculation of the contact flexibility matrix, as it remains constant within the contact iteration layer. In addition, the constitutive model of concrete developed by Lee and Fenves is utilized. This model adopts two independent variables to describe tensile and compressive damage, together considering the strength recovery of the concrete. Numerical examples demonstrate the accuracy of the proposed method by comparing the results from Abaqus. Furthermore, the present algorithm is applied to static and dynamic analyses of a concrete arch dam with several transverse joints, where the effects of gravity, water level, the number of contact surfaces, and seismic load are considered, and some conclusions are obtained.

Dynamic Modal Reanalysis Using Flexibility Disassembly Perturbation Method

In structural optimization design and reliability analysis, it is necessary to repeatedly modify the structure and calculate the corresponding vibration modal parameters. It will require significant computational costs if a complete analysis is used to calculate the vibration modes of each modified structure. In order to improve computational efficiency, this work develops a dynamic modal reanalysis method based on flexibility disassembly perturbation, which utilizes the modal data of the original structure to quickly calculate the modal parameters of the modified structure. The core idea of the proposed method is to use the flexibility matrix decomposition formula to quickly calculate the flexibility matrix after each modification of the structure and then obtain a high-precision reduced eigenvalue problem for solving the vibration modes of the modified structure. Three numerical examples are used to validate the proposed modal reanalysis method. It has been shown that the proposed method has higher computational accuracy and efficiency than the existing modal reanalysis method, especially for high-rank and large modification scenarios.

High-Emissivity Double-Layer ZrB2-Modified Coating on Flexible Aluminum Silicate Fiber Fabric with Enhanced Oxidation Resistance and Tensile Strength.

Fibers crystallize and become brittle at high temperatures for a long time, so the surface coating must maintain long-lasting emission performance, which requires superior antioxidant properties of the high-emissivity fillers. To improve the radiation performance of the coating and the tensile strength of the fiber fabric, a double-layer coating with high emissivity was prepared on the surface of flexible aluminum silicate fiber fabric (ASFF) using MoSi2 and SiC as emissive agents. The incorporation of borosilicate glass into the outer coating during high-temperature oxidation of ZrB2 results in superior encapsulation of emitter particles, effectively filling the pores of the coating and significantly reducing the oxidation rate of MoSi2 and SiC. Furthermore, the addition of an intermediate ZrO2 layer enhances the fiber bundle's toughness. The obtained double-coated ASFF exhibits an exceptionally high tensile strength of 57.6 MPa and a high bond strength of 156.2 kPa. After being subjected to a 3 h heating process, the emissivity exhibits a minimal decrease of only 0.032, while still maintaining a high value above 0.9. The thermal insulation composites, consisting of a flexible ASFF matrix and a ZrB2-modified double-layer coating, exhibit significant potential for broad applications in the field of thermal protection.

Phonon Engineering in Solid Polymer Electrolyte toward High Safety for Solid-State Lithium Batteries.

Extensively-used rechargeable lithium-ion batteries (LIBs) face challenges in achieving high safety and long cycle life. To address such challenges, ultrathin solid polymer electrolyte (SPE) is fabricated with reduced phonon scattering by depositing the composites of ionic-liquid (1-ethyl-3-methylimidazolium dicyamide, EMIM:DCA), polyurethane (PU) and lithium salt on the polyethylene separator. The robust and flexible separator matrix not only reduces the electrolyte thickness and improves the mobility of Li+, but more importantly provides a relatively regular thermal diffusion channel for SPE and reduces the external phonon scattering. Moreover, the introduction of EMIM:DCA successfully breaks the random intermolecular attraction of the PU polymer chain and significantly decreases phonon scattering to enhance the internal thermal conductivity of the polymer. Thus, the thermal conductivity of the as-obtained SPE increases by approximately six times, and the thermal runaway (TR) of the battery is effectively inhibited. This work demonstrates that optimizing thermal safety of the battery by phonon engineering sheds a new light on the design principle for high-safety Li-ion batteries.

Bionanocomposite MIL-100(Fe)/Cellulose as a high-performance adsorbent for the adsorption of methylene blue

World production of dyes is estimated at more than 800,000 t·yr−1. The purpose of this research falls within the scope of the choice of an effective, local, and inexpensive adsorbent to remove dyes from wastewater. Adsorptive elimination of dyes by commonly accessible adsorbents is inefficient. The metal–organic frameworks (MOFs) are an important class of porous materials offering exceptional properties as adsorbents by improving separation efficiency compared to existing commercial adsorbents. However, its powder form limits its applications. One way to overcome this problem is to trap them in a flexible matrix to form a hierarchical porous composite. Therefore, in this work, we prepared MIL-100 (Fe) embedded in a cellulose matrix named MIL-100(Fe)/Cell, and used it as an adsorbent of methylene blue (MB) dye. According to the BET analysis, the specific surface area of the synthesized MOF is 294 m2/g which is related to the presence of the cellulose as efficient and green support. The structure of this composite is approximately hexagonal. Adsorption was studied as a function of contact time, adsorbent mass and pollutant load (concentration), and pH, and the effect of each of them on absorption efficiency was optimized. The MIL-100(Fe)/Cell was capable of removing 98.94% of MB dye with an initial concentration of 150 mg/L within 10 min at pH = 6.5 and room temperature. The obtained maximum adsorption capacity was 384.615 mg/g. The adsorption isotherm is consistent with the Langmuir models. The mechanism of MB adsorption proceeds through п-п and electrostatic interactions.

Computational study on the electrical conductivity of hybrid composites under mechanical deformation

This study explores the hybrid composite’s electrical conductivity response under uniaxial tensile strain, wherein conductive nanowires and insulating particulate fillers are integrated within a flexible polymer matrix. We develop a Monte Carlo–based computational model and analyze the significant influence of particulate fillers on the strain response of the electrical conductivity. The particulate fillers induce both the exclusive volume and nanowire bending effects, significantly contributing to determining the hybrid composites’ electrical conductivity. The exclusive volume effect mitigates conductivity changes under external deformation, decreasing the conductivity change rate as the particulate filler content increases when the exclusive volume effect is dominant. Conversely, the nanowire bending effect boosts conductivity change under external deformation, so when it predominates over the exclusive volume effect, the conductivity change rate increases with higher particulate filler content. The insights from the study aid in designing and optimizing flexible electronic materials resilient to mechanical deformation.

A fast analysis algorithm for structural vibration modal sensitivity

Vibration modal sensitivity analysis has a wide range of applications in structural optimization design, model correction, fault detection, and reliability analysis. The existing methods for calculating modal sensitivity mainly include modal superposition method, Nelson’s method, and some improved algorithms derived from them. However, the existing algorithms have the drawback of low computational efficiency when applied to modal sensitivity analysis of the large-scale structures. In view of this, the objective of this work is to develop a fast modal sensitivity analysis method that can more efficiently calculate the modal sensitivity of the large structures with thousands of degrees of freedom. This new sensitivity analysis technique integrates Sherman-Morrison-Woodbury formula, subspace iteration and forward-difference to achieve the goal of fast calculation. The innovations of the proposed method mainly include the following aspects. Firstly, the Sherman-Morrison-Woodbury formula is used to quickly calculate the perturbed flexibility matrix due to the minor modification in the structure. Then, the perturbed flexibility matrix is introduced into the subspace iteration method to calculate the perturbed modal parameters. Finally, the forward-difference algorithm is used to calculate the modal sensitivity. Two numerical examples are used to verify the superiority of the proposed modal sensitivity algorithm. Taking the 1952-bar structure as an example, the calculation time of the proposed algorithm is only 8.3 % and 18.2 % of that of the existing approximate modal superposition method and the improved Nelson’s method, respectively. In terms of calculation accuracy, the results obtained by the proposed method are exactly the same as the exact solution when the perturbation scale is set to 10−5. It is found that the proposed method significantly reduces computation time compared to the existing methods on the premise that the calculation accuracy is basically unchanged.

Study on the contact performance of the variable hyperbolic circular arc tooth trace cylindrical gear with installation errors

Abstract. Installation errors are important factor for the contact performance of the variable hyperbolic circular arc tooth trace (VH-CATT) cylindrical gear; the study of the relationship between installation errors and contact performances is beneficial for gear vibration and noise reduction. Firstly, based on the meshing theory, the tooth surface equation and contact ellipse of the VH-CATT cylindrical gear were deduced, and the tooth surface imprinting experiment was realized. Next, the tooth contact analysis model of the VH-CATT cylindrical gear was developed to investigate the influence of the installation errors on the elliptical contact area. Then, the calculation formulas of the tooth surface gap and contact point flexibility matrix were carried out to develop the load tooth contact analysis model of the VH-CATT cylindrical gear. Finally, the influence of the installation errors on the load distribution was investigated. Research shows that the elliptical contact area of the VH-CATT cylindrical gear is a line contact within a certain range and is located in the middle section of the tooth width. The elliptical contact area of the VH-CATT cylindrical gear increases or decreases rapidly when meshing in and out, and all the installation errors have a certain influence on the elliptical contact area, except for the center distance error. The single-tooth meshing area with the installation errors is greater than that of the ideal gear pair. The load distribution area with the installation errors deviates from the middle section, except for the center distance error. The installation rotation errors around the x and y axis have a certain influence on the maximum load of the single-tooth meshing area. The research results provide a basis for improving the bearing capacity of the VH-CATT cylindrical gear and optimizing the design.

Synergistic improvement of mechanical and piezoelectric properties of the flexible piezoelectric ceramic composite and its high-precision preparation

Flexible piezoelectric ceramic composites (FPCCs) hold promising applications in fields such as flexible sensing and energy harvesting. However, the previous methods are difficult to achieve high-precision preparation of the FPCCs with complex structures, as well as the synergistic enhancement of piezoelectric performance and flexibility. In this study, by configuring a flexible resin matrix and employing a surface functionalization treatment on the piezoelectric ceramic particles, the flexibility and piezoelectric performance of the FPCCs are synergistically improved. Moreover, the addition of a light absorber, TiO2, significantly improves the 3D printing precision. The mechanical properties, piezoelectric performance, and printing precision of the FPCCs are analyzed. It is found that the printing error is less than 2 μm, the tensile fracture strength is 4.07 MPa, the elongation at break is 350 %, and the piezoelectric constant d33 can reach 7.7 pC/N. In addition, the cyclic loading tests show that FPCCs with high-precision 3D complex microstructure have good recovery performance. This study not only enriches the formulation of FPCCs slurry for 3D printing, but also provides a research foundation for the multifunctional applications.

A generalization of B-differentiable equations method for elastoplastic contact problems with dual mortar discretization

In this study, a novel method based on the B-differentiable equations (BDEs) is proposed to solve the three-dimensional (3D) static and dynamic elastoplastic contact problems with friction. The contact conditions are formulated as the BDEs system, which can precisely satisfy Coulomb’s law of friction. Based on the mortar segment-to-segment contact model, the contact constraints are enforced by dual Lagrange multipliers for nonconforming meshes of the contact boundary. The non-smooth and nonlinear system equations composed of equilibrium and contact equations are simultaneously solved by the B-differentiable damping Newton method (BDNM), which has global convergence property. In each iteration, firstly, some contact displacements and contact forces, called substituted contact variables, are expressed by others according to the different contact states and contact conditions. The equilibrium equation is then solved, where the stiffness matrix is updated by substituting the contact variables. At last, the substituted contact variables will be restored. In the proposed method, the contact flexibility matrix is no longer needed, which saves the time for calculating the contact flexibility matrix due to changes in the stiffness matrix resulting from the update of stresses in the iteration step. By comparing with the results obtained by finite element commercial software ANSYS, the accuracy of the proposed algorithm is verified, and the property of convergence and efficiency are demonstrated for the elastoplastic contact problems by several numerical examples.

Effect of NASCION‐Type ceramic dispersion in PAN/PVA‐based blend polymer electrolyte: A structural, thermal, and electrical study

AbstractSolid flexible separators having adequate ion conductivity at ambient temperature along with good thermal and voltage stability are potential candidates for separators in all solid‐state ion batteries. In the present work, zirconium and niobium‐doped Li1.3Al0.3Ti1.7 (PO4)3 ceramic particles have been incorporated into a polyvinyl alcohol (PVA) and polyacrylonitrile (PAN)‐based blend that served as a flexible matrix to create a flexible polymer–ceramic framework and have been examined for conductivity, dielectric properties, voltage stability, thermal stability, and electrochemical performance. The flexible polymer–ceramic framework shows high thermal stability, improved conductivity, and a high‐voltage window. Optimized dc conductivity of 9.8 × 10−5 S cm−1 has been observed among all investigated samples, with an improved voltage stability of 4.94 V. Further, the Trukhan model has been used to understand the effect of filler loading on ion migration properties. The optimized solid polymer electrolyte (SPE) shows improved ion mobility (μ) of 5.13 × 10−2 cm2 V−1 s, number density (n) = 2.39 × 1015 cm3, and diffusion coefficient (D) of 2.09 × 10−3 cm2 s−1. It also shows a very high specific capacitance of ~10−4 Fg−1, excellent cycling stability, and 93.75% capacity retention after 100 cycles.

Development, modeling and analysis of a differential lever-bridge amplification mechanism

The displacement amplification mechanism is commonly utilized in micro/nano-manipulating systems to enhance the output stroke of piezoelectric actuators. Aiming at large amplification ratio, this paper proposes a symmetrical dual-stage amplification mechanism consisting of a differential lever mechanism and a half-bridge mechanism. With consideration of the coupling effect between the dual-stage amplification mechanism, a kinematic modeling method is developed for the symmetrical differential lever-bridge hybrid (SDLBH) mechanism on top of the static balance and constraint conditions of the branch chain. In particular, the force-deformation relationship of the flexible hinge is derived according to the flexibility matrix method. Based on the path constraint conditions of the branch chain, the static equilibrium equation as well as the displacement constraint conditions are obtained. Consequently, the input-output model of the SDLBH mechanism is established, which is capable of accurately predicting the amplification ratio and the mechanical stiffness. Finite element simulations and real time experiments on the SDLBH prototype effectively validate the mechanical performance as well as the accuracy of proposed modeling method. The performance sensitivity of the developed SDLBH mechanism is further analyzed by the Taguchi method, aiming to offer the optimization guideline for real applications.

Dynamic Response of the Tunnel Lining with a Circumferential Crack Subjected to a Harmonic Point Load

Cracks are one of the most common diseases of tunnel lining, and the structural dynamic response can be used to assess the health of a tunnel. Hence, this paper investigates the dynamic response of shield tunnel lining with a partly circumferential crack. The shield tunnel lining is regarded as a thin cylindrical shell and analyzed independently. The research methodology integrates the wave propagation method, the local flexibility matrix, the line spring model and the wave superposition principle. The results show that the position and depth of a partly circumferential crack can influence the natural frequency of the shield tunnel lining. Under the fixed-position load, as the distance from the monitoring point to the crack increases, the difference in displacement response amplitude between the undamaged and cracked linings diminishes. Moreover, deepening cracks enlarge the magnitude of amplitude differences. When the load approaches the crack, the radial amplitude difference first increases and then decreases as the monitor moves away from the crack. This finding helps determine the required monitor position. The displacement response of the selected monitor indicates that the closer the load position is to the crack, the larger the amplitude difference. The results aid in identifying the crack position and selecting corresponding load and monitor locations.

A closed-form Timoshenko beam element with multiple localized singularities for nonlinear material behavior using the strong discontinuity approach

The development of a novel closed-form beam element for nonlinear material behavior in structures is described, which is formulated according to Timoshenko beam theory and the embedded strong discontinuity approach. Multiple strong transverse and rotation discontinuities are considered to model several dissipative mechanisms due to localized singularities in the shear strain and curvature fields. Issues of dependence on numerical techniques, as occurs in displacement- and forced-based beam elements with the finite element method, are overcome since the formulated element is derived from a pure mathematical treatment. Theoretical principles are stemming from a Lagrangian variational model, from which singularities are naturally derived. The proposed formulation is solved by the conventional methods of calculus of variations, resulting in the boundary value problem. Then, closed-form expressions for any boundary conditions are obtained. By particularizing closed-form expressions for a basic system, a symmetric closed-form flexibility matrix is obtained. This matrix naturally leads to a symmetric closed-form stiffness matrix for any type of loading and unloading process, in which the nodeless degrees of freedom of the multiple embedded strong discontinuities are naturally condensed. Since Gauss integration methods are not used, the multiple localized singularities are not influenced by predefined positions of the integration points. However, the accuracy depends on the chosen number of singularities and their positions. Then, the proposed element is mesh independent when sufficient discontinuities are considered, which does not imply an increase in the degrees of freedom. Softening discontinuities are modeled at arbitrary positions in a single element, which overcomes the drawbacks of other embedded beam theories where more than one element is necessary to identify failure since strong discontinuities are generally located at the midpoint of the beam element. The obtained closed-form stiffness matrix is not always positive definite for strain-softening problems. Nevertheless, there are no major convergence issues as it is a symmetric matrix that does not require a constraint equation, so even the complex snap-back behavior in structures is adequately modeled. The capability of the formulated beam element for nonlinear material behavior in structures is validated with representative examples.

Structural damage localisation based on generalised flexibility change rate curvature and data fusion technology

ABSTRACT Damage localisation is the key to structural damage identification. Based on the study of damage index using the flexibility method, this paper presents a damage localisation index using the generalised flexibility matrix before and after structural damage. To enhance the accuracy of structural damage localisation, it is necessary to improve the sensitivity of damage index. Therefore, this paper puts forward a generalised flexibility change rate curvature index with the objective of improving the accuracy in localising structural damage. The curvature index is defined as the second-order difference of the generalised flexibility change before and after damage. Consequently, the curvature-based index usually is more sensitive to structural damages. To enhance the accuracy and efficiency of multiple damage localisation, the generalised flexibility change rate curvature index is combined with data fusion technology based on Dempster-Shafer’s theory. Numerical simulations and experimental studies have validated the capability and efficiency of the proposed method for damage localisation also in the case of multiple damages, noise impact, and limited modal orders.

3D porous structure Fe3O4@SnO2/MXene composites with enhanced electrochemical performance for lithium ion battery anode

The low theoretical capacity of the commercial graphite electrodes used in lithium-ion batteries (LIBs) necessitates the development of novel anode materials with higher rate performance, reversible specific capacities, long cycle lives, and low costs. In this work, three-dimensional porous structure Fe3O4 nanosphere with extremely thin SnO2 coatings are prepared by a method of getting twice the result with half the effort. And it was uniformly dispersed in an MXene flexible conductive matrix to fabricate a 3D porous heterogeneous Fe3O4@SnO2/MXene composite to act as an anode material for LIBs. The 3D porous heterojunction structure integrates the advantages of Fe3O4@SnO2 and MXene, achieving rapid electron and ion transport at the interface and the effective release of structural stress. The introduction of MXene markedly enhances the conductibility of the materials, limits the expansion of Fe3O4 during the Li+ insertion/removal process, and inhibits its aggregation. The Fe3O4@SnO2/MXene anode exhibits excellent electrochemical performance (1609 mAh g−1 over 200 cycles at 100 mA g−1 and 626.1 mAh g−1 over 900 cycles at 1000 mA g−1). These findings demonstrate that the Fe3O4@SnO2/MXene composite is a promising anode material for LIBs.

Research on roller bearing fault diagnosis method based on flexible dynamic adjustable strategy under data imbalance

In engineering practice, the collection of equipment vibration signals is prone to interference from the external environment, resulting in abnormal data and imbalanced data in different states. Traditional support vector machine, support matrix machine and other methods have advantages in balancing sample classification, but have limitations in obtaining low rank information, making it difficult to perform classification tasks under data imbalance. Therefore, a novel classification method that targets matrices as the input, called flexible dynamic matrix machine (FDMM), is proposed in this paper. First, FDMM establishes a regularization term using a flexible low-rank operator and sparse constrain, which can better take into account matrix structure information. Then, the upper bound of the loss function is truncated, reducing the impact of the loss on the construction of the decision hyperplane. Finally, the recognition performance of imbalanced data is improved by adjusting the game values of different categories of samples through dynamic adjustment function. Experimental results demonstrate that superior classification accuracy and generalization performance can be achieved with the FDMM method when applied to two roller bearing datasets.