Equivalent Stiffness Research Articles

The Performance of Fixed Step Size and Adaptive Step Size Numerical Methods for Solving Deterministic Cell-Growth Models

Deterministic cell-growth models describe the growth of cell populations using fixed mathematical rules, assuming no randomness in the system. These models are often based on differential equations that account for the rates of cell division, death, and other biological processes. The solution to the system is obtained via numerical methods. Most of the developed approaches are based on fixed step sizes. However, fixed step size implementation failed to offer the optimal solutions when dealing with stiff challenges. Fixed step size methods can be unstable for stiff equations, where some components of the solution change much more rapidly than others. The step size, required to maintain stability can become impractically small. Thus, the adaptive step size method is required. Adaptive step size methods adjust the step size dynamically based on the behavior of the solution, aiming to maintain a desired level of accuracy while optimizing computational efficiency. These methods are particularly useful for solving ordinary differential equations (ODEs) where the solution can vary rapidly in some regions and slowly in others. This study is devoted to comparing the implementation of fixed step size and adaptive step size in solving ordinary differential equations (ODEs). The fixed step size and adaptive step size numerical method are solved in this study via the fourth order Runge-Kutta method (RK4) and Runge-Kutta Fehlberg 45 method (RKF45). The performance of both numerical methods used will be analyzed by comparing the numerical results approximated with the actual data. Subsequently, the absolute error, relative error, and rounding-off error will be calculated to compare both approaches. Based on the more precise findings, this work has shown that adaptive step size is predicted to be the optimal representation for solving ODEs. As a result, this may help mathematicians to choose the most effective numerical approach for solving ODEs.

Mechanical study and equations for gravity flow pipe liners stretching across ring fractures or joints under shear action

Cured-in-place-pipe (CIPP) liners have been widely used in rehabilitation of gravity flow pipelines. However, the host pipe rehabilitated by the CIPP liner may be subject to shear force and shear displacement at the joint. In this study, a finite element model of a rigid host pipe with liner under shear action is established and used to study the resulting behaviour. Controlling factors such as the gap spanned by the liner between host pipes across the joint, diameter, the liner thickness, the elastic modulus of the liner, and the coefficient of friction between host pipe and liner are studied. The liner stress, displacement, and shear force are reported. Shear stiffness and stress equations are then fitted based on 286 data points. The results show that the maximum stress on the inner surface of the liner occurs at the shoulder and haunch, and the maximum stress on the outer surface occurs at the springline. The inner surface stresses at the crown and invert decrease with increases in liner-host pipe friction, but increase at the shoulder and haunch. Coefficient of Friction has almost no effect on the stresses that develop on the outside surface of the liner.

Application of the Finite Element Method for Analyzing the Vibration Characteristics of a Spindle System and Fault Diagnosis

The performance of a spindle will gradually decline, the vibration intensity will increase, and the temperature rise will become abnormal with the accumulation of service time. Consequently, the accuracy of the machining product will not meet its production requirements. Studies on the variation characteristics of the spindle unit have clarified the reasons for its abnormal vibration and temperature rise, in principle, to help enterprises conduct preventive maintenance before any serious failure occurs and improve production efficiency. Based on the Timoshenko beam model and rotor dynamics theory, this study uses the finite element method (FEM) to analyze the vibration characteristics of the spindle rotor system. Moreover, it thoroughly analyzes the influence of the spindle bearing heat on the stiffness of the spindle system and identifies the resonance conditions of the spindle rotor within the power frequency range. This research has identified that when the vibration frequency of the spindle operates at a speed of 12,000 r/min, if its vibration frequency is lower than 200 Hz, it will be affected by abnormal vibrations during startup, which will weaken the health status of the spindle and reduce its service life. Similarly, when the working speed of the spindle is 30,000 r/min, if its vibration frequency is lower than 50 Hz, abnormal vibration will occur during startup and operation, thereby reducing its service life.

Anthropomorphic modular gripper finger actuated by antagonistic wire and shape-memory alloy (SMA) springs

Abstract. The traditional underactuated grippers can only passively adapt to the contour of the object, and the passive contact process may lead to the object slipping, affecting the stability of the grasping process. In this paper, an anthropomorphic modular gripper finger actuated by antagonistic wire and shape-memory alloy (SMA) springs, which can actively control the grasping morphology according to the characteristics of the objects to be grasped, is proposed. The wire drive simulates the flexor muscle, and the SMA and reset springs simulate the extensor muscles of the finger, which antagonistically control the grasping morphology of the finger. It is more in line with the grasping characteristics of the human hand. According to the moment equilibrium principle of the finger joints, the deformation model of the gripper is established, the influence of the wire tension and the equivalent stiffness of the finger joints on the grasping morphology is analyzed, and the theoretical joint angle results are verified by the Adams simulation; finally, the experimental system of the gripper is constructed, and the verification of the deformation morphology of the single finger and the gripper's enveloping–grasping experiments is completed. The results show that according to the contour size of the object, by actively controlling the wire force of the gripper and the equivalent stiffness of the interphalangeal joints, the enveloping–grasping action of different objects can be completed and the stable grasping of objects of different shapes and sizes can be realized.

Determination of hydrodynamic coefficients for open-frame ROVs through free oscillation tests in 1-DOF

ABSTRACT This study introduces an economical experimental approach for measuring the hydrodynamic inertia ( C M ) and drag ( C D ) coefficients of an open-frame ROV to support the stock assessment of scallops in the North Sea of Peru. A 1:3 scale ROV model was tested, suspended on springs, and set to oscillate freely in still water. The multiple spring groups provide equivalent stiffness, initial displacement, and natural frequencies for different cases. Three damping models—linear, quadratic, and linear-plus-quadratic—were applied to describe the motion equations, with the linear plus-quadratic model best fitting the experimental data. The coefficients and were analyzed against Reynolds (Re) numbers from 0.2×10 5 and 0.6×10 5 and Keulegan Carpenter (KC) numbers from 0.5 to 2. A strong correlation was observed with previous forced oscillation tests on cylinders and irregular bodies; thus, this methodology can be used to determine the hydrodynamic coefficients of ROVs.

Ship-shaped vessel hydroelastic numerically supported analysis in a narrow ultra-reduced model tank with full scale extrapolation

Although the rigid body hypothesis is broadly used when studying floating bodies dynamics, it is known that a ship-shaped vessel will have hydroelastic responses. Considering a conventional closed main deck hull in which the ship's length is considerably greater than its breadth, it is expected that the vertical bending moments can represent an important load that must be considered to guarantee structural integrity. Numerical models can be developed to assess the hydroelastic response, but the validation process is necessary. Model tests can be performed to validate the numerical model and require specific considerations to properly represent hydroelastic phenomena, such as having equivalent bending stiffness when compared to the full-scale body. Many experimental facilities that can be used to perform such experiments consist of narrow wave channels, in which the wall effect will influence the model's dynamics. This work implements a Tank Green Function (TGF) to a numerical model developed in Capytaine to represent the wall effect on the body's response. The numerical results were then compared to experimental data from tests in a narrow wave channel and good adherence was found. The validated numerical model can then be used to simulate open-water conditions, so the results can be extrapolated to full scale without the need to perform model tests in an ocean tank in which the wall effect would not be relevant.

Liquefaction evaluation on sand-like gravelly soil deposits based on field Vs measurements during the 2008 Wenchuan earthquake

During the 2008 Wenchuan earthquake, extensive liquefaction of sand-like gravelly soil deposits was observed over an area of about 500 × 200 km2. Since gravel content significantly affects the stiffness and liquefaction resistance of gravelly soils, it has become an ongoing challenge for engineers to reliably and cost-effectively assess the liquefaction resistance of such soil deposits with different gravel contents. To this end, the procedures for consistently assessing the liquefaction resistance of sand-like gravelly soils were first put forward based on the previously proposed improved CRR-Vs1 characterization model for binary mixtures, which converts the liquefaction evaluation of sand-like gravelly soils into the assessment of liquefaction resistance of the base sand matrix with an equivalent stiffness. Then, in-situ gravelly soils sampled from the earthquake-impacted area were tested to parameterize the proposed characterization model. Lastly, liquefaction case histories of gravelly soils compiled during the 2008 Wenchuan earthquake were recompiled and restudied to validate the performance of the proposed characterization model. Typical liquefaction case history studies show that the proposed characterization model successfully predicts the severe liquefaction hazard at the Banqiao school site and the marginal liquefaction phenomenon at the Jiangyou thermal power plant site. Comparisons between the proposed characterization model and the 54 recompiled liquefaction case history datasets demonstrate that the proposed characterization model can accurately discriminate both the liquefied and non-liquefied case histories. These validation results in turn suggest that the proposed characterization model is highly feasible for engineering applications on a regional scale covering various gravel contents.

A novel mapping method for equivalent stiffness and equivalent damping of [formula omitted]-DOF series hydraulic robot

Impedance control is a commonly used approach for robots to interact with environments. At present, the impedance control is mostly implemented at the foot end, while the impedance control at the joint space offers faster response speed and is a more favorable option. However, due to the influence of installation position and moment arm of hydraulic drive unit (HDU), it is more complicated to establish the mapping relationship of equivalent stiffness and equivalent damping between the foot end and joint HDU. To address this challenge, this paper provides a general calculation expression of mapping matrices between the foot end and joint HDU, which also considers the influence of above nonlinear factors. Additionally, the accuracy of mapping matrices is verified through the impedance control, and the “finite difference method” (FDM) is used to enhance the accuracy of validation. Finally, the accuracy of mapping matrices is validated through the single leg of a 2-DOF series hydraulic robot.

Flexibility, malleability, and high mechanical strength phase change composite films for solar-thermal and electro-thermal energy storage

Phase change materials (PCMs) are widely used in a range of energy storage applications due to high latent heat absorption and release capacities during phase change processes. There is still a lot to be done to resolve the inherent leakage, stiffness problems, and poor solar-thermal and electrical-thermal conversion capacities of PCMs to functionalize them. Here, a novel solid-solid phase change material (IGPCM) is created using block copolymerization. The IGPCM has a tunable enthalpy (from 58.16 to 99.60 J g−1) by adjusting the molecular weight of the PEG. The obtained IGPCM10K has high toughness (479.1 MJ/m3), excellent bending and malleability. Since IGPCM10K suffers from poor thermal conductivity, photo responsiveness, and electro-thermal conversion, carbon nanotubes (CNT) can be added to our IGPCM10K in a simple way to improve these issues. The thermal conductivity of IGPCM10K-CNT-3 is improved by 55.6 % compared to IGPCM10K. The photothermal conversion efficiency is 84.9 % at 300 mW/cm2. The electrothermal conversion efficiency is 82.3 % at 12 A. The prepared flexible PCM composites have super toughness, high enthalpy, excellent thermal conductivity, and photo-thermal and electro-thermal conversion capabilities, which will show great potential in future applications.

Step-by-step time discrete Physics-Informed Neural Networks with application to a sustainability PDE model

The use of Artificial Neural Networks (ANNs) has spread massively in several research fields. Among the various applications, ANNs have been exploited for the solution of Partial Differential Equations (PDEs). In this context, the so-called Physics-Informed Neural Networks (PINNs) are considered, i.e. neural networks generally constructed in such a way as to compute a continuous approximation in time and space of the exact solution of a PDE.In this manuscript, we propose a new step-by-step approach that allows to define PINNs capable of providing numerical solutions of PDEs that are discrete in time and continuous in space. This is done by establishing connections between the network outputs and the numerical approximations computed by a classical one-stage method for stiff Initial Value Problems (IVPs). Links are also highlighted between the step-by-step PINNs derived here, and the time discrete models based on Runge–Kutta (RK) methods proposed so far in literature. To evaluate the efficiency of the new approach, we build such PINNs to solve a nonlinear diffusion-reaction PDE model describing the process of production of renewable energy through dye-sensitized solar cells. The numerical experiments show that not only the new step-by-step PINNs are able to well reproduce the model solution, but also highlight that the proposed approach can constitute an improvement over existing continuous and time discrete models.

Experimental investigation of seismic performance of precast concrete shear walls with overlapping U-bar loop connections

This paper discusses the seismic performance of five reduced-scale shear walls, including one cast-in-place (CIP) concrete shear wall, two precast concrete (PC) shear walls with overlapping U-bar loop connections, and two PC shear walls with modified form-overlapping U-bar loop connections combined with extruded sleeve connections. A quasi-static test was conducted to evaluate the reliability of the overlapping U-bar loop connections and the modified form by comparing the corresponding mechanical parameters of PC specimens with those of the CIP specimen. Moreover, the differences in seismic performance between the CIP specimen and PC specimens with different connection methods were also analyzed in terms of damage process, hysteretic loops and skeleton curves, load carrying capacity, ductility, equivalent stiffness, and energy dissipation. The experimental findings indicated that the mechanical performances of PC specimens with the modified connection form outperformed those of PC specimens with pure overlapping U-bar loop connections, closely resembling the properties of cast-in-place specimens; the failure mode of PC specimens was consistent with that of the CIP specimen; the generation, distribution and development of cracks in PC specimens were also similar to those in the CIP specimen. Furthermore, although the load-bearing capacity and peak displacement of PC specimens were lower than those of the CIP specimen due to the failure of the post-casted concrete strength to meet the requirements, the ductility, equivalent stiffness, and energy dissipation of PC specimens with the modified connection form closely matched that of the CIP specimen.

Multi-step Residual Power Series Method for Solving Stiff Systems

In this paper, an efficient algorithm based on the residual power series method (RPSM) is presented to solve stiff systems of Caputo fractional order. We apply the RPSM on subintervals to get approximate solutions of these types of systems. The RPSM has advantages that it is suitable to solve linear and nonlinear systems and it gives high accurate results. Modifying this technique to multi-step RPSM considerably reduces the number of arithmetic operations and so reduces the time, especially when dealing with Stiff systems. Several numerical examples are given to show the efficiency, simplicity and the accuracy of the proposed method. Comparing classical RPSM with the new multi-step scheme shows that multi-step RPSM controls the convergence behaviour of the stiff systems. That is, the comparison reveals that MS-FRPSM reduces both absolute and residual errors. More iterations and a smaller step size lead to higher accuracy. Moreover, in MS-FRPSM, the intervals of convergence for the series solution will increase.

Optimization and synthesis on the dynamics performance of the tensioning and relaxing wearable system in a novel knee exoskeleton using co-simulation

Abstract In this paper, a novel tensioning and relaxing wearable system is introduced to improve the wearing comfort and load-bearing capabilities of knee exoskeletons. The research prototype of the novel system, which features a distinctive overrunning clutch drive, is presented. Through co-simulation with ANSYS, MATLAB, and SOLIDWORKS software, a comprehensive multi-objective optimization is performed to enhance the dynamics performance of the prototype. Firstly, the wearing contact stiffness of the prototype and the mechanical parameters of the relevant materials are simulated and fitted based on the principle of functional equivalence. And then, its equivalent nonlinear circumferential stiffness model is obtained. Secondly, to enhance the wearing comfort of the exoskeleton, a novel comprehensive performance evaluation index, termed wearing comfort, is introduced. The index considers multiple factors such as the duration of vibration transition, the acceleration encountered during wear, and the average pressure applied. Finally, through the utilization of this indicator, the system’s dynamics performance is optimized via multi-platform co-simulation, and the simulation results validate the effectiveness of the research method and the proposed wearable comfort index. The theoretical basis for the subsequent research on the effectiveness of prototype weight-bearing is provided.

Effects of Connecting Structures in Double-Hulled Water-Filled Cylindrical Shells on Shock Wave Propagation and the Structural Response to Underwater Explosion

In conventional double-hulled submarines, the connecting structures that facilitate the linkage between the two hulls are crucial for load transmission. This paper aims to elucidate the effect of these connecting structures on resistance to shock waves generated by underwater explosions. Firstly, a self-developed numerical solver is built for the one-dimensional water-filled elastically connected double-layer plate model. The shock wave propagation characteristics, shock response of structure, water cavitation, and impact loads transmitted through the gap water and the connecting structures are analyzed quantitatively. The results reveal that the majority of the shock impulse is transmitted by the gap water if the equivalent stiffness of the connecting structures is much less than that of the gap water. Then, a three-dimensional model of the double-hulled, water-filled cylindrical shell is constructed in Abaqus/Explicit, utilizing the acoustic-structural coupling methodology. The analysis focuses on the influence of the thickness and density distribution of the connecting structures on the system’s shock response. The results indicate that a densely arranged connecting structure results in a wavy deformation of the outer hull and a notable reduction in both the impact response and strain energy of the inner hull. When the stiffness of the densely arranged connecting structure is comparatively low, the internal energy and plastic energy of the inner hull are decreased by 16.5% and 24.1%, respectively. The findings of this research are useful for assessing shock resistance and for the design of connecting structures within conventional double-hulled submarines.

A Biomechanical Analysis of Instrumentation Constructs During Vertebral Column Resection: Stability When You Need It!

Biomechanical Testing. Investigate the optimal construct for stabilization of the spine during vertebral column resection (VCR). VCR is a powerful technique for achieving correction in severe cases of spinal deformity. However, this also creates an unstable spine which requires stable fixation to prevent iatrogenic neurologic injury. It is common practice to place a temporary unilateral rod configuration to achieve this stability during surgery but no study to date has investigated the optimal construct configuration. A unilateral VCR model representing an acute 50° kyphotic deformity with a standardized 30mm resection was created. Three conditions underwent testing: 1) Rod material and diameter, 2) rod configuration, and 3) number of fixation points. Six unique samples were tested in each group in both flexion-extension. Prior to testing a 10N preload and underwent cyclical testing in flexion/extension. System stiffness was calculated and compared across groups. Assessment of rod size and composition using a single screw construct (2 total screws) demonstrated that for Titanium (Ti) rods, increasing rod size significantly increased the construct stiffness (P=0.001). Although Cobalt-chromium (Co-Cr) rods where significantly stiffer than the corresponding sized Ti rods, there was no significant difference between rod diameters for Co-Cr (P=0.98). However, when tested using a dual screw (4 total screws) construct, these constructs were significantly stiffer than the corresponding single screw constructs (P<0.0001). Of the various rod configurations, the dual rod demonstrated the greatest stiffness (34.8±2.1N/mm; P<0.0001). Surgical construct stiffness during a VCR is multifactorial. Larger rod diameter, increased number of fixation points, stiffer rod material, and increased number of rods across the resection site increase the construct stiffness. With minimal points of fixation using Co-Cr rods, increasing rod diameter does not impart greater construct stiffness unless additional fixation points are included.

Sound transmission characteristics of piezoelectric metamaterial plates with resonant shunt circuits

Abstract In this study, a comprehensive investigation is conducted into the sound transmission characteristics of piezoelectric metamaterial plates, which feature five distinct resonant shunt circuits. To begin with, the intrinsic equations that pertain to piezoelectric materials, along with their equivalent models under external circuit conditions are established. Subsequently, the sound transmission loss of the plate and its corresponding equivalent bending stiffness model are constructed. Five resonant shunt circuits are employed, encompassing a basic resonant shunt circuit, one with series/parallel capacitance, and another with series/parallel negative capacitance. Ultimately, the influence of these diverse shunt circuits and their respective parameters on the sound insulation capabilities of piezoelectric metamaterial plates is comprehensively calculated and analyzed. Research results show that the inductance and resistance within the resonant shunt circuit influence the sound transmission characteristics exhibited by the piezoelectric metamaterial plate. Irrespective of whether the capacitance is configured in parallel or series within the resonant shunt circuit, the low-frequency sound transmission loss of the piezoelectric metamaterial plate experiences a notable modification. The effect of negative capacitances in the resonant shunt circuit on the sound transmission loss of the plate exhibits a contrasting pattern compared to the influence of the capacitances within the resonant shunt circuit on the sound transmission loss.

VENICE: A multi-scale operator-splitting algorithm for multi-physics simulations

Context. We present VENICE, an operator-splitting algorithm to integrate a numerical model on a hierarchy of timescales. Aims. VENICE allows a wide variety of different physical processes operating on different scales to be coupled on individual and adaptive time-steps. It therewith mediates the development of complex multi-scale and multi-physics simulation environments with a wide variety of independent components. Methods. The coupling between various physical models and scales is dynamic, and realised through (Strang) operators splitting using adaptive time-steps. Results. We demonstrate the functionality and performance of this algorithm using astrophysical models of a stellar cluster, first coupling gravitational dynamics and stellar evolution, then coupling internal gravitational dynamics with dynamics within a galactic background potential, and finally combining these models while also introducing dwarf galaxy-like perturbers. These tests show numerical convergence for decreasing coupling timescales, demonstrate how VENICE can improve the performance of a simulation by shortening coupling timescales when appropriate, and provide a case study of how VENICE can be used to gradually build up and tune a complex multi-physics model. Although the examples provided here couple dedicated numerical models, VENICE can also be used to efficiently solve systems of stiff differential equations.

A ninth-order first derivative method for numerical integration

In this paper, we present a ninth–order block hybrid method for the numerical solution of stiff and non–stiff systems of first–order differential equations. The method is based on an interpolation and collocation approach which results in a single continuous formulation; from which eight discrete schemes that make the block method were obtained. A convergence analysis of our method illustrated that it is A–stable, consistent, and convergent. We applied our method to some numerical examples which showed that the new method not only outperformed a second derivative method of order fourteen in the literature but also compared well with the exact solution.

Association between body shape index and arterial stiffness: results of the EVasCu study and a meta-analysis.

The aim of this study was to analyse the association between body shape index (ABSI) and arterial stiffness in healthy subjects using data from the EVasCu study. In addition, a meta-analysis was performed to compare the association between ABSI and central, peripheral and systemic arterial stiffness in the general population. The EVasCu study included 390 healthy subjects. ABSI was calculated from waist circumference, body mass index and height, and arterial stiffness was assessed with aortic pulse wave velocity (a-PWv) and cardio-ankle vascular index (CAVI). A meta-analysis of previous studies, including data from the EVasCu study, was performed to obtain pooled estimates of correlation coefficients (r) and their respective 95% confidence intervals (95% CIs) for the association between ABSI and central, peripheral and systemic arterial stiffness. In addition, pooled OR estimates and their 95% CIs were calculated. In the EVasCu study, the correlation coefficient estimate was 0.458 (p < 0.01) for the association of a-PWv and ABSI and 0.408 (p < 0.01) for the association of CAVI and ABSI. In the meta-analysis, the pooled correlation coefficient estimate was 0.22 (95% CIs: 0.16, 0.28) for central arterial stiffness and ABSI, 0.21 (95% CIs: 0.14, 0.28) for peripheral arterial stiffness and ABSI, and 0.28 (95% CI: 0.21, 0.3) for systemic arterial stiffness and ABSI. When pooled ORs were calculated, the pooled OR estimate was 2.12 (95% CIs: 1.68, 2.56) for central arterial stiffness and ABSI, 2.21 (95% CIs: 1.81, 2.60) for peripheral arterial stiffness and ABSI, and 2.99 (95% CIs: 2.14, 3.85) for systemic arterial stiffness and ABSI. Based on both the results obtained in the EVasCu study and the meta-analysis, there is a positive association between ABSI and arterial stiffness, both in healthy subjects and in participants with comorbidities. For each unit of cm/kg/m²/m increase in ABSI, the risk of arterial stiffness increased by 112% for central arterial stiffness, 121% for peripheral arterial stiffness, and 199% for systemic arterial stiffness. However, further research is needed in this field of knowledge.

Vibration Suppression and Energy Harvesting of Nonlinear Energy Sink-Based Piezoelectric System with Combined Damping and Bistability Properties for Nonlinear Oscillator

Nonlinear energy sink (NES) as a new type of dynamic absorber has received widespread attention due to its broadband vibration suppression capability, but it has a certain requirement of energy triggering threshold. In this work, a bistable NES-based piezoelectric system with combined damping (BCPNES) and low threshold requirement is proposed. Electromechanical-coupled equations for the nonlinear oscillator coupled with BCPNES (NO-BCPNES) are established. The vibration suppression and vibration energy harvesting performance for the coupled system are investigated numerically and analytically. The frequency–energy plots of the conservative system are investigated using the complex-variable averaging method and the electromechanical decoupling method. The influence of circuit parameters on the target energy transfer threshold and harvested energy is discussed through the equivalent stiffness and damping of the circuit. The vibration suppression performance and the target energy transfer characteristics are analyzed in terms of the time–history response, the time–frequency response and the slowly varying dynamic flow, respectively. The results show that the electromechanical coupling coefficient affects the skeleton curve of frequency–energy plots in the form of equivalent stiffness. The NO-BCPNES system exhibits higher energy dissipation performance and better targeted energy transfer form under various excitations. From the phase perspective, NES-based piezoelectric system achieves vibration suppression of the main structure through the phase locking phenomenon. The mechanism of the influence of piezoelectric device parameters on the energy harvesting performance of the systems is clarified.