Optimal Stiffness Research Articles

Stiffness Optimization of Squirrel Cage in Aircraft Engines

squirrel cage is a component used in engine shafts to make the shaft stiffer and able to withstand high cycle fatigue loads continuously for a long time. A squirrel cage can be of many shapes and sizes. The critical speed and the stresses acting on the shaft play a key role in determining the performance of shafts in engines. The squirrel cage in the shaft absorbs stress and extends shaft life. This paper deals with the structural design and analysis of the squirrel cage of an aircraft engine. The design of the squirrel cage was done on SolidWorks, and analysis was carried out on the Ansys workbench. To meet the strength and stiffness, the squirrel cage was optimized by introducing slots in it. Stress analysis of the bearings has been carried out for axial and radial loads from 1 to 20 kg. The radial load is applied to individual bearings, and then the axial load is applied to only one bearing. Then results are plotted into curves, and a slope is obtained based on deformations obtained. The stiffness value is noted, and the same procedure is performed for an optimized slotted squirrel cage. These values are compared, and then the squirrel is proved to be weight optimized and has improved stiffness.

Experimental Evaluation of an Innovative Connection for the Reinforcement of Existing Infilled RC Buildings

The retrofitting of existing reinforced concrete (RC) buildings with cross-laminated timber (CLT) panels presents a promising approach for enhancing seismic performance and overall structural resilience. However, effective integration of CLT with existing RC structures poses significant challenges, particularly concerning the design of connections between CLT panels and the RC structure. This paper introduces a novel connection that addresses these challenges by focusing on both structural and architectural considerations. Structurally, the connection is engineered to provide optimal stiffness, strength, and deformation capacity, ensuring robust performance under seismic and dynamic loads. Architecturally, the design incorporates a predefined weak component that facilitates easy access and rapid replacement of damaged parts, thereby reducing downtime and maintenance efforts. The proposed connection was evaluated through a series of monotonic and cyclic loading tests, demonstrating its structural efficiency and reliability. The results indicate that the new connection system not only meets the necessary structural requirements but also offers practical benefits for maintenance and repair, contributing to the overall sustainability and resilience of retrofitted RC buildings. This innovative approach represents a significant advancement in the field of structural retrofitting, providing a viable solution for integrating CLT panels into existing RC frameworks.

A Study of Sliding Base Isolation System: A Review

Seismic isolation systems are crucial for protecting structures by minimizing the transmission of acceleration during seismic events, and among the various types, the resilient sliding system, which combines restoring springs and sliders, is highly effective in mitigating seismic impacts. This system controls structural responses by balancing stiffness and friction, ensuring safety while maintaining the functionality of buildings. However, optimizing the design of this system requires carefully selecting combinations of stiffness and the coefficient of friction to achieve low acceleration levels, while simultaneously managing the relative displacement within the isolation system to protect both the structure and its occupants. Excessive displacement may compromise the integrity of the isolation system or cause damage to the structure it is meant to protect. The challenge lies in finding the optimal friction and stiffness levels that provide sufficient energy dissipation and restore forces without allowing displacement to exceed acceptable thresholds. Studies show that restoring forces generated by springs help limit excessive displacements, while sliders dissipate seismic energy, and adjustments in these parameters must account for variations in ground motion intensity and frequency. Thus, a balance between flexibility and resistance is essential in sliding systems to ensure maximum structural safety and occupant protection during earthquakes. This paper reviews different sliding isolation systems which fulfils the requirements of controlling the earthquake and functioning accordingly. It include systems such as PF, FPS, VFPI , CFPI,VFPS,PFPE, VCFPS,VFFPI etc.

Seismic analysis and performance of semi-active spring for base-isolated structures

The present study investigates the performance of a semi-active spring (SAS) in the mitigation of the seismic response of base-isolated structures. Initially, under stationary filtered white-noise earthquake excitation, the response of the multi-floor flexible base-isolated structure with SAS is examined to observe the response control effects. The equivalent linearization technique is used to obtain the stochastic response, as the force-deformation behaviour of SAS is non-linear. The performance of SAS in terms of added stiffness, damping, and response mitigation to the isolated structure is also investigated. It is found that the SAS controls the isolator displacement effectively. Furthermore, it was noted that there is an optimum stiffness value for the SAS devices for a particular system and excitation, at which point the RMS top floor acceleration reaches a minimum value. Next, approximate formulas are proposed for the RMS isolator displacement, the top floor absolute acceleration, and the optimum stiffness of the SAS. It is observed that these formulas accurately predict the expected response and can be applied to the initial design of base-isolated structures using SAS. Finally, using the non-linear model of the SAS, the seismic response of flexible base-isolated structures is determined for actual near-fault earthquakes, considering different values of the isolation periods and stiffness of the SAS device. The SAS was effective in controlling the isolator displacement under near-fault motions. The trends of the results of isolated structures with SAS devices under near-fault earthquake motions were also in good agreement with those under stochastic excitation.

Failure mechanism and crashworthiness optimization of variable stiffness nested origami crash box

In recent years, the study of the crashworthiness of lightweight and efficient thin-walled energy-absorbing structures has received increasing attention. In this work, 3D printing technology was adopted to create a nested origami crash box with stiffness variation, which was made of short carbon fiber reinforced nylon material. The structure effectively inhibits the development of failure behavior of short carbon fiber-reinforced nylon origami crash box due to material brittleness. The quasi-static compression experiment results indicate that compared to origami crash box, nested origami crash box improves by 40% in specific energy absorption and 50% in crash force efficiency, while the initial peak crushing force remains unchanged. The effects of three key geometrical parameters, namely dihedral angle, distance between tubes, and height difference on the damage mechanism of the nested origami crash box are discussed in detail using the finite element method, and the response surface model combined with the non-dominated sorting genetic algorithm II is used for multi-objective optimization. In this work, the concepts of origami theory and nested systems are integrated for the first time, aiming to achieve a stable and efficient energy-absorbing deformation mode by precisely modulating the stress transfer path of the structure and its stiffness. This work provides new ideas for the design and fabrication of novel lightweight energy-absorption boxes.

Coordinated base disturbance and Cartesian stiffness optimization of a cable-driven redundant space robot

Coordinated base disturbance and Cartesian stiffness optimization of a cable-driven redundant space robot

The influence of elastic pads deterioration in the fastening system on the dynamic characteristics of the vehicle-turnout system

The deterioration of the elastic pads in the fastening system in high-speed turnout areas increases longitudinal stiffness irregularities along the track, posing potential hazards to wheel-rail impact and train running safety. This paper takes the frog area of No. 18 turnout as an example and constructs a vehicle-turnout rigid-flexible coupling model considering the detailed structure of the fastener elastic pads. By increasing the stiffness of the rubber pad under the tie plate to simulate the deterioration of the elastic pads in the turnout area, the study investigates the effects of deterioration location, degree, and number on the dynamic characteristics of the vehicle-turnout system, providing theoretical guidance for stiffness optimization and maintenance of the turnout area. The results indicate that: 1) the deterioration of the elastic pads significantly affects wheel-rail interaction and safety indicators, while having a minor effect on vehicle running stability; 2) the 95th sleeper (point rail with a top width of 60 mm) is identified as the most critical location for the deterioration of elastic pads; 3) comprehensively considering, the stiffness replacement limit for elastic pads in ballastless turnout areas can be set to twice the design stiffness, which is 50 kN/mm.

Matrix Stiffness of GelMA Hydrogels Regulates Lymphatic Endothelial Cells toward Enhanced Lymphangiogenesis.

Lymphatic vessel regeneration is crucial for various tissue engineering strategies, particularly in resolving inflammation and restoring tissue homeostasis. In our study, we focused on investigating how hydrogel matrix stiffness influences lymphatic endothelial cells (LECs) in promoting lymphatic vessel regeneration. Gelatin methacrylate (GelMA) was chosen as our biomaterial due to its versatility in tissue engineering and biofabrication. We fabricated GelMA hydrogels at concentrations of 5, 7.5, and 15% (w/v) with corresponding Young's modulus values of 1.55 kPa (soft matrix), 12.02 kPa (medium matrix), and 48.50 kPa (stiff matrix). Among these, the 7.5% GelMA hydrogel exhibited optimal stiffness for promoting lymphangiogenesis. LECs seeded either on the hydrogel surface or within spontaneously formed a more stable lymphatic capillary network compared with other GelMA formulations. Furthermore, we investigated the enhancement of lymphangiogenesis by incorporating VEGF-C into the GelMA hydrogel, leveraging the synergistic effects of mechanical and chemical cues. Our results underscored the critical role of FAK-phosphorylation in this process; treatment with an FAK-specific inhibitor prevented the formation of tube-like structures by LECs and attenuated the expression of lymphatic markers. Overall, our findings highlight how the mechanical and chemical cues provided by GelMA hydrogels can effectively regulate LEC behavior toward enhanced lymphangiogenesis via the integrin/FAK mechanotransduction pathway. This study proposes a promising strategy for developing hydrogel-based scaffolds or bioinks tailored to promote lymphatic vessel regeneration in therapeutic applications.

H∞ optimum design and nonlinear seismic performance assessment of tuned-mass-damper-inerter (TMDI) supported by an auxiliary structure

Tuned Mass Damper Inerter (TMDI) and its simplified form, Tuned Inerter Damper (TID), are highly effective in mitigating seismic responses in buildings, particularly when rigidly connected to the ground. However, practical constraints often limit the feasibility of this ideal setup. This study introduces a novel configuration: the AS-type TMDI, which connects the TMDI to an auxiliary structure (AS) adjacent to the main building to simulate a ground connection. To design the AS-type TMDI, this research builds upon insights from studies on TMDIs in adjacent buildings and develops an analogous 3-DOF model representing the TMDI-linked adjacent-building system. This model incorporates two buildings of different heights, allowing the TMDI to be connected at any floor level. Utilizing fixed-point theory, the study derives an analytical solution for the optimal design of TMDI systems within this novel configuration. Additionally, a method is introduced to determine the optimal stiffness and design procedure for the AS itself. The performance of the proposed AS-type TMDI is evaluated through comprehensive nonlinear seismic analysis of a benchmark nine-story steel frame structure, accounting for material and geometric nonlinearities. Results demonstrate that the AS-type TMDI performs comparably to a virtually grounded TMDI in effectively reducing the seismic responses. Furthermore, this innovative configuration outperforms both a conventional retrofitting technique, where the building is rigidly connected to the AS, and a system where a viscous damper alone connects the main building to the AS. This highlights the AS-type TMDI's potential to significantly improve the building’s seismic performance.

Prediction of the optimal ankle foot orthosis stiffness using peak ankle moment when walking on shoes-only in neuromuscular diseases

Prediction of the optimal ankle foot orthosis stiffness using peak ankle moment when walking on shoes-only in neuromuscular diseases

Effects of stiffness-altered sport compression garments on lower-limb biomechanics in cutting maneuvers

Athletes commonly use compression garments (CGs) for perceived effectiveness in preventing injury occurrence. However, limited evidence is available on whether lower-limb CGs reduce the risk of injury. This study aimed at (1) evaluating the effects of CGs on mitigating the risk factors of cutting-related knee injuries; (2) identifying undesirable side-effects of CGs on other joints and cutting performance; and (3) identifying possible interactions between sex and condition. 62 healthy adults performed pre-planned 90˚ cutting tasks under four conditions: control, knee sleeves, placebo leggings and stiffness-altered leggings. Joint angle at initial contact, range of motion, moments, and ground reaction force were measured. A mixed two-way (sex*condition) ANOVA was performed, followed by post-hoc comparisons and subset analyses for sexes. Results showed that the leggings restricted hip sagittal (45.4 ± 1.3 vs. control 50.0 ± 1.3˚, p = 0.001) and rotational (16.8 ± 0.8 vs. control 22.5 ± 1.1˚, p < 0.001) motion. At initial contact, the stiffness-altered leggings reduced knee valgus (0.4 ± 0.8 vs. control −2.1 ± 0.8˚, p = 0.031). However, the altered alignment of lower-limb joints did not reduce multiplanar knee joint moments (p > 0.05). CGs were not effective protective equipment yet. There was no significant difference between knee sleeves and control, nor between leggings conditions (p > 0.05). Force plate measurements, such as increased rate of force development (stiffness-altered 42.6 ± 1.1 & placebo 42.9 ± 1.1 vs. control 39.9 ± 1.0 BW/s, p < 0.028), implied the possibility of performance enhancement through CGs. While further investigations on the optimal compression and stiffness alterations are warranted, athletes are recommended to be aware of the discrepancies between the claimed and actual biomechanical effects of CGs.

Stiffness optimization design of wheeled-legged rover integrating active and passive compliance capabilities

Compliance capability is one of the most important properties of suspension systems for rough-terrain robots. This imposes specific requirements on system stiffness design, which directly determines the platform's performance in response to external stimuli. To address the challenge of stiffness optimization design in active and passive compliant systems, this paper proposes a novel and practical method for optimizing stiffness for a terrain-adaptive wheel-legged rover. Firstly, the kinematic model of this multi-degree-of-freedom platform is established. Secondly, the deformation capability coefficient, load capacity coefficient, energy efficiency coefficient, and dynamic stability coefficient are derived as performance indices to assess the behavior of the system. By establishing the relationship between joint configuration variation and system stiffness, stiffness parameters could be evaluated through these performance indices. Ultimately, the global optimum stiffness parameters are selected from the refined intersection of the individual performance optimal domains. Thirdly, the optimum parameters are calculated and applicability verified numerically. The designed parameters are verified experimentally on a wheeled-legged rover. The experimental results demonstrate that the proposed algorithm can find the parameter combination that achieves optimal system performance, thereby enhancing the system's terrain adaptability.

Cyclic response of floating geosynthetic-encased steel slag columns in soft clay

Geosynthetic-encased stone column (GESC) technology for strengthening soft clay offers significant advantages in terms of cost-effectiveness, environmental sustainability, and engineering applicability. It is widely applied in treating soft foundations for railways, bridges, and embankments. This study evaluates the cyclic response of the geosynthetic-encased steel slag column (GESSC) composite foundation employing three-dimensional nonlinear finite element analysis. A numerical study is conducted to assess the cyclic response of floating GESSC considering the influence of key design variables, including cyclic load amplitude, loading frequency, geosynthetic encasement stiffness, and length-to-diameter ratio. Results show that both cyclic load amplitude and frequency affect the cumulative settlement and excess pore pressure within the GESSC foundation. Within specified limits, increasing the encasement stiffness and column length can significantly improve the GESSC load-bearing characteristics. The parametric study suggests an optimal geosynthetic encasement stiffness for the field prototype columns within the range of 4480–5760 kN/m and a critical steel slag column length of 10 times the column diameter.

Transient mode-III problem of the elastic matrix with a line inclusion

The method of pull-out test has been used to identify the mechanical performance of hybrid and fiber-reinforced composite materials. This paper investigates the elastic phase preceding the pull-out of a rigid line inclusion from the polymer matrix with fixed top and bottom surfaces. The mode-III problem is investigated such that the pull-out force is applied from the out-of-plane direction and it can be either transient or static. By applying the singular integral equation technique, the semi-analytical elastic field expressions are obtained. Under the static pull-out force, the stress intensity factor (SIF) near the inclusion tip shows a monotonic increase as the length and height of the matrix increase, whereas for the transient pull-out force, the SIF displays an initial increasing and followed by a decline. The maximum SIF is obtained for (1) the matrix length is 2 to 2.5 times of the inclusion length, and (2) the matrix height is 1 to 2 times of the inclusion length. Moreover, this paper provides a solution approach that incorporates the elasticity of the inclusion, showing that there is an optimal shear stiffness that minimizes the stress singularity of system. The conclusions of this study hold significance for the design and performance evaluation of fiber-reinforced composite materials.

Multifunctional Aspects of Mechanical and Electromechanical Properties of Composites Based on Silicone Rubber for Piezoelectric Energy Harvesting Systems.

Energy harvesting systems fabricated from rubber composite materials are promising due to their ability to produce green energy with no environmental pollution. Thus, the present work investigated energy harvesting through piezoelectricity using rubber composites. These composites were fabricated by mixing titanium carbide (TiC) and molybdenum disulfide (MoS2) as reinforcing and electrically conductive fillers into a silicone rubber matrix. Excellent mechanical and electromechanical properties were produced by these composites. For example, the compressive modulus was 1.55 ± 0.08 MPa (control) and increased to 1.95 ± 0.07 MPa (6 phr or per hundred parts of rubber of TiC) and 2.02 ± 0.09 MPa (6 phr of MoS2). Similarly, the stretchability was 133 ± 7% (control) and increased to 153 ± 9% (6 phr of TiC) and 165 ± 12% (6 phr of MoS2). The reinforcing efficiency (R.E.) and reinforcing factor (R.F.) were also determined theoretically. These results agree well with those of the mechanical property tests and thus validate the experimental work. Finally, the electromechanical tests showed that at 30% strain, the output voltage was 3.5 mV (6 phr of TiC) and 6.7 mV (6 phr of MoS2). Overall, the results show that TiC and MoS2 added to silicone rubber lead to robust and versatile composite materials. These composite materials can be useful in achieving higher energy generation, high stretchability, and optimum stiffness and are in line with existing theoretical models.

Application of the artificial neural network and enhanced particle swarm optimization to model updating of structures

AbstractAn efficient and accurate two-stage approach, based on the artificial neural network (ANN) and an enhanced particle swarm optimization (EPSO) approach for model updating of structures using incomplete measurements, is proposed in this study. The first stage, preliminary model updating, employs the ANN to quickly learn the mapping relationship between the natural frequencies and stiffness of the structure using a few training, validation, and testing instances. The inputs and outputs of the ANN are the natural frequencies and stiffness of the structure, respectively. The ANN’s training, validation, and testing instances are extracted through Latin hypercube sampling. The ANN-predicted stiffness provides an excellent basis for determining and reducing the search space of the optimal stiffness in the second stage. The second stage, detailed model updating, searches for the optimal stiffness of the structure by using the EPSO approach. The EPSO approach improves particle swarm optimization (PSO) by employing an elite crossover strategy to avoid trapping in the local optimum and premature convergence. The feasibility and effectiveness of the proposed two-stage approach for stiffness updating of shear building structures using incomplete measurements are demonstrated by numerical and experimental examples. The results present that the proposed two-stage approach improves the computational efficiency and solution quality of the GA (Genetic Algorithm) and PSO for stiffness updating of shear building structures.

Application of Perturbation Method to Analytical H2 Optimization for a Damped Structure with Inerter-Based Control

Inherent damping exists in all real engineering systems and it affects the dynamic behavior of the structures in vibration reduction. However, it is generally neglected in existing analytical H2 optimization for inerter-based vibration control. Hence, an analytical H2 optimization of a tuned inerter damper (TID) based on the perturbation method is presented to control the vibration of a damped structure subjected to stochastic acceleration ground excitations. Since relative displacement and velocity are crucial to structural damage and absolute acceleration is related to vibration comfort, three sets of closed-form solutions for the optimal stiffness ratio and damping ratio are derived to suppress the corresponding responses. The expressions of these optimal parameters are functions of the inherent damping and inerter-mass ratio. The accuracy of these analytical solutions is demonstrated by comparison with the results provided by the numerical optimization procedure. The relevant parameters affecting the vibration control performance and the robustness of the TID in a damped structure are analyzed in frequency domain. Finally, time–history response and energy dissipation of TID are also explored by numerical examples under real and artificial seismic waves. The results highlight that more than 10% reduction ratio of the mean square value can be further achieved for a structure with a low inherent damping ratio ([Formula: see text]) if the present multi-order perturbation solutions are used for optimization, instead of the existing method which neglects the inherent damping. This superiority of the present perturbation method will become more prominent with the increase of the inherent damping ratio. Therefore, the present perturbation method has a great significance for designing a TID to achieve the best control performance.

Fabrication of chitin-fibrin hydrogels to construct the 3D artificial extracellular matrix scaffold for vascular regeneration and cardiac tissue engineering.

As the cornerstone of tissue engineering and regeneration medicine research, developing a cost-effective and bionic extracellular matrix (ECM) that can precisely modulate cellular behavior and form functional tissue remains challenging. An artificial ECM combining polysaccharides and fibrillar proteins to mimic the structure and composition of natural ECM provides a promising solution for cardiac tissue regeneration. In this study, we developed a bionic hydrogel scaffold by combining a quaternized β-chitin derivative (QC) and fibrin-matrigel (FM) in different ratios to mimic a natural ECM. We evaluated the stiffness of those composite hydrogels with different mixing ratios and their effects on the growth of human umbilical vein endothelial cells (HUVECs). The optimal hydrogels, QCFM1 hydrogels were further applied to load HUVECs into nude mice for in vivo angiogenesis. Besides, we encapsulated human pluripotent stem cell-derived cardiomyocytes (hPSC-CMs) into QCFM hydrogels and employed 3D bioprinting to achieve batch fabrication of human-engineered heart tissue (hEHT). Finally, the myocardial structure and electrophysiological function of hEHT were evaluated by immunofluorescence and optical mapping. Designed artificial ECM has a tunable modulus (220-1380 Pa), which determines the different cellular behavior of HUVECs when encapsulated in these. QCFM1 composite hydrogels with optimal stiffness (800 Pa) and porous architecture were finally identified, which could adapt for in vitro cell spreading and in vivo angiogenesis of HUVECs. Moreover, QCFM1 hydrogels were applied in 3D bioprinting successfully to achieve batch fabrication of both ring-shaped and patch-shaped hEHT. These QCFM1 hydrogels-based hEHTs possess organized sarcomeres and advanced function characteristics comparable to reported hEHTs. The chitin-derived hydrogels are first used for cardiac tissue engineering and achieve the batch fabrication of functionalized artificial myocardium. Specifically, these novel QCFM1 hydrogels provided a reliable and economical choice serving as ideal ECM for application in tissue engineering and regeneration medicine.

Finite Element Analysis and Optimization of the Rotational Stiffness of Semi-Rigid Base Connection under Simultaneous Moment and Tension

The base connection is flexible, not fully pinned/fixed, implying a nonlinear moment–rotation relationship. This deviates from a linear response, where rotation is not directly proportional to the applied moment. Numerical investigations using the commercial software ABAQUS were conducted to analyze the steel base plate connections. The finite element (FE) models were verified against previous experimental results. Moreover, numerical findings of a comprehensive parametric investigation were conducted. The studied connections were examined with different configurations, including variations in the diameter, spacing, and number of the anchor bolts; the thickness of the base plate; and the applied axial force. The current study aims to use numerical results combined with the whale optimization algorithm (WOA) and classical genetic algorithm (GA) to derive a formulation for the moment–rotation (M-θr) relationship. The distinctive aspect of this formulation is that it aims to simulate the nonlinear rotational behavior exhibited by flexible base connections under combined moment and tension loads, while also considering various parameters such as bolt number/diameter and plate thickness. The findings indicate that the WOA is capable of obtaining an optimal equation for accurately simulating the M-Ɵr relationship. This underscores the ability of the WOA to effectively address the complexity of the problem and provide a reliable equation for predicting the rotational behavior of such connections. Consequently, the WOA method can be utilized to calculate the rotational stiffness at H/150, offering valuable support for engineering design processes.

Sloshing reduction with passive spring–mass baffles in partially filled containers

The potential for sloshing reduction of passive, moving baffles with translational motion constrained by springs is investigated numerically in partially filled containers. Simulations are based on the level-set formulation, considering water as the liquid under study and a baffle made of aluminum; this selection allows for direct validation of the model against experimental and analytical data. Depending on the filling ratio V∈(0,1), which simply measures the volume of liquid relative to the total container size, one can find an optimal spring stiffness K(V) that minimizes the kinetic energy and decay time of the sloshing response when subjected to a pulse-like acceleration. Results show that moving baffles significantly reduce sloshing compared to their fixed counterparts, with decreases up to 84.6% in decay time, τd. Frequency analyses for different V reveal one or two resonances in the range of 0.1–1.5Hz whose amplitudes are directly influenced (lowered) by K, analogous to the behavior of Tuned Mass Dampers. For potential applications, the selection of K should look for an adequate sloshing response over the entire range of V, and account for both quasi-static and harmonic excitation, conveniently weighted in accord with the expected operational loads.