Load Distribution Research Articles

Effects of structural parameters on the load distribution unevenness in CFRP hybrid bonded‐bolted joint

AbstractCarbon Fiber Reinforced Polymer (CFRP) Hybrid Bonded/Bolted (HBB) joint structures are distinguished for their superior jointing performance among current mechanical joint systems, making them a favored option for mechanical joints. These structures are characterized by many structural parameters, with the relationship between these parameters and jointing performance being notably complex. Additionally, the laminate's brittleness and the uneven distribution of bolt loads in multi‐bolt joint structures impair the overall jointing performance. To investigate the impact of structural parameters on the uneven load distribution within CFRP HBB joint structures and improve their jointing performance, a finite element analysis (FEA) model grounded in 3D Hashin failure criterion is developed. Validation of the model with experimental data confirmed the uneven load distribution among bolts in multi‐bolt joints. The study elucidated the influence of changes in structural parameters (overlap length, bolt‐hole spacing, and clearance fit) on the uneven load distribution and the connection strength of CFRP HBB joint structures. A negative correlation is found between the unevenness of load distribution and connection strength, offering insights for enhancing and researching connection strength in CFRP HBB joint structures.Highlights Developed a FEA model based on the 3D Hashin failure criterion for CFRP Bonded‐Bolted joints. Identified key factors affecting HBB joint load distribution and jointing performance. Evaluated the impact of overlap length, bolt‐hole spacing, and clearance fit on CFRP joints. Suggested design optimizations for enhancing the performance of HBB joints.

How do young soccer players train? A 5-year analysis of weekly microcycle training load characteristics in an elite youth academy

This study aimed to describe the distribution of training load (session rating of perceived exertion (sRPE), duration, and sRPE-training load) across weekly microcycles of an elite youth academy and assess the differences between four different age groups (U15-U16-U17-U19). Training load variables were recorded during in-season training weeks over 5 competitive seasons (from 2014–15 to 2018–19, evaluating new squads for each age group each season) for a total of 456 player observations. Mixed models assessed the variability of the three load variables across the different training days of a weekly microcycle and between the four different age groups. Estimated marginal means, 95% confidence intervals (CI), and effect sizes (d) were calculated for each training day of the microcycle. The main findings were significant differences in the training load variables three and four days before the next Match Day (i.e., MD-3 and MD-4, respectively), with U15 recording lower sRPE (−2.0 AU, d = 0.43–0.72) and U19 a lower duration (−35 min, d < -1.10). All age groups reduced sRPE-training load in the two days before a match, mainly due to a decrease in training duration (−160 AU & −17 min respectively). Match days provided the highest training loads within the weekly microcycle, with moderate-to-large differences between the four age groups (d = 0.77, 1.16 and 1.38 for U15 vs U16-U17-U19 respectively). The low variability in sRPE values in the three central sessions of a weekly microcycle indicates that training duration is an important factor to control when aiming to manipulate within-week training loads in elite youth soccer players.

An Effective Method for Identifying Uneven Load Distribution on the Tooth Faces of Misaligned Wide-Faced Helical Gear Pairs

An Effective Method for Identifying Uneven Load Distribution on the Tooth Faces of Misaligned Wide-Faced Helical Gear Pairs

Biomechanical impact of progressive meniscal extrusion on the knee joint: a finite element analysis.

While measuring meniscal extrusion quantitatively is an early risk factor for knee osteoarthritis (KOA), the biomechanics involved in this process are not well understood. This study aimed to investigate the effects of varying degrees of medial and lateral meniscal extrusion and their material softening on knee osteoarthritis progression. Finite element analysis (FEA) was utilized to simulate varying degrees of meniscal extrusion (1-5mm) in 72 knee joint models, representing progressive meniscal degeneration and material softening due to injury. Changes in von Mises stress of the cartilage and menisci and the load distribution on the tibial plateau's meniscus and cartilage were studied under balanced standing posture in both healthy and injured knees, and statistical analysis was performed using Spearman correlation. Compared to healthy knees, peak stress in medial compartment tissues increased by over 40% with 4mm of medial meniscus extrusion, and in lateral compartment tissues with 2mm of lateral meniscus extrusion. Meniscus extrusion reduced the contact load between the meniscus and femoral cartilage but increased it between the tibial and femoral cartilages, with a maximum increase up to fivefold. Spearman correlation analysis indicated that meniscal extrusion significantly affected peak stress and contact loads in the respective knee compartment (p < 0.001), with a lesser impact on the opposite compartment. Notably, medial meniscal extrusion also significantly increased peak stress in the lateral tibial cartilage (p < 0.05). The quantitative analysis revealed that meniscal extrusion significantly affected the biomechanics of soft tissues within the same compartment, with limited impact on the opposite side. Specifically, Medial extrusion beyond 4mm significantly affected the biomechanics of the medial compartment, while lateral extrusion over 2mm had a similar impact on the lateral compartment. Meniscal softening, without altering joint contact characteristics, primarily affected the biomechanics of the meniscus itself, with minimal impact on other soft tissues.

The Effect of a Single Temporomandibular Joint Soft Tissue Therapy on Cervical Spine Mobility, Temporomandibular Joint Mobility, Foot Load Distribution, and Body Balance in Women with Myofascial Pain in the Temporomandibular Joint Area—A Randomized Controlled Trial

In contemporary times, a significant portion of the population experiences symptoms of temporomandibular joint (TMJ) dysfunction. The objective of this study was to evaluate the effects of a single-session TMJ soft tissue therapy on the TMJ and cervical spine mobility as well as on body balance and the foot load distribution. This study was a parallel-group, randomized, controlled trial with a 1:1 allocation ratio. Fifty women aged 20–30 years diagnosed with myofascial pain in the TMJ area were included in the study and divided into two groups. The experimental group received TMJ soft tissue therapy. The following research tools were used: a Hogetex electronic caliper, a CROM Deluxe, and a FreeMed Base pedobarographic platform. In the experimental group, an increase in mobility within all assessed jaw and cervical spine movements was observed. This change was statistically significant (p &lt; 0.05) for lateral movement to the left, abduction, and protrusion of the jaw (an increase of 10.32%, 7.07%, and 20.92%, respectively) and for extension, lateral bending to the right and left, and rotation to the right and left, of the cervical spine (an increase of 7.05%, 7.89%, 10.44%, 4.65%, and 6.55%, respectively). In the control group, no significant differences were observed. No significant changes were observed in the load distribution and body balance assessment. A single session of TMJ soft tissue therapy increases jaw and cervical spine mobility but does not impact body balance or foot load distribution in static conditions in women diagnosed with myofascial pain in the TMJ area.

High Availability Database Infrastructure with Galera and HAProxy

High Availability (HA) is crucial in the cloud environment to render the services according to the Service Level Agreement (SLA) to the customers. This paper provides an novel solution for 99.99% high availability and scalability of database infrastructures using Galera Cluster, along with HAProxy. The Galera Cluster delivers synchronous multi-master replication over multiple nodes, guaranteed data consistency while in real-time and for each transaction, high availability through automatic failover. HAProxy strikes a balance here by distributing the traffic across nodes and achieving optimal load distribution with less or minor effect on downtime. Real-time monitoring and alerts are also enabled by using Prometheus &amp; Grafana to monitor cluster health as well performance.

Advanced Design of Naval Ship Propulsion Systems Utilizing Battery-Diesel Generator Hybrid Electric Propulsion Systems

As advanced sensors and weapons require high power, naval vessels have increasingly adopted electric propulsion systems. This study aims to enhance the efficiency and operability of electric propulsion systems over traditional mechanical propulsion systems by analyzing the operational profiles of modern naval vessels. Consequently, a battery-integrated generator-based electric propulsion system was selected. Considering the purpose of the vessel, a specification selection procedure was developed, leading to the design of a hybrid electric propulsion system (comprising one battery and four generators). The power management control technique of the proposed propulsion system sets the operating modes (depending on the specific fuel oil consumption of the generators) to minimize fuel consumption based on the operating load. Additionally, load distribution control rules for the generators were designed to reduce energy consumption based on the load and battery state of charge. MATLAB/Simulink was used to evaluate the proposed system, with simulation results demonstrating that it maintained the same propulsion performance as existing systems while achieving a 12-ton (22%) reduction in fuel consumption. This improvement results in cost savings and reduced carbon dioxide emissions. These findings suggest that an efficient load-sharing controller can be implemented for various vessels equipped with electric propulsion systems, tailored to their operational profiles.

Effect of Geometric Parameters of High-Speed Helical Gears on Friction Flash Temperature and Scuffing Load Capacity in Electric Vehicles

High-speed reducers in electric vehicles, characterized by high rotation speeds, heavy loads, large helix angles, and high contact ratios, are prone to tooth surface scuffing due to high sliding speeds. This scuffing is caused by adhesion wear from excessive instantaneous friction flash temperatures. The prevailing approach to gear scuffing analysis relies on the standard formula method, which is a relatively rudimentary technique. This method lacks the precision required to accurately assess the intricate distribution of tooth surface flash temperature (TSFT), limiting its efficacy in targeted tooth optimization. This study introduces an enhanced semi-analytical method to calculate TSFT and analyzes its variation under different conditions: increased tooth number and reduced module, altered pressure angle, and varied helix angle. The aim is to understand how these geometric parameters affect TSFT and the scuffing load capacity of high-speed reducer gears. This study calculates load distribution and TSFT under peak operating conditions and shows that increasing the tooth number, pressure angle, and helix angle can reduce maximum TSFT by more than 30%, improving scuffing safety and load capacity. However, these improvements must consider the gear’s allowable bending safety factor and bearing service life. The research concludes that optimizing these geometric parameters can significantly enhance the scuffing load capacity of gearsets.

Comparison of static balance and pressure distribution in individuals with unilateral lower limb amputation: The role of barefoot, heel support, and vision.

In some cultures, shoes are not worn indoors. Prosthesis use barefoot can lead to pressure injuries and loss of balance due to abnormal residual limb loading. This study aimed to compare the effect of wearing standard alignment prostheses using barefoot at home and visual alteration on static balance and pressure distribution in individuals with unilateral transfemoral amputations (TFAs) or transtibial amputations (TTAs). Prospective parallel experimental study. Participants with unilateral TTAs (n = 44) and TFAs (n = 37) were included. Balance and load distribution were assessed using MatScan pressure platforms, both with a heel (3 × 2 cm2 area; 1.8 cm height) support (the use of shoes with a heel is mimicked) and barefoot. Balance parameters were disrupted in all groups when eyes closed position (p < 0.05). Using heels reduced anterior-posterior and medial-lateral sway in TTA group during eyes closed (p < 0.05). When standing barefoot with the eye open position, TFA group had more load on the rear foot of the prosthetic foot and less load on the forefoot than TTA group (p < 0.05). The opposite pattern was observed in the intact foot (p < 0.05). Using heels in TTA group increased the load on the front of the intact side and the rear of the prosthetic side (p < 0.05). The balance parameters were impaired in both groups while standing barefoot in the absence of vision. However, using heel supports improved static balance in the TTA but not in the TFA group. Using heel support changed this load distribution in both groups, especially in the TTAs, and created positive changes.

On the Optimal Distribution of Traction Forces in Cable Propulsors of Mobile Robots

The analysis of methods of distribution of traction forces in various propellers of mobile robotic complexes and transport vehicles is carried out. The problem of synthesizing a method for controlling the distribution of the total traction load between interconnected electric drives of mobile robot propellers, discretely interacting with the support surface, is considered. An underwater mobile robot is simulated with several "walking-like" anchor-cable propellers, which ensure the movement of the underwater mobile robot by pulling the body to the supports located on the bottom. A mathematical model of the rectilinear motion of a mobile robotic device with walking-type propellers has been compiled. A mathematical description of the electric drive of the propulsion of such a mobile robot is proposed, taking into account its kinetic transfer function. It is shown that the total traction effort realized by a mobile robot is the source of the moment of resistance in the electric drive of each mover. In this regard, coefficients characterizing the distribution of traction force have been introduced into the differential equation of electric drives. A feature of the functions of these coefficients is their dependence on the distance traveled, speed and strength of resistance to movement. To optimize the distribution of the total power load between the thrusters, a target functional has been compiled. It is shown that as such a target functional, a requirement for a minimum of total heat losses in an interconnected electric drive of propellers can be formulated. To find the minimum of the accepted functional, the Euler-Poisson equations are compiled. As an additional limitation, the condition of physical feasibility is introduced. The results of solving such an optimization problem are presented on the simplest calculation scheme of two DC electric drives, between which the load is distributed along the rectilinear movement of a solid. As a result of solving the formulated optimization problem, the dependences of control actions for electric drives (voltage for DC electric drives), graphs of changes in the target function providing optimal distribution of traction forces between them are obtained, and the optimality of such distribution is proven.

In silico formulation optimization and particle engineering of pharmaceutical products using a generative artificial intelligence structure synthesis method

Pharmaceutical drug dosage forms are critical for ensuring the effective and safe delivery of active pharmaceutical ingredients to patients. However, traditional formulation development often relies on extensive lab and animal experimentation, which can be time-consuming and costly. This manuscript presents a generative artificial intelligence method that creates digital versions of drug products from images of exemplar products. This approach employs an image generator guided by critical quality attributes, such as particle size and drug loading, to create realistic digital product variations that can be analyzed and optimized digitally. This paper shows how this method was validated through two case studies: one for the determination of the amount of material that will create a percolating network in an oral tablet product and another for the optimization of drug distribution in a long-acting HIV inhibitor implant. The results demonstrate that the generative AI method accurately predicts a percolation threshold of 4.2% weight of microcrystalline cellulose and generates implant formulations with controlled drug loading and particle size distributions. Comparisons with real samples reveal that the synthesized structures exhibit comparable particle size distributions and transport properties in release media.

Experimental Study of Wave Load Distributions on Pile Groups Affected by Cap Structures and Pile Spacings Under Varied Wave Conditions

Experimental Study of Wave Load Distributions on Pile Groups Affected by Cap Structures and Pile Spacings Under Varied Wave Conditions

Characteristics, Relationships, and Differences in Muscle Activity and Impact Load Attenuation During Tennis Forehand Stroke with Different Grips

In forehand strokes with different grips in tennis, the forearm muscle activities, the distribution and attenuation of the impact loads, and the effects of the muscles on the impact load attenuation exhibited different characteristics. This study aimed to explore these characteristics by analyzing electromyography (EMG) and acceleration data, and comparing the differences between the Eastern and Western grips. Fourteen level II or above tennis players (ten males, aged 22.4 ± 3.6 years; four females, aged 19.8 ± 2.0 years) were recruited and instructed to perform forehand strokes using the Eastern and Western grips, respectively. The EMG of eight forearm muscles and the acceleration data at the ulnar and radial sides of the wrist and elbow were collected. The root mean square (RMS), the peaks of the impact load, the amplitude of impact load attenuation (AC), and the jerk value (Jerk) were calculated. The cross-correlation coefficients and time delays of EMG–EMG, EMG–AC, and EMG–jerk were obtained using the cross-correlation method. The results showed that in the Eastern grip group (group E), the RMS of the flexor carpi ulnaris (FCU) was significantly greater than that in the Western grip group (group W). In group E, the peaks of impact load, AC, and Jerk on the Y axis of the wrist ulnar side were all significantly higher than those in group W. The activity of the extensor digitorum commonis (EDC) had significantly different effects on the amplitude and rate of impact load attenuation at specific locations in different grips, especially at the elbow (p &lt; 0.05). The conclusion indicated that the FCU exhibited higher levels of EMG activity in the Eastern grip. This grip responded to greater impact loads with more substantial and rapid attenuation on the wrist ulnar side. Furthermore, the EDC appeared to contribute more to the amplitude of impact load attenuation in the Western grip and to have a more significant influence on the rate of impact load attenuation in the Eastern grip, especially at the elbow. These results suggest that tennis players and coaches should pay more attention to improving the strength of the EDC and FCU, which can improve sports performance and comfort, as well as prevent sports injuries.

Effects of openings on postbuckling behavior of large‐size composite C‐beam under bending‐shear coupling load

AbstractProper design and accurate mechanical assessment of composite C‐beam after opening are of great importance in structure engineering. This paper aims to experimentally and analytically investigate the postbuckling response of large‐size C‐beam with web opening under bending‐shear coupling load. New specimen with four different open shapes were designed and tested. Strain gauges and displacement measurements were applied to monitor its buckling behavior, strain field distribution and critical failure load. Four specimens with various openings were loaded until catastrophic failure occurred. Additionally, an analytical model was introduced to predict the residual strength of circular opening. The results indicate that while the presence of an opening significantly decreases the load carrying capacity, it has minimal effect on the bending stiffness. Compared with intact specimen, the initial delamination, buckling and ultimate strength of the circular opening decreases less than those of the rectangular opening. By altering the position of the rectangular opening, improvements can be made in terms of initial delamination resistance and buckling load; however, ultimate strength remains largely unaffected. Reinforcing the edge of an opening further reduces resistance to initial delamination but other two indicators are improved. Overall, from buckling to failure stages, post‐buckling bearing capacity after opening decreases by 40%. Moreover, the shear failure mode is observed during catastrophic failures. And the analysis method employed is relatively conservative.Highlights Ten large size composite C beams are conducted under coupling loads. Deformation, strain distribution and failure mode are presented. Influence of openings on postbuckling behavior of beam is analyzed. An analysis method is employed to predict the residual strength of beam. It could provide valuable insights for assisting in designing beam openings.

Reinforcing polyvinyl alcohol films with layered double hydroxide and tannic acid to enhance tensile strength, tribological performance, and corrosion resistance in biomedical coating applications

Abstract This study investigates the synergistic effects of incorporating layered double hydroxide (LDH) and tannic acid (TA) into polyvinyl alcohol (PVA) films to enhance their mechanical, tribological, and corrosion resistance properties for biomedical applications. Composite coating films were prepared by blending PVA with LDH and TA in various concentrations. The addition of LDH and TA significantly increased the crystallinity index of the composite films, with the highest crystallinity observed at 66.3% for the sample containing 1 wt% TA and 2 wt% LDH (PVA/TA1/LDH2). This enhancement in crystallinity contributed to improved mechanical performance, as demonstrated by tensile tests, where the PVA/TA1/LDH2 composite exhibited the highest tensile strength among all samples. Tribological testing revealed that the PVA/TA1/LDH2 composite also achieved the lowest coefficient of friction (COF), along with a minimal wear rate, indicating superior wear resistance. SEM analysis of the wear scars confirmed a narrow wear track and smoother surface morphology for this composite, which suggests effective load distribution and reduced surface degradation. The addition of TA was further shown to improve the corrosion resistance of the PVA composite films, with the PVA/TA1/LDH1 sample exhibiting the lowest corrosion current density (Icorr) of 0.36 µA cm⁻², representing a significant improvement over neat PVA. These findings highlight the potential of PVA/LDH/TA films for coating applications in biomedical devices, where enhanced mechanical strength, wear resistance, and corrosion protection are critical. The synergistic effects of LDH and TA provide a pathway for developing durable and functional coatings, expanding the practical utility of PVA films in demanding biomedical environments.&amp;#xD;

Sustainability in bridge design—investigation of the potential of topology optimization and additive manufacturing on a model scale

AbstractBridge design represents a typical challenge in civil engineering. The high material usage in combination with the considerable construction effort makes their longevity a strongly desirable property. A mechanically efficient design contributes to optimum load distribution within the structure. Numerical topology optimization represents a valuable tool that can be applied for form finding of load‐appropriate structural layouts within a predefined design‐space. This study takes application of topology optimization to bridge design into focus. Different bridge types are designed using topology optimization considering self‐weight based on a routine that was presented in a previous work. The bridge designs are examined in detail and compared to already existing bridges with regard to the requirements of modern structures. In order to demonstrate manufacturability of the designs, they are realized on a model scale using an additive manufacturing (am) technique in the powder bed. The knowledge gained from this small scale consideration is transferred to the context of civil engineering to highlight the potential of AM in realization of resource efficient construction.

Robust Distributed Load Frequency Control for Multi-Area Power Systems with Photovoltaic and Battery Energy Storage System

The intermittent power generation of renewable energy sources (RESs) interrupts the balance between power generation and demand load due to the increased frequency fluctuation, which challenges the frequency stability analysis and control synthesis of power generation systems. This paper proposes a robust distributed load frequency control (DLFC) scheme for multi-area power systems. Firstly, a multi-area power system is constructed by integrating photovoltaic (PV) and battery energy storage systems (BESSs). Then, by employing the linear matrix inequality (LMI) technique, the sufficient condition capable of ensuring that the proposed controller satisfies H∞ robust performance in the sense of asymptotic stability is derived. Finally, testing is conducted on a four-area renewable power system, and results verify the strong robustness of the proposed controller against load disturbance and intermittence of RESs.

Aerodynamic Analysis of Rotor Spacing and Attitude Transition in Tilt-Powered Coaxial Rotor UAV

Complex aerodynamic characteristics and optimal control during the attitude transition of tilt-powered coaxial twin-rotor unmanned aerial vehicles (UAVs) represent key challenges in flight control design. This study investigates aerodynamic mechanisms and control parameter optimization during the transition of UAVs from vertical to forward flight. By establishing a dynamic model and combining theoretical and numerical analyses, the optimal rotor spacing is determined to be h = 0.5 R. The load distribution and aerodynamic characteristics of the aircraft are analyzed at different initial tilt angles during attitude transitions. At an initial tilt angle of δ = 9°, the thrust force increases by 439% compared with that at δ = 3°, and the tip speed increases by 15% and 35% compared with that at δ = 3° and δ = 13°, respectively. The results indicate that a tilt angle of δ = 9° results in a higher turbulent dissipation rate and rotor layout efficiency, with a smoother vortex flow and more orderly distribution. The interference between the twin-rotor tip vortices is relatively weak, resulting in excellent symmetry and aerodynamic stability. Through the improvement of the theoretical model and parameter optimization of a novel tilt-powered coaxial twin-rotor UAV, this study enhances UAV flight stability and provides valuable insights and validation for the further development of UAV technology.

A Universal Target Plate Design Scheme for Stellarators: theoretical basis and its application to heat load control

Abstract This study introduces a novel divertor target design scheme for stellarators, grounded in mathematical treatments and tailored to control toroidal heat load distributions. Initially, a differential equation characterizing toroidally uniform heat load distribution has been established in a two-dimensional (2D) slab configuration, and its analytic solution has been obtained. Subsequently, a numerical scheme has been developed to adapt the analytic solution into the 3D surface shape of stellarator target. The effectiveness of this design scheme has been validated through simulations of the Chinese First Quasi-axisymmetric Stellarator (CFQS) using a suite of codes including HINT, FLARE and EMC3-EIRENE, where a toroidally uniform heat load distribution has been achieved with an island configuration. Further, the effects of input parameters on the target shape and heat load distribution have been studied. The robustness of the designed target has been investigated by simulation results with varying magnetic island configurations, confirming that the toroidal uniformity of heat load distribution is insensitive to changes in island configurations. Moreover, the designed target has been assessed with gas puffing of neon, which shows that neon injections effectively reduce the heat loads without altering the toroidal uniformity of heat load distributions. The proposed scheme highlights the importance of theoretical and mathematical foundations of target design, offering an advantageous alternative/complement to the traditional numerical schemes.

Chrysin-loaded Soluplus-TPGS mixed micelles: Optimization, characterization and anticancer activity against hepatocellular carcinoma cell line

Chrysin is a natural flavonoid found in various plants, and it has shown potential therapeutic benefits such as anti-inflammatory, antioxidant, and anticancer properties. However, its clinical application is limited due to poor solubility and low bioavailability. Mixed micelles can help overcome these problems. This study focuses on preparation of Chrysin-loaded mixed micelles with the help of solvent diffusion evaporation method. Soluplus and TPGS were the main components of the formulation, and their proportions were optimized with the help of the central composite design matrix. Thirteen batches were constructed to optimize the mixed micelle formulation based on different Soluplus: Chrysin ratios and TPGS percentages. Response surface methodology and various models were employed to analyze micellar size, size distribution, encapsulation efficiency, and drug loading. The optimized formulation, CHR-MM1, exhibited a particle size of 132.2 ± 7.9 nm, encapsulation efficiency of 98.01 ± 2.27 %, and a zeta potential of −2.10 mV. TEM images revealed that the micelles were spherical in shape. Characterization studies, including FTIR and X-ray diffraction, confirmed the successful encapsulation of Chrysin in an amorphous form within the mixed micelles. The in vitro release studies demonstrated a sustained release behavior in both acidic and neutral pH conditions. The Korsmeyer-Peppas model best described the drug release kinetics. Cellular uptake studies using fluorescence microscopy revealed enhanced internalization of the mixed micelles into Hep G2 cells. Moreover, MTT assays indicated a concentration- and time-dependent cytotoxicity of Chrysin-loaded mixed micelles against Hep G2 cells, outperforming free Chrysin. The flow cytometry analysis results suggested an enhanced apoptotic activity of Chrysin in the mixed micelles as compared to free drug. This study provides a promising strategy for improving the solubility, cellular uptake, and cytotoxicity of Chrysin. Therefore, our results point to the potential of Chrysin-loaded mixed micelles to serve as a therapeutic option for hepatocellular carcinoma.