Stiffness Distribution Research Articles

Distributed stiffness assessment of bridges based on macro-strain envelope curve under moving trainloads

Due to the limited gauge length of traditional strain gauges, the bridge strain influence line cannot be obtained from actual measurement, rendering the evaluation of the longitudinal stiffness distribution of bridges by monitoring results a difficult task. To address this issue, a distributed long-gauge strain sensing technology was used to evaluate the stiffness of high-speed railway bridges. Firstly, the distributed macro-strain influence line of bridges under train load was derived, followed by the clarification of the mechanical relationship between the longitudinal stiffness of railway bridges and the distributed macro-strain of the bridges. Then, a stiffness evaluation method was proposed based on the distributed macro-strain time history envelope curve. Secondly, the feasibility of the method was verified through finite element simulations. By establishing a refined dynamic macroscopic strain calculation model for railway bridges, the proposed method was explored for the accuracy and feasibility of bridge stiffness under different damage conditions. Finally, a real bridge verification test was conducted on a bridge on the Shanghai-Kunming Railway, and the test results showed how the thickness of the bottom plate would vary with the bridge span in the bridge design.

Mechanical complexity of living cells can be mapped onto simple homogeneous equivalents.

Biological cells are built up from different constituents of varying size and stiffness which all contribute to the cell's mechanical properties. Despite this heterogeneity, in the analysis of experimental measurements one often assumes a strongly simplified homogeneous cell and thus a single elastic modulus is assigned to the entire cell. This ad-hoc simplification has so far mostly been used without proper justification. Here, we use computer simulations to show that indeed a mechanically heterogeneous cell can effectively be replaced by a homogeneous equivalent cell with a volume averaged elastic modulus. To demonstrate the validity of this approach, we investigate a hyperelastic cell with a heterogeneous interior under compression and in shear/channel flow mimicking atomic force and microfluidic measurements, respectively. We find that the homogeneous equivalent cell reproduces quantitatively the behavior of its heterogeneous counterpart, and that this equality is largely independent of the stiffness or spatial distribution of the heterogeneity.

Quantifying Plantar Flexor Muscles Stiffness During Passive and Active Force Generation Using Shear Wave Elastography in Individuals With Chronic Stroke

ObjectivesThis study aims to investigate the mechanical properties of paretic and healthy plantar flexor muscles and assesses the spatial distribution of stiffness between the gastrocnemius medialis (GM) and lateralis (GL) during active force generation. MethodsShear wave elastography measurements were conducted on a control group (CNT, n=14; age= 59.9 ± 10.6 years; BMI= 24.5 ± 2.5 kg/m2) and a stroke survivor group (SSG, n = 14; age = 63.2 ± 9.6 years; BMI = 23.2 ± 2.8 kg/m2). Shear modulus within the GM and GL was obtained during passive ankle mobilization at various angles of dorsiflexion (P0= 0°; P1= 10°; P2= 20°; P3= -20° and P4= -30°) and during different levels of maximal voluntary contraction (MVC) (100%, 30%, 50%, 70%). Muscle activation of GM, GL, and tibialis anterior was also evaluated. ResultsThe results revealed a significant increase in passive stiffness within the paretic plantar flexor muscles under high tension during passive mobilization (p<0.05). Yet, during submaximal and maximal MVC, the paretic plantar flexors exhibited decreased active stiffness levels (p<0.05). A notable discrepancy was found between the stiffness of the GM and GL muscles, with the GM demonstrating greater stiffness from 0° of dorsiflexion in the SSG (p<0.05), and from 10° of dorsiflexion in the CNT (p<0.05). No significant difference in stiffness was observed between the GM and GL muscles during active conditions. ConclusionStroke affects the mechanical properties differently depending on the state of muscle activation. Notably, the distribution of stiffness among synergistic plantar flexor muscles varied in passive condition, while remaining consistent in active condition.

Quantifying the impact of stiffness distributions on the dynamic behaviour of railway transition zones

Railway transition zones (RTZs) are regions where abrupt track stiffness changes occur that may lead to dynamic amplifications and subsequent track deterioration. The design challenges for these zones arise due to variations in material properties in both the depth (trackbed layers composed of different materials) and longitudinal directions of the track, as well as temporal variations in mechanical properties of materials due to several external factors over the operational period. This research aims to investigate the effects of these variations in material properties (i.e., of the resulting stiffness distributions in vertical and longitudinal directions) on the behaviour of RTZs, assess from this perspective the performance of a novel transition structure called the SHIELD, and establish a methodology for designing a robust solution to mitigate the dynamic amplifications in these zones. Results indicate that stiffness variations in both vertical and longitudinal directions significantly influence the dynamic behaviour of the RTZs. The study also suggests a permissible range of stiffness ratios to control the amplification of strain energy in the most critical components of RTZs, both in the initial state as well as during the operational phase (where material properties may vary over time). Moreover, the proposed methodology offers a valuable tool for the design and evaluation of RTZs and is applicable to various transition types and a broad spectrum of material properties.

Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions

Functionally graded materials have broad engineering applications including mechanical engineering, electronics, chemistry, and biomedical engineering. One notable advantage of such materials is that their stiffness distribution can be optimized to avoid stress concentration. A novel approach for solving the equations describing the longitudinal vibration of functionally graded rods with viscous and elastic boundary conditions is proposed. The characteristic equation of the system is derived for the solution of the undamped case for the constant stiffness rod. Then, a homotopy method is applied to compute the eigenvalues and mode shapes of graded rods for viscoelastic boundary conditions. The changes of the eigenvalues and mode shapes as function of the damping parameters are investigated. The optimal damping of the system is computed. It is shown that the qualitative behavior depends on the relation between the actual damping and the optimal damping of the system. The energy density distribution of graded rods is also discussed. An energy measure, the mean scaled energy density distribution is introduced to characterize the energy distribution along the rod in the asymptotic time limit. The significance of such a measure is that it reveals how the energy tends to distribute along the rod. It is shown that the energy distribution can be manipulated by changing the damping parameters. Qualitative changes depending on the relation between the actual damping and the optimal damping are highlighted.

Investigation on the performance of a torque-driven undulatory swimmer with distributed flexibility

The locomotion of fish provides insight for the design of efficient swimming robotic devices. The current study presents a systematic investigation of the locomotion performance of a fish-like swimmer with a wide range of parameter settings. Two-dimensional simulations with the immersed boundary method in the framework of Navier–Stokes equations are employed for the fluid–structure interaction analysis. Unlike most previous studies where the kinematics of the swimmer is predetermined, the locomotion of the current swimmer is the response of a single periodic torque applied to the anterior part. In addition, current simulations applied a direct correspondence between code units and real-world units, providing more engineering-related guidance for the future design of microrobotic swimmers. The effect of the distribution of body stiffness on swimming performance and propulsion generation is discussed with different pitch frequencies and amplitudes. It was shown that swimmers with a more flexible posterior part have an advantage in undulatory swimming performance when the pitch angle is low or moderate. However, such an advantage disappears when the pitch angle or actuating frequency exceed a certain level. An analysis of the phase-averaged vorticity field and thrust sequence is given to clarify the change in performance due to the variation of flexibility.

Research on the Influence of Disc–Drum Connection Bolt Preloading Rotor Assembly Modal Characteristics and Diagnosis Technology

The drum rotor of an aero-engine is connected by one or multiple mounting edges through bolts, and their dynamics are significantly influenced by the preload state of the bolts. Long working hours in challenging environments can result in the deterioration of bolt pre-tightening during assembly or service, which impacts the rotor’s dynamic stability and overall performance. Currently, there are no available methods for detecting the dynamic characteristics of the drum connection components. This paper analyzes the impact of the natural characteristics of the drum composite structure of a high-pressure aero-engine turbine based on the refined finite element method when the preloading state changes. Two conditions of deviation and uneven stiffness distribution were applied to the connected components of the drum. The analysis focused on the impact of the pre-tightening state on its natural frequency. After analyzing the feasibility of identifying the pre-tightening state, two methods are proposed. These methods focus on changes in natural frequency and mode shape, specifically the sensitive natural frequency change method and the mode step change method. The methods proposed in this paper can serve as a reference for evaluating the quality of assembling complex disc–drum structures with multiple bolt connections.

Optimizing fiber paths of tow-steered laminated composites for parametric stability using isogeometric analysis and genetic algorithm

An isogeometric formulation is presented for fiber path optimization of tow-steered composite laminates (TSCL) with minimal parametric instabilities. Here, the fiber path functions of a TSCL is expressed smoothly by Cp−1 continuous non-uniform rational B-splines (NURBS) for engineering shapes, providing accurate field solutions. In this way, the motion equations of a TSCL plate is developed based on the third-order shear deformation theory (TSDT) and the Bolotin’s approximation is used to determine the parametric instability region. Primarily, the accuracy and efficiency of presented framework is measured for a TSCL example with respect to the existing solutions. Then, the optimal fiber paths of TSCL plates are searched using the genetic algorithm (GA) for various geometries, force component combinations, and dynamic-to-static force ratios. Results reveal that the optimal fiber paths are not necessarily symmetric even for regular domains, demonstrating the non-uniform coupling of bending and twisting stiffness in TSCL plates. The optimal design of TSCL fiber paths necessitates the consistency of local stiffness distribution and the resultant bending–twisting mode shape, specially when the dynamic force is high with respect to the static one. Geometry, force component combination, and dynamic-to-static force ratio impose case-specific fiber paths for optimal TSCL plates, requiring both minimal deformation and instability opening.

Dynamic characteristics of segmental assembled HH120 wind turbine tower

The analysis of dynamic characteristics is crucial in the design of wind tower structures. The dynamic behavior of wind towers is primarily influenced by structural stiffness and mass distribution. In particular, the segment thickness of prefabricated concrete towers should be selected and optimized based on computed results of stress distribution in order to achieve the desired dynamic performance. The main objective of this research is to investigate the effects of design factors, such as segmental thickness and top mass of wind blades, hub, and nacelle, on the natural frequencies and vibration modes of the precast concrete towers. For the finite element analysis, a high-rise wind turbine tower with a hub height of 120 m (HH120 tower) is utilized. Finally, the theoretical model for the reduced degrees of freedom system is validated using the results from the finite element analysis.

Natural Frequency Response of FG-CNT Coupled Curved Beams in Thermal Conditions

This study investigates the sensitivity of dynamic properties in coupled curved beams reinforced with carbon nanotubes (CNTs) to thermal variations. Temperature-dependent (TD) mechanical properties are considered for poly methyl methacrylate (PMMA) to be strengthened with single-walled CNTs (SWCNTs), employing the basic rule of mixture to define the equivalent mechanical properties of nanocomposites. The governing equations of motion are derived using a first-order shear deformation theory (FSDT) and Hamilton’s principle, accounting for elastic interfaces modeled using elastic springs. A meshfree solution method based on a generalized differential quadrature (GDQ) approach is employed to discretize the eigenvalue problem and to obtain the frequency response of the structure. The proposed numerical procedure’s accuracy is verified against predictions in the literature for homogeneous structural cases under a fixed environmental temperature. The systematic investigation assesses the impact of various geometric and material properties, including curvature, boundary conditions, interfacial stiffness, and CNT distribution patterns, on the vibrational behavior.

The Aerodynamic Effect of Biomimetic Pigeon Feathered Wing on a 1-DoF Flapping Mechanism.

This study focused on designing a single-degree-of-freedom (1-DoF) mechanism emulating the wings of rock pigeons. Three wing models were created: one with REAL feathers from a pigeon, and the other two models with 3D-printed artificial remiges made using different strengths of material, PLA and PETG. Aerodynamic performance was assessed in a wind tunnel under both stationary (0 m/s) and cruising speed (16 m/s) with flapping frequencies from 3.0 to 6.0 Hz. The stiffness of remiges was examined through three-point bending tests. The artificial feathers made of PLA have greater rigidity than REAL feathers, while PETG, on the other hand, exhibits the weakest strength. At cruising speed, although the artificial feathers exhibit more noticeable feather splitting and more pronounced fluctuations in lift during the flapping process compared to REAL feathers due to the differences in weight and stiffness distribution, the PETG feathered wing showed the highest lift enhancement (28% of pigeon body weight), while the PLA feathered wing had high thrust but doubled drag, making them inefficient in cruising. The PETG feathered wing provided better propulsion efficiency than the REAL feathered wing. Despite their weight, artificial feathered wings outperformed REAL feathers in 1-DoF flapping motion. This study shows the potential for artificial feathers in improving the flight performance of Flapping Wing Micro Air Vehicles (FWMAVs).

Tissue palpation in endoscopy using EIT and soft actuators.

The integration of soft robots in medical procedures has significantly improved diagnostic and therapeutic interventions, addressing safety concerns and enhancing surgeon dexterity. In conjunction with artificial intelligence, these soft robots hold the potential to expedite autonomous interventions, such as tissue palpation for cancer detection. While cameras are prevalent in surgical instruments, situations with obscured views necessitate palpation. This proof-of-concept study investigates the effectiveness of using a soft robot integrated with Electrical Impedance Tomography (EIT) capabilities for tissue palpation in simulated in vivo inspection of the large intestine. The approach involves classifying tissue samples of varying thickness into healthy and cancerous tissues using the shape changes induced on a hydraulically-driven soft continuum robot during palpation. Shape changes of the robot are mapped using EIT, providing arrays of impedance measurements. Following the fabrication of an in-plane bending soft manipulator, the preliminary tissue phantom design is detailed. The phantom, representing the descending colon wall, considers induced stiffness by surrounding tissues based on a mass-spring model. The shape changes of the manipulator, resulting from interactions with tissues of different stiffness, are measured, and EIT measurements are fed into a Long Short-Term Memory (LSTM) classifier. Train and test datasets are collected as temporal sequences of data from a single training phantom and two test phantoms, namely, A and B, possessing distinctive thickness patterns. The collected dataset from phantom B, which differs in stiffness distribution, remains unseen to the network, thus posing challenges to the classifier. The classifier and proposed method achieve an accuracy of and on phantom A and B, respectively. Classification results are presented through confusion matrices and heat maps, visualising the accuracy of the algorithm and corresponding classified tissues.

Role of additive size in the segmental dynamics and mechanical properties of cross-linked polymers.

Thermoset materials often involve the addition of molecular and nanoparticle additives to alter various chemo-physical properties of importance in their ultimate applications. The resulting compositional heterogeneities can lead to either enhancement or degradation of thermoset properties, depending on the additive chemical structure and concentration. We tentatively explore this complex physical phenomenon through the consideration of a model polymeric additive to our coarse-grained (CG) thermoset investigated in previous works by simply varying the size of additive segments compared to those of polymer melt. We find that the additive modified thermoset material becomes chemically heterogeneous from additive aggregation when the additive segments become much smaller than those of the thermoset molecules, and a clear evidence is observed in the spatial distribution of local molecular stiffness estimated from Debye-Waller factor 〈u2〉. Despite the non-monotonic variation trends observed in dynamical and mechanical properties with decreasing additive segmental size, both the structural relaxation time and moduli (i.e., shear modulus and bulk modulus) exhibit scaling laws with 〈u2〉. The present work highlights the complex role of additive size played in the dynamical and mechanical properties of thermoset polymers, which should provide a better understanding for the glass formation process of cross-linked polymer composites.

Bianchi type III inflationary universe with flat potential and stiff fluid distribution in general relativity

In this study, we looked at the “Bianchi Type III stiff fluid cosmological model in general relativity”. To get an inflationary solution we have used appropriate condition between matric potential. Here n is non-negative integer and B and C are dependent function of time “t”. The structure characteristics of model are also pointed. The behaviour of the model under different physical conditions is also discussed.

Investigation of Seismic Response of Irregular Steel Buildings: A Case Study of U-Shaped Structures

Tills paper presents a dynamic analysis focusing on the influence of plan shape on tall steel structures. The study specifically investigates the seismic behavior of two 22-story buildings, one with a square plan and the other adopting a U-shaped configuration. Utilizing OpenSEES platform for nonlinear time history analysis, the research sheds light on the impact of plan irregularities on fundamental time periods, displacements, drift ratios, and base shear. Results reveal that the U-shaped building experiences liiglier dynamic response compared to the square shaped reference building, the U-shaped building experiences liiglier time periods across all modes due to increased mass and irregular stiffness distribution in the building's grid. Top story displacements reveal an increase in maximum displacement by 30% compared to the reference structure, showing a non-linear pattern. Inter-story drift ratios had peaks at the 8th and 18th floors showing increments of 43% and 117%. respectively. The time liistoiy response illustrates a liiglier response over time for the U-shaped building, indicating distinct behavioral differences. Base shear time liistoiy revealed liiglier values for the U-shaped building over time, including a 48% increase in maximum base shear compared to the reference building. These findings reveal the significant effect of plan regularity in tall steel building design on the seismic response and the importance of considering it in building design.

Investigation of the Fatigue Strength of Shape Optimized Gusset Plates in Rectangular and Circular Hollow Section K-Joints

The fatigue strength of structures made of rectangular (RHS) and circular hollow sections (CHS) is characterized by inhomogeneous stiffness distributions in the connection areas of braces and chord, which lead to high stress concentration factors (SCF). Using these SCFs in conjunction with structural SN-curves, the fatigue life can be estimated. In the preceding research project P1132, K-joints made of CHS used a special weld design resulting in a local reinforcement of the gap area. The fatigue tests showed an increase in fatigue strength compared to conventional CHS K-joints. Based on this, in the research project FOSTA P1442, numerical and experimental fatigue investigations were carried out on K-joints with shape-optimized gusset-plates. The use of gusset-plates was intended to increase the fatigue strength of K-joints by relocating the position of the hot spot to areas with lower stresses or by reducing the stresses at the hot spot. For this purpose, three different gusset-plate geometries were investigated for five RHS- respectively three CHS-geometries. Variant 1 (shortened, slotted braces and gusset-plate attached to the chord), variant 2 (slotted braces also attached to the chord) and variant 3 (like V2, gusset-plate additionally passed through the underside of the chord). All components are circumferentially welded. The SCF of the three gusset-plate geometries are compared with the SCF of conventional K-joints. In addition, the SCF are compared with the required fabrication effort for the geometries under investigation. Finally, on this basis, a manufacturing recommendation for practical use is presented.

ANALYSIS OF NATURAL FREQUENCIES FOR EARLY DAMAGE DETECTION IN CFRP SHAFTS USING RSM-BASED FREQUENCY CONTOUR PLOTS

This study explores early damage detection in carbon fiber-reinforced polymer shafts by analyzing natural frequencies. Modern engineering components often face increased flexibility and high stress levels, leading to cracks in rotating parts, which can result in premature failures. To address this issue, modal analysis, specifically natural frequency analysis, is employed to identify deviations caused by cracks. Cracks alter stiffness and mass distribution, leading to shifts in natural frequencies. The study employs finite element models to simulate various crack locations and depths, normalizing them with respect to shaft diameter and length. A cantilever shaft configuration is utilized with refined mesh structures near the transverse crack. The analysis leverages the frequency contour method with response surface methodology to visualize how crack depth and location influence normalized natural frequencies. Results indicate that crack depth has a significant impact on natural frequencies, while crack location has a subtler effect. Combining depth and location produces the most pronounced frequency variations. The corresponding R² values for the normalized first and third natural frequencies are 95.69% and 96.32%, while for the normalized second natural frequency this value is 75.70%. The study also demonstrates the use of frequency contour curves for accurate crack detection, with the 1st and 3rd natural frequencies being reliable indicators.

Seismic Designs Based on Pain Points of High-rise Buildings

With the continuous improvement of the degree of urbanization, in order to alleviate the pressure brought by the increase in population, more and more high-rise buildings appear, and high-rise buildings become the symbol and main body of urbanization. Due to the increase of height, horizontal load and other factors, high-rise buildings have higher requirements for safety and stability. However, with the frequent occurrence of earthquakes, the design requirements for high-rise buildings are more stringent. This paper introduces the structural types and characteristics of tall buildings, studies the effects of earthquakes on them, and discusses four suitable seismic design methods. The establishment of multi-level fortification of structural earthquakes is mainly to take relevant anti-seismic treatment measures and monitoring and maintenance programs to improve the anti-seismic ability of buildings. Reasonable arrangement of lateral force resisting members and uniform distribution of overall stiffness of building structure can realize reasonable building structure system to ensure the ability of building to resist earthquake load. The installation of isolation and shock absorption devices can also significantly improve the seismic level of high-rise buildings.

Bianchi Type-VIII Inflationary Cosmological Models with Flat Potential and Stiff perfect Fluid Distribution in General Relativity

The objective of this paper is to investigate the behaviour of Bianchi Type-VIII Inflationary Cosmological Models with Flat Potential for Stiff Fluid Distribution. To find the solution of thes models we consider that the expansion theta is proportional to the shear sigma, which leads to B = An and potential V (phi ) as a constant. The behaviour of these models from physical and geometrical aspects are also discussed.

An approach for identification of bridge bending stiffness distribution using improved Gaussian peak function

Bridge damage and bending stiffness deterioration can lead to a decrease in the bearing capacity of a bridge, posing significant safety concerns. To ensure the safe operation of bridges, it is crucial to accurately identify bending stiffness deterioration and assess the bridge performance. The bridge influence line (IL), which reflects the deterioration of bending stiffness, was widely used in the assessment of bending stiffness deterioration. Existing IL-based methods mostly assume a uniform reduction in bending stiffness for identification. In reality, the deterioration of bridge bending stiffness is far more complex, which causes difficulty in accurately identifying the bending stiffness distribution using the uniform reduction model. This paper proposes a novel method for identifying bridge stiffness distribution using an improved Gaussian peak function model. The improved model incorporates additional parameters, allowing for considering a wider range of stiffness variation and thus addressing the limitations of traditional models. The parameters of the improved Gaussian peak function model are estimated by minimizing the residual between the predicted deflection influence line (DIL) and the actual DIL using the Levenberg-Marquardt (LM) algorithm. This approach enables the accurate identification of bending stiffness distribution without baseline information. Numerical simulation and laboratory experiment are used to verify the effectiveness of the proposed method in identifying bridge bending stiffness distribution. A comparison between the identified and actual bending stiffness distribution curves under various forms of damage assesses the applicability of the proposed method.