Bending Strain Energy Research Articles

Preparation and thermal performance testing of diatomite-modified asphalt pavements

In this study, the efficacy of diatomite as a modifier in asphalt pavements is thoroughly examined. The research primarily focuses on evaluating the thermal performance of asphalt mixtures modified with varying diatomite contents. Key findings indicate significant improvements in the rutting resistance, with the dynamic stability of the 15% diatomite mixture being 3.4 times higher than the control mixture. Additionally, the 10% diatomite mixture shows a 20% increase in bending strain energy density, enhancing low-temperature performance. However, a diatomite content beyond 10% tends to diminish these benefits. Fatigue life at 10% diatomite content is improved by 18%–24%, demonstrating the material’s potential in extending pavement longevity. Water stability tests also reveal notable improvements, with the 15% diatomite mixture exhibiting a 15% increase in tensile strength ratio post-water conditioning. These results collectively establish diatomite as a cost-effective and efficient modifier for asphalt pavements, promoting enhanced durability and performance.

New insights into folding tape-spring

The tape-spring is widely used in aerospace, mechanical, and civil engineering due to its unique mechanical properties and compact size. This paper aims to establish a new analytical model to more accurately predict the folding behavior of the tape-spring, including the geometric configuration, folding moment versus longitudinal curvature curve, peak moment, and propagation moment. This model comprehensively considers the influence of stretching strain energy and bending strain energy on the total strain energy, and determines the folding behavior of the tape-spring through the minimum energy principle. The proposed analytical model was compared with Wuest’s model, Yee’s model, and Yao’s model. Experiments of tape-springs made from two different materials were utilized for validation. The study shows that the proposed model has the highest prediction accuracy compared with the classical models, with the error of approximately 10%. The reason for the significant difference in the prediction results between the proposed model and Yao’s model was given, and the relationship between stretching strain energy and bending strain energy during the folding process of the tape-spring was analyzed. The proposed model has broader applicability than classical models and provides new insights and solutions for accurate prediction of the folding behavior of the tape-spring.

Ground fracturing of multi-strata for strong ground pressure control in extra-thick coal seams with hard roofs: Numerical simulation and case study

Strong ground pressure in the mining field is the key factor restricting safe mining of hard-roof mining areas. A hard roof combines high strength with a large breakage step, and the large breakage area would easily cause ground pressure disasters in the working face with gradual breakage of multi-hard rock strata. The study investigated the characteristics of the dynamic hazards under multi-hard rock strata conditions. The method of graded ground fracturing of multi-hard rock strata was proposed to control the ground pressure, and the characteristics of the bending strain energy release of the rock strata breakage and instability under the condition of equivalently decreasing the thickness of the strata by ground fracturing were theoretically analyzed. A numerical simulation model of weakening in multi-strata rock formations by fracturing was established, and the structural characteristics of rock strata breakage under the ground fracturing effects were analyzed. The results showed that the breakage characteristics of the overlying hard roofs were altered by ground fracturing, the bearing properties of the fractured rock strata were drastically reduced, while the effect of the breakage and destabilization of the rock strata was subsequently weakened. The ground fracturing practice of the L1 and L2 hard rock strata in the Tashan Coal Mine, China, taken as a case study, revealed that the cracks extension length reached approximately 220 m, and the crack’s width was 30 ∼ 120 m. During the working face was mined in the area covered by the cracks, the average supports resistance was reduced by 21 %, the rate of rib spalling was reduced by 23 %, greatly alleviating the intensity of ground pressure in the working face. The application of ground fracturing technology to multi-hard rock strata effectively weakened the hard rock strata, improving the ability of ground pressure control.

Modeling compliant bistable mechanisms: An energy method based on the high-order smooth curvature model

This paper applies an energy method based on the high-order smooth curvature model to address the challenges of kinetostatically modeling the complicated nonlinear post-buckling behavior of inclined compliant beams. The proposed energy method is grounded in the principle of minimum strain energy, implying that the total strain energy is minimized at the equilibrium configuration. In this work, the high-order smooth curvature model is adopted to accurately model the bending strain energy of large deformation beams. Subsequently, the Lagrange multiplier method is employed to ascertain the minimum of strain energy while concurrently determining the corresponding tip loads. Additionally, the deformation shape and maximum stress are determined via the smooth curvature model. The proposed method is introduced for the first time in modeling compliant bistable mechanisms, and it is proven that the method can be used for modeling compliant beams with inclined angles ranging from 0 to 90 degrees. Following the modeling, finite element analysis and experimental tests are conducted to verify the accuracy of the proposed energy method. A comprehensive comparative analysis between proposed method and existing methods is conducted. The comparison results prove that the model is more computationally efficient without compromising modeling accuracy The proposed modeling method can not only be used for modeling compliant bistable mechanisms but also has extendable applications in modeling initially-curved compliant beams, contact-aid design problems, and distributed load problems.The present work not only advances the practical application of the proposed energy method but also lays the foundation for future research in modeling compliant mechanisms.

Research on the Dynamic Characteristics of Cantilever Rotor System With ISFD

Aiming at the common vibration problem of the cantilever rotor system and the nonlinear problem of traditional squeeze film damper (SFD), an integral squeeze film damper (ISFD) for the cantilever rotor system was proposed based on the traditional SFD. In order to investigate the effect of the ISFD on the dynamic characteristics of the cantilever rotor system, the vibration reduction experiment of the rotor system was carried out. The mechanical model and finite element model of the cantilever rotor system were established. The first‐order critical speed, strain energy, stability, and steady‐state response of the cantilever rotor system were numerically analyzed. Experimental research on the vibration reduction of the cantilever rotor system by the ISFD under different unbalance conditions and different rotational speed conditions was carried out on the test rig of the cantilever rotor system. The results showed that the ISFD has remarkable performance, which can reduce the bending deformation and strain energy of the rotating shaft, increase the logarithmic decay rate, and improve the overall stability of the system. Under various working conditions, the ISFD can effectively suppress the unbalanced vibration of the rotor and the shaft center displacement of the rotor, and the amplitude of the rotor system at the working frequency (1X) is greatly reduced.

A New Bottom-Hole Assembly Design Method to Maintain Verticality and Reduce Lateral Vibration

Well deviation is a prevalent problem in deep oil and gas exploration, leading to a significant increase in drilling costs. The conventional bottom-hole assembly (BHA) anti-deviation design method does not consider the impact of the BHA structure on lateral vibration. This paper proposes an integrated BHA design method that takes into account both anti-deviation and vibration reduction. This method evaluates the BHA’s anti-deviation ability using the drilling trend angle. A negative value of the drilling trend angle indicates that the BHA can correct well deviation. A finite element linearized dynamics method is used to evaluate the lateral vibration intensity of the BHA. This method involves calculating the bending displacement caused by mass imbalance and then determining the magnitude of the bending strain energy based on this displacement. The structural factors affecting the anti-deviation ability and potential lateral vibration intensity of pendulum BHAs and bent-housing mud motor (BHMM) BHAs were studied, and field tests were conducted for verification. The research shows that for pendulum BHAs, the factor that has the greatest impact on anti-deviation ability and vibration intensity is the distance from the stabilizer to the drill bit. For BHMM BHAs, the length of the short drill collar has a significant impact on the vibration intensity. Compared with current design methods, the mechanical specific energy (MSE) of the single stabilizer pendulum BHA decreased by 12%, while the MSE of the BHMM BHA decreased by 26.4%. Both decreases indicate a reduction in vibration intensity. This study will help to further increase drilling speed while preventing well deviation.

Modeling the flexural rigidity of spunlace nonwoven fabrics

Nonwoven fabrics, especially spunlace varieties, find application across diverse fields. This study presents an analytical model that utilizes the energy method, factoring in bending and torsion strain energies. This model is integrated with the dynamic recursive splitting (DYRES) algorithm to predict the flexural rigidity by estimating fiber-to-fiber contacts within spunlace nonwoven fabrics. The input parameters for this proposed model encompass the number of bending couples, the bending stiffness of fibers, and the orientation characteristics of spunlace nonwoven fabrics. To validate the predictive capability of the model, six samples with varying fiber types, basis weights, and thicknesses were fabricated. A comparison between experimental and theoretical values reveals a consistent trend but with overestimated values in both the machine direction (MD) and cross-machine direction (CD). Through the utilization of two coefficients (0.7854 and 0.7823) to refine the presented model, an average relative error of 4.22% and 8.92% was achieved for the MD and CD directions, respectively. This research proposes a theory that utilizes fewer parameters compared to other studies in the field of nonwoven textiles. The proposed approach offers a more convenient and accessible method for obtaining these parameters, as well as determining the bending stiffness of the fabric. Moreover, advanced and more suitable techniques, including knot theory and image processing, have been employed to obtain accurate parameter measurements. This work is believed to lay the foundation for future investigations into the mechanical behavior of nonwoven fabrics.

Design and optimization of lightweight bending strain energy harvesters using irradiation cross-linked polypropylene ferroelectret

In this work, a concept for bending strain energy harvesting with lightweight ferroelectrets subject to metallic host structures is proposed. The energy harvester (EH) works with the ferroelectret irradiation cross-linked polypropylene (IXPP) and uses the piezoelectric δ 33-mode by transferring in-plane bending strain energy of a host structure to a compression of an IXPP stack. This is achieved with a simple and lightweight transmission made of structural steel. In this way, a high ratio of generated power per used EH mass can be achieved, being the main design goal of this paper. To demonstrate this, miniature EHs as unit cells for larger EH systems are investigated. The strain magnitude of the excitation in an aircraft wing of at 1.5 Hz from previous work is partly taken into account for calculations. In an analytical modeling approach, the energy conversion abilities of the presented concept is compared to concepts using lead zirconate titanate ceramics to stress the usefulness in cases where strain energy is the prominent source of vibration energy. Further, an optimization algorithm is presented for a static and a dynamic case without a host structure and for a dynamic case with an aluminum host structure. The optimized power output and power output per total EH mass for the three cases is calculated to and , 0.7 mW and 80 mW kg−1 as well as (at 1 N excitation magnitude) and (at 1 N excitation magnitude) respectively. Finally, experimental results for case three are presented to validate the model of the proposed and optimized EH topology up to 500 Hz. The results further show a good mechanical reproducibility of the measured transfer behavior and a fairly good reproducibility of the mechanical-electrical results due to deviations in material properties. A comparison of the model with the experimental results shows a good agreement. Therefore a linear ferroelectret model appears to be suitable to predict the system behavior in lower and higher frequency ranges as well as for high ferroelectret material strains. The optimized EH provides a comparably high ratio of power output per mass when added to a structure like an aircraft which is shown in a comparison to other research works. The performance in a real application can be further improved to 52 mW within a 1 m2 area using a clustering approach, discussed in the paper. Large deformations of lightweight structures like aircraft wings at low and high frequencies can thus be exploited to provide enough electrical power decentrally for low-power consumers.

Research on the spatial structure of environmental art design based on topology optimization and morphology optimization

Abstract In this paper, firstly, a mathematical model of spatial structure topology optimization is constructed, and sensitivity analysis, approximate model fitting and optimization finding strategy for topology optimization in environmental art design are carried out. Secondly, morphological optimization is carried out from the morphological model of spatial structure and the urban thermal environment through urban environmental art design and morphological optimization. Finally, the optimization of structural morphology is explored under static multiple working conditions and single-objective optimization, considering the dynamic frequency of the structure. The results show that as the optimization proceeds, the total strain energy, axial strain energy and bending strain energy of the space structure increase to 0.45, 0.52 and 0.5 of the initial structure, respectively. At the 9th iteration of optimization, the performance is at its peak. The load-carrying capacity is 1.59 times that of the 35th step and 1.5 times that of the initial structure. The research results of this paper can provide references and guidance for structural design and optimization in the fields of environmental art design and urban planning.

Design and analysis of ultra-low moment noise flexure pivot in space gravitational wave detectors

To control the pointing accuracy of the telescope in the space gravitational wave detector at the nano-radian level, it is essential to design a flexure pivot with extremely low rotational moment nonlinearity during rotation. This study derives the theoretical equation of the nonlinear rotational moment of flexure pivot based on the beam bending strain energy equation and completes the design of ultra-low moment noise flexure pivot by integrating the structural form of conventional cross-spring flexure pivot. The nonlinear moment noise distribution in the frequency domain of three kinds of flexure pivots is then compared regarding TianQin’s circular high orbits. Then the relevant finite element simulation analysis will be performed for the flexure pivot structures, respectively, to ensure the accuracy of its rotational stiffness model and verify the correctness of nonlinear moment theory optimization through physical experiments. The results show that the optimized flexure pivot can effectively reduce the nonlinearity, and basically meet the nonlinear moment requirements in space gravitational wave detection.

Determining the Reasonable Completed Bridge State of a Self-Anchored Suspension Bridge with a Spatial Cable System Based on Minimum Bending Strain Energy: An Analytical Algorithm

Determining the Reasonable Completed Bridge State of a Self-Anchored Suspension Bridge with a Spatial Cable System Based on Minimum Bending Strain Energy: An Analytical Algorithm

A Novel Method for Deflection Calculation of Reinforced Concrete Stair Slabs considering Step Stiffness

Stair slabs are some of the most common structural members with zigzag shapes in various buildings. However, the calculated deflection is usually overestimated during the design of stair slabs. In this article, the overestimated deflection is amended by utilizing step stiffness. To this end, it is assumed that the stress distribution of a unit cell in stair slabs is linear or bilinear under a constant bending moment. Stair slabs can be approximately regarded as flat slabs to derive the equivalent thickness based on the same bending strain energy. Subsequently, finite element (FE) models are established to verify that the obtained equivalent thickness can be applied to reinforced concrete (RC) stair slabs. To improve computational efficiency, the normalized models of stair slabs are adopted for further analysis. On this basis, a novel design method is proposed considering step stiffness for RC stair slabs. Furthermore, numerical examples are presented to compare the improved design method with the FE method and the conventional method. The results demonstrate that the design method considering step stiffness can not only ensure structural safety but also reduce concrete and steel consumption, making the design of stair slabs more economical and reasonable.

Determining the hanger force of the suspension bridge with short extended spans: An analytical algorithm

Single-main-span suspension bridges with short extended spans usually combine significant stiffness with high economic efficiency, making them lucrative as railway bridges. However, short extended spans induce negative side hanger forces according to the conventional continuous multiple-rigid-support beam method (CMRSBM). Therefore, the support reaction of the rigid support cannot be directly used as a hanger force, thus necessitating a new solving method for hanger force assessment. This study proposes a calculation method for hanger force optimization considering the live load effect for a single-main-span suspension bridge with short extended spans. Under the combined action of dead and live loads, we optimize the hanger force to utilize the main beam material economically. It is noteworthy that the optimized hanger forces are not equal to those obtained by the CMRSBM. Therefore, the bending strain energy of the main beam is no longer the minimal, and the corresponding geometry of the main beam under the dead load differs from that at the completed bridge state. We incorporate specified hanger forces into the finite element method (FEM) to facilitate further calculation of the suspension bridge after hanger force optimization. Thus, the main beam deformation and the processing geometry of the main beam during manufacture are then estimated. The proposed method is verified by applying it to an exemplary suspension bridge. It is found that the optimized hanger forces are uniform. Under the action of dead and live loads, there are two flat bending moment envelopes for the entire main beam: one in the upper and one in the bottom. This indicates an efficient use of the material, which agrees with the initial goal. The main beam displacement manifests itself as the downwarping of the extended spans and arching of the main span. Therefore, the main beam should be pre-arched or pre-deflected during manufacturee.

Study on the Low Temperature Cracking Mechanism of Steel Slag Asphalt Mixture by Macroscale and Microscale Tests

Steel slag’s physical and mechanical properties are close to natural gravel, which can replace natural aggregate with paving asphalt mixture pavement. Based on macro- and microscales, it is necessary to study the low-temperature cracking characteristics of steel slag asphalt mixture (SAM). This paper aims to study the low-temperature cracking characteristics and influence mechanism of steel slag asphalt mixture by macro- and microscale tests. This article analyzes the strain field distribution and cracks propagation law of SAM at low temperatures by the three-point bending test combined with digital image correlation (DIC). The microscopic pore characteristics of SAM were studied by nuclear magnetic resonance (NMR). Based on fracture mechanics and weight function theory, the variation law of the stress intensity factor at the crack tip of the asphalt mixture with crack propagation is derived. The correlation between microscopic pores and low-temperature cracking characteristics of asphalt mixture was analyzed based on the grey correlation theory. The results show that SAM has more small and less large pores, and its total porosity is lesser than that of the basalt asphalt mixture (BAM). The initial elastic stage of SAM resisting bending deformation is longer than that of BAM, the bending strain energy density (dW/dV) is larger, and the crack penetration is slower. The horizontal strain energy density (DE) of SAM is greater than BAM, and the crack tip stress is greater. The porosity correlates well with the low-temperature crack resistance of the asphalt mixture.

Research on new integral squeeze film damper vibration control of micro turbojet engine at high speed

Abstract In view of the problem that the vibration of the centrifugal impeller of the compressor exceeds the standard when a micro turbojet engine crosses the first-order critical speed, this research proposes a vibration control technology for the engine rotor system based on the new integral squeeze film damper (NISFD) according to the unique structure and assembly characteristics of the rotor bearing seat of the micro turbojet engine. Through numerical analysis and experimental research, the dynamic characteristics of NISFD are analyzed, and the vibration reduction mechanism of NISFD is revealed. The engine test verification based on NISFD is carried out. The results show that NISFD has good damping characteristics, which can improve the bending stress and strain energy distribution of the rotor. The engine test proves that NISFD can well solve the problem of excessive vibration of the engine when passing through the first-order critical speed, greatly reduce the vibration level within the working speed range, and significantly improve the reliability of the engine during operation. It provides a solid theoretical basis for the design of aeroengine, and provides a reference for the practical engineering application of NISFD in aeroengine.

Mechanical Properties of Coupled Bending and Contact to Hollow Cylindrical Roller Contacts

A numerical analysis model of the hollow cylindrical roller is established by coupling the bending of the curved beam and elastic half-space contact theory. Slicing technology is applied to solve the bending deformation of every circle slice. Discrete fast Fourier transform (DC-FFT) and a conjugate gradient method are employed to solve the contact deformation and contact pressure, considering the bending effect in both radial and axial directions. The influence of hollowness on deformation, contact pressure, stiffness, and strain energy for a straight roller contacting a flat plane is studied using the numerical model. The results reveal that with the increase of hollowness, the contact pressure decreases at the end, the edge effect weakens apparently, the contact width and contact deformation increase slightly in the middle part, and the stiffness decreases. The bending deformation and strain energy increase sharply as the hollowness reaches 60%. What's more, the profile of the contact region gradually changes from "outer convex" to "inner concave" at the end, which is also validated by photographing the shapes of the static contact region under various hollowness conditions using an optical interference test.

Influence analysis of performance of semi-flexible pavement based on aggregate distribution characteristics of matrix skeleton

In this study, five different gradation types of semi-flexible pavement (SFP) were formed by changing the gradation and porosity of the matrix skeleton. The porosity and its distribution of the matrix skeleton were characterized by two aggregate distribution characteristics indexes: aggregate total area index (IA) and aggregate average area index (IAA). The specific influence relationship between independent and related changes of IA and IAA on the performance of SFP was investigated, and the influence of IA and IAA on the same performance and different performance of SFP was compared. The results showed that the effect of IA on each performance of SFP with single-particle size gradation was more significant. In contrast, the impact of IAA on each performance of SFP with continuous gradation was much more significant than its effect on single-particle size gradation. When IA and IAA were analyzed independently, the influence of IAA on the properties of SFP was much more significant than that of IA. When IA and IAA were analyzed correlatively, the properties of SFP were more influenced by IA. When IA and IAA are changed associated, the influence degree of each performance of SFP from large to small is: maximum bending strain > bending strain energy > dynamic stability = Dynamic modulus (54 °C) = Dynamic modulus (21.1 °C) > TSR > phase angle (54 °C) > residual stability > phase angle (21.1 °C). To obtain SFP with suitable high-temperature stability, low-temperature stability, and water stability simultaneously, it is suggested that the IA of the designed matrix skeleton is between 72 % and 78 %, and IAA is between 1 % and 1.8 %.

Analytical modelling of low-velocity impact response characterization of titanium and glass fibre reinforced polymer hybrid laminate composites

The low-velocity impact behaviour and energy absorption mechanisms of fibre​ metal laminates (FMLs) at different impact energy levels before the first composite failure are derived analytically using a mass–spring arrangement. Four FML layups comprise glass fibre/epoxy layers and titanium alloy Ti-6Al-4V sheets, unveiling the same total metal layer thickness. The impactor mass consequence is also predicted. The results specify that the deformation energy of FML constituents accounts primarily for the FMLs overall energy absorption, 86%–93%, and 87%–93%, with both membrane and bending strain energy, and membrane strain energy only, separately. Here, a higher percentage of energy is absorbed by FML 4/3–0.3, followed by FMLs 3/2–0.3(O), 3/2–0.4, and 2/1–0.6. FMLs are 16 % more impact resistant than equivalent monolithic titanium. Also, the predicted force history of FMLs is in good comparison with experiments at 30 J, with membrane energy only correlating well than with both membrane and bending energy. The estimated maximum force, entire energy absorption of FMLs is realistic with experiments at 30 J, 45 J, and 60 J. The predicted response of aluminium-based FMLs also matches well with experiments at various energy, preserving the presented model strength. Further, the behaviour of FMLs is to be comparable under low- and high-mass impactors. However, FMLs maximum force and energy absorption seem to be correspondingly lower and higher under a high-mass impactor. Higher impact resistance seems to be displayed by titanium- to aluminium-based FMLs. Also, the above FMLs appear to display higher total energy absorption under low- to high-velocity impact.

Effect of G-type integral squeeze film damper on the dynamic characteristics in rotor system

Abstract To solve the problems of the nonlinear damping force in the traditional squeeze film damper (SFD), a novel structure of G-type integral squeeze film damper (GISFD) based on ISFD is proposed for the first time. The finite element model and test rig of the ball bearing-rotor system are established to explore the influence of GISFD and ISFD on the dynamic characteristics of the unbalanced rotor system. The results show that both GISFD and ISFD can change the critical speed of the rotor system, reduce the bending strain energy of the shaft, and reduce the bearing dynamic load of the rotor system. Through comparison, it is found that the effect of GISFD is more obvious. The experimental results show that, compared with the unbalanced rotor system without damper, the peak-peak value of amplitude in the rotor system with GISFD and ISFD at 3000 rpm is reduced by 25.53 and 15.81%. The amplitude in the disk at the first-order critical speed is effectively reduced, and the reduction range reach 52.01 and 35.44%, respectively. GISFD has a more significant effect of suppressing unbalanced vibration, and has superior vibration damping performance when compared with ISFD.

Low-Temperature Performance of Asphalt Mixtures Modified by Microencapsulated Phase Change Materials with Various Graphene Contents

Microencapsulated phase change materials (PCMs) added to conventional ones can store excessive heat energy and reduce thermal stresses. In this study, melamine–formaldehyde resin phase change microencapsulated PCMs, with different contents of graphene (CG), were added to asphalt mixtures, in order to reduce their low-temperature cracking, induced by thermal stresses. Low-temperature and heat-conducting/storing performance of the obtained mixtures was examined via beam bending tests, semi-circular bending low-temperature performance tests, thermal conductivity tests and volume-specific heat capacity tests. Besides, the prepared asphalt mixtures’ water stability and high-temperature stability values were obtained via freeze-thaw splitting and wheel tracking tests. The low-temperature performance of PCM-modified asphalt mixtures was evaluated via their bending strain energy densities, with one of the PCM-modified asphalt mixtures, namely CGMFPCM3, synthesized by the authors, was 1.7 times higher than that of the common asphalt mixture. Although the dynamic stability of all three PCM-modified mixtures was deteriorated by 68, 50, and 20% compared to the common one, that of CGMFPCM3 still complied with the standard requirement. Thermal conductivity and volume-specific heat capacity of the asphalt mixture at 278.15 K was enhanced by 5 and 43%, respectively, after adding CGMFPCM3. It is recommended for reducing the temperature variation-induced cracking in the asphalt pavement. Thermal conductivity and volume-specific heat capacity can be used for evaluating the temperature-regulating performance of asphalt mixtures.