Static Response Research Articles

A finite difference method on crack resistance of reinforced glass beam with non-linear adhesive

Reinforced glass beam (RG beam) is a type of structural glass member that has been developed in recent years. This RG beam consists of a glass beam to which reinforcement material, such as steel, is adhesively attached in the tensile side to improve crack resistance. The adhesive plays a critical role in the structural performance of RG beam. However, the effect of non-linear shear-slip behavior of the adhesive layer remains unclear and has been neglected in most previous studies, which can result in inaccurate estimations. To address this issue, this paper presents a finite difference model (FDM) that utilizes an explicit step-by-step method and trial-and-error iterative method for interfacial stress analysis. The model predicts the static structural response of a simply-supported RG beam that simulates the adhesive with non-linear stress-slip behavior. Furthermore, the model describes the adherend’s shear deformation in elastic. The FDM results are then compared with the finite element method (FEM), adopting discrete nonlinear connectors (springs) to simulate the adhesion, and available analytical methods. Detailed parametric studies are further conducted to investigate the influences of glass strength, load pattern, reinforcement ratio and height-to-span ratio for proposing design recommendations.

An isogeometric analysis of solar panels with a bio-inspired substrate

We in this paper propose a high-performance design using bio-inspired metamaterials for multilayered perovskite solar cell (MPSC) plates. The static bending and free vibrational responses of the newly designed MPSC panels with the presence of the triply periodic minimal surface (TPMS) substrate are subsequently investigated numerically. The displacements of the present plate model are then approximated by five-variable higher-order shear deformation theories (HSDTs). The weak forms are established for both the static bending and free vibration problems and subsequently derive the discrete forms using the NURBS-based isogeometric approach. To enhance the operational efficiency of solar panels in challenging environments, we integrate advanced lightweight architectures based on bio-inspired TPMS structures as a substrate layer into the original solar panel design. In this research, three widely employed TPMS structures: Primitive, Gyroid, and I-graph and Wrapped Package-graph (IWP), are examined in conjunction with two functional grading patterns implemented through the thickness direction. For the first time, the static bending performance of MPSC plates integrated into a TPMS-based substrate layer and subjected to wind pressure as well as thermal conditions is comprehensively studied. In addition, the influence of several significant factors on the free vibration behavior of MPSC plates is also elucidated. The findings show a promising and intriguing design avenue, particularly in the application of high-performance metamaterials to address contemporary challenges in renewable energy usage and environmental protection.

Амплитудно-частотные характеристики виброзащитной системы сиденья с трехсегментной статической силовой характеристикой и участком квазинулевой жесткости

Vibration protection for heavy equipment operators is important. Exposure to vibration is harmful to health. Vibration protection seats are used for protection. Reliable passive systems with quasi-zero stiffness are promising. For the developed design of the seat on the basis of parallelogram mechanism, spring, cable and rollers, the study of vibration-protective properties is carried out. The design scheme has been developed, key parameters have been selected, and their study on vibration protection parameters has been carried out. The static force response was approximated by three linear segments with a horizontal mean. The known dynamic model describing forced oscillations of the mass was used. The displacement of the base was given by a harmonic function. Vibration protection systems with three-segment and with one-segment static force response were compared. The comparison was carried out in terms of transmission coefficients, accelerations and suspension displacement. The results of the computational experiment are presented in the form of graphs: amplitude-frequency characteristics in the form of transmission coefficients in acceleration and displacement, at different amplitudes of base vibrations, damp-ing and stiffness coefficients. Dependences of average values of transmission coefficients in the investigated frequency range are given. Vibration damping is effective when the maximum suspension travel does not exceed the middle section of the static characteristic. The most effective vibration damping, according to the average value of the acceleration transfer coefficient, is achieved at minimum, and for a single-segment characteristic — zero values of the stiffness coefficient. The presence of extreme segments in the characteristic significantly increases the average values of the accelera-tion and displacement transfer coefficients of the suspension. Seat vibration protection systems in real conditions should have a limitation of suspension displacement for ergonomic reasons. The values of the stiffness coefficients of the extreme parts of the static force response, according to the criterion of minimizing the average value of the acceleration transfer coefficient, should be minimized. To substantiate the optimal values of the stiffness coefficients of the extreme sections of the characteristic and viscous friction coefficients, it is advisable to conduct additional studies under step and stochastic impacts.

Nonlinear bending and buckling analysis of 3D-printed meta-sandwich curved beam with auxetic honeycomb core

The present study investigates the static responses of a 3D-printed polymeric meta-sandwich curved beam with an auxetic honeycomb core, including buckling and nonlinear bending behavior. After extracting the mechanical properties of the core material, the nonlinear governing equations for the curved beam under two types of loading, namely uniform transverse and axial mechanical loads, are derived based on the first-order shear deformation theory and von-Kármán nonlinearity. After examining the convergence of the static responses and validating them by using the Ritz method, the influence of various geometrical parameters of the 3D-printed meta-sandwich structure on the results of buckling and nonlinear bending behavior as well as their optimization using the response surface methodology (RSM) are studied. The results indicate that by increasing the thickness-to-length ratio of the inclined wall, the critical load of the auxetic sandwich beam is enhanced due to improved stiffness, and its lateral displacement declines. The amount of buckling load increase from m = 0.005 to m = 0.1 is 1.92% in the clamped-clamped boundary conditions, 1.56% in the clamped-simply supported conditions, and 1.2% in the simply supported-simply supported edge conditions. Therefore, by selecting appropriate geometrical parameters for the core cells, the occurrence of instability can be delayed, leading to enhanced buckling resistance of the structure. Furthermore, optimizing the results by using the RSM showed that the highest critical load value and the lowest transverse deflection value of the meta-sandwich curved beam are obtained when θc = 15, n = 1, m = 0.1, 2θ0= 30, b = 0.07, λ= 1.1, h/h2= 1.2, and the edge conditions are of the clamped-clamped type.

Path integration solutions for stochastic systems with Markovian jumps

A path integration method for solving Markovian jump stochastic dynamical systems is presented. The Markovian jump process and the state vector of the system are combined into a new augmented state vector. The randomness of the Markovian jump is modeled by a stochastic process, which is merged with the stochastic perturbations to form the stochastic source affecting the evolution of the augmented system. Then a probability mapping is constructed, mapping the probability space of the stochastic source to the short-time transition probability density function of the augmented system. By solving this probability mapping, the short-time transition probability density function of the path integration method is obtained, thus a path integration method is customized for Markovian jump stochastic systems. Finally, a hydraulic relief valve system is used as an application example to demonstrate the availability of the path integration algorithm. The results suggest that the pre-compression parameters and coefficient of restitution of the plug can induce stochastic P-bifurcation phenomena. When the above two parameters are small, the system becomes unstable with the parameters taken in this example. Monte Carlo simulations prove that the proposed method effectively captures the transient and stationary responses of Markovian jump systems.

Exploring hopfion stability and dynamics in ring-like structures

Using numerical simulations, we explore the static and dynamic response of hopfions to an external magnetic field in cylindrical and toroidal nanorings. Results evidence that the nucleation and stability of hopfions are intricately linked to geometry. When including an external field, due to the Dzyaloshinskii–Moriya interaction and the field direction-dependent annihilation mechanism, the hopfion displays distinct behavior under magnetic fields pointing along opposite directions. We have also obtained the spin wave resonance modes of the magnetization patterns nucleated in both nanorings and show the impact of geometry on the suppression of some of them. The interplay between curvature, topology, and magnetization dynamics opens new possibilities toward hopfion-based spin torque oscillator fabrication.

Static deformation of a two-phase medium consisting of a rigid boundary elastic layer and an isotropic elastic half-space induced by a very long tensile fault

An analytical model is proposed to determine the static response of a multi-layered medium comprising of an underlying isotropic (ISO) elastic half-space that is in welded contact with an isotropic (ISO) elastic layer of uniform thickness H with a rigid boundary, induced by a tensile dislocation embedded in the layer. The integral expressions for stress fields are obtained by using the airy stress function. These integrals are calculated approximately, using Sneddon’s approach, by substituting the terms under the integral sign with a finite sum of exponential expressions. It is studied numerically and graphically how stresses vary with the change in the epicentral distance for different source locations embedded in the layer. The effect of the rigidity ratio is also analysed on the stress field. To examine the impact of the internal boundary, the stress fields in the layered and uniform half-spaces are compared graphically.

Detailed development and validation of a finite element model for studying the entire spinal vibration behavior within a seated human body

Studying the vibration behavior of the entire spine can guide the design of seat comfort and vibration safety. However, due to simplification of traditional biomechanical models, very few studies have analyzed in detail the vibration behavior characteristics of the entire spine inside a seated human body. Therefore, this study aimed to provide guidance and reference for spinal modeling and biomechanical research in ergonomics. A developed finite element model of three-dimensional seated human body was validated and adjusted based on anatomical data of human spine in detail. Static analysis, modal analysis and random response analysis (under vertical excitation between 0 and 20 Hz at 1 m/s2 r.m.s.) were conducted. The range of motion, modal frequencies and the tri-axial transmissibility of the developed models matched well with experimental results. In the vertical resonance mode, the entire spine contained both vertical deformation (60% of the total) and vertical displacement (40%), in addition, the cervical spine, especially the lumbar spine, also contained bending deformation which could alleviate the impact, but led to complex alternating stresses, increasing the risks of the spinal injuries under vertical whole-body vibration. From the bottom to the top of the spine, the frequency distribution of vertical transmissibility became steeper, the peak value increased, and the number of peaks decreased. This study provided new insights into the vibration behavior and frequency response of the entire spine inside a seated human body for improving seat comfort and vibration safety.

Characterization of the static and dynamic response of a post-tensioned concrete box girder bridge with vertically prestressed joints showing vertical deflections due to concrete creep deformation

Characterization of the static and dynamic response of a post-tensioned concrete box girder bridge with vertically prestressed joints showing vertical deflections due to concrete creep deformation

Monitoring of static and vibration responses of laminated composite materials using integrated carbon nanotube fibers

Carbon nanotube fibers or yarns (CNTYs) are lightweight, stiff, strong, electrically, and thermally conductive fiber-like materials that exhibit a piezoresistive response and could be integrated in glass-fiber/epoxy laminated composite materials to measure strain and to detect damage. Aiming at extending the scope of previous studies, this work is about the piezoresistive response of CNTY sensors integrated in composite laminates of industrial interest, accounting for interactions between the CNTY and the typical heterogeneous, anisotropic surrounding media, including the effects induced by the curing process of the composite matrix. This study reports experimental results on the mechanical response of laminated composite materials under quasi-static and vibration loading monitored using integrated CNTY sensors. A combination of CNTY sensor configurations and experimental setups were used to monitor the deformation and strains among the various layers of the laminated composites. As the laminated composites were mechanically loaded under quasi-static four-point bending, the CNTY sensors captured instantaneously the deformation as demonstrated by the change in their electrical resistance. Also, as the laminated composites were subjected to sinusoidal loading at specific frequencies, the integrated CNTY sensors were able to capture the loading cycles exactly including durations and peaks. Integrated sensing using CNTYs may offer a highly adaptive, practical, and sensitive structural monitoring method for a variety of applications.

A comparative analysis of numerically simulated and experimentally measured static responses of a floating dock

ABSTRACT Two numerical methods, dynamic and static analyses, are proposed to calculate the static responses of a floating dock under different ballast water distributions. Model-scale experimental tests were conducted to compare with these numerical methods. The dynamic analysis includes a 6-degree-of-freedom (6-DOF) model, a hydrostatic force model and a hydrodynamic force model to simulate the dock's freely floating processes. The dock's equilibrium position is identified when the difference in the dock’s motions between two successive time steps is below a specified tolerance value. In the static analysis, the static equilibrium equations in draught, heel, and trim are solved using the Newton-Raphson method. Both dynamic and static results of the draughts at the four corners, heel, and trim are in good agreement with the corresponding experimental results, which shows the reliability of the proposed numerical methods. Moreover, the static analysis exhibits quicker convergence, requiring fewer iteration steps than the dynamic analysis.

Static response of wind turbine blades: Comparison of low- and high-fidelity numerical models

As wind turbine blades become longer and more flexible, the structural models employed in current aeroelastic simulation tools, usually based on beam formulations, are challenged. Effects previously considered negligible in the response of these beam-like structures might now become significant to obtain accurate predictions of their behaviour. To assess this, a test matrix covering key geometric and material characteristics of wind turbine blades is defined and three test cases are analysed as an initial stage of this study. For each case, the static deflection of the beam model from the aeroelastic tool HAWC2 is compared against higher-fidelity shell/solid finite element models. Three structures are studied: an isotropic box beam, a composite box beam and a 12.6 m wind turbine blade from DTU. A good match is observed for the box beam test cases, which study the effects of out-of-plane and distortion warping and bend-twist coupling. Important aspects of high-fidelity models (such as end effects) are highlighted. The study of the DTU 12.6 m blade shows a significant difference (15%) in the torsion natural frequencies of the beam model, though a good agreement in twist angle under torsional loading. More pronounced differences in twist angle are observed when a load distribution based on the steady state response is applied, likely resulting from challenges in modelling complex structural features and three-dimensional effects.

Static response of vertically loaded pile in inhomogeneous soil

In this study, an analytical model is developed to obtain the static response of the vertically loaded pile in the inhomogeneous soil with arbitrary properties varying along the depth. The soil displacement is expressed by the product of the axial displacement function and the shape function attenuating with the distance from the pile periphery. Through the minimum potential energy principle, the governing equations are established for the axial displacement function and the shape function. The governing equation for the shape function is independent of soil properties and it can be explicitly solved. The governing equation for the axial displacement function contains variable coefficients due to the inhomogeneity of soil and it is solved using the weighted residual method. An iterative procedure is introduced to implement the solution. The proposed model is validated by comparing the present solutions with those obtained by the available methods. The parametric study shows that the pile head stiffness is affected by the distribution of soil shear modulus heavily, in which the average shear moduli are the same for these distributions. Moreover, the relationship between the pile head stiffness and the pile slenderness ratio for a floating pile is different from that for an end-bearing pile.

Coupled DEM/CFD analysis of impact of free water on the static and dynamic response of concrete in tension regime

In this paper, the quasi-static and dynamic behavior of partially fluid-saturated concrete under two-dimensional (2D) uniaxial tension at the mesoscale is investigated numerically. It was calculated what effect the free pore fluid content (gas and water) had on the fracture process and strength of concrete in a tension regime. An improved pore-scale hydro-mechanical model based on DEM/CFD was used to simulate the behavior of fully and partially fluid-saturated concrete in quasi-static and dynamic conditions. The foundation of the fluid flow idea was a network of channels in a continuous area between discrete elements. In very porous, partially saturated concrete, a two-phase laminar fluid flow was proposed. To track the liquid/gas content, the position and volumes of the pores and cracks were considered. Numerical simulations of bonded granular specimens of a simplified spherical mesostructure that resembled concrete were carried out under dry and wet circumstances for two different strain rates. Investigations were conducted on the effects of fluid pore pressures, fluid saturations, and fluid viscosities on the strength and fracture process of concrete. The quasi-static tensile strength dropped nonlinearly with increasing fluid saturation and fluid viscosity during fluid migration through pores and cracks which contributed to a promoted fracture process. However, during rapid dynamic tensile deformation, a fracture process attenuated due to a fluid migration constraint from insufficient time to exit the pores. It caused the dynamic tensile strength to rise nonlinearly as fluid saturation and fluid viscosity increased.

Static and dynamic responses of buried steel pipe under truck load: An experimental study

The behavior of a buried pipe under static and dynamic loading conditions has been investigated through full-scale field tests. A plain steel pipe with a diameter of 762 mm was gauged at the outer surface of two pipe sections. A dump truck was employed for the static and dynamic loading tests. Under static loading, the measured pipe strains increase with increasing axle load and decreasing cover depth. The measured strains under dynamic loading show three peaks, which correspond to the times at which the front, middle, and rear axles, respectively, reach the pipe centerline. The offset loading pattern produces greater strains than the non-offset one while keeping the axle load constant under both static and dynamic loads. It is discovered that the pipe strains caused by each truck axle vary with truck speed. Since the load transfer is influenced by a number of factors, including the truck load, road roughness, truck speed, and others, a moving truck load does not always result in higher pipe strains as compared to a static load. The complexity of dynamic pipe responses can be explained in part by a single-degree-of-freedom (SDOF) model.

Chirality tuning and reversing with resonant phase-change metasurfaces.

Dynamic control of circular dichroism in photonic structures is critically important for compact spectrometers, stereoscopic displays, and information processing exploiting multiple degrees of freedom. Metasurfaces can help miniaturize chiral devices but only produce static and limited chiral responses. While external stimuli can tune resonances, their modulations are often weak, and reversing continuously the sign of circular dichroism is extremely challenging. Here, we demonstrate the dynamically tunable chiral response of resonant metasurfaces supporting chiral bound states in the continuum combining them with phase-change materials. Phase transition between amorphous and crystalline phases allows for control of chiral response and varies chirality rapidly from -0.947 to +0.958 backward and forward via the chirality continuum. Our demonstrations underpin the rapid development of chiral photonics and its applications.

Characteristics and analysis of static strain response on typical asphalt pavement using fiber Bragg grating sensing technology

To study the real internal strain response of asphalt pavement and provide crucial data for optimizing pavement design. By burying the fiber grating sensors on site, the strain tests of four asphalt pavement structures under different working conditions were carried out, and the results showed that the static strain time curve is viscoelastic and conforms well to the Bugers model, and the fitting coefficient of determination is 0.98. The strain response of the asphalt surface courses of the four pavement structures under static load shows a double hump variation with the transverse position, with peaks occurring directly beneath the wheel load center. The transverse strain fluctuated between tension and compression, mirroring changes in the lateral position. While longitudinal strains, always tensile, were symmetrically aligned with the centerline of the longitudinal sensors, this pattern differed notably from that of the transverse sensors. In the base layers, the strain profile typically presented a single peak, located at the wheel gap, underscoring a critical area of stress concentration. Numerically, the peak strain of asphalt surface course is larger than that of base course. The most unfavorable loading position of the base course occurs at the wheel gap of the lower base course. The most adverse loading position of the surface course appears at the wheel load at the bottom of the upper or middle course. The research results can provide data support for improving the design method of asphalt pavement.

Magnetic proximity sensor based on colossal magnetoresistance effect

Magnetic proximity sensors are widely used to determine the distance to ferromagnetic or highly conductive materials and to investigate their shape or to detect their motion. In this study, a magnetic proximity sensor incorporating a cylindrical permanent magnet and a scalar magnetic field sensor (measuring the magnitude of the field independently from its orientation) based on the phenomenon of colossal magnetoresistance in manganite films is presented. Two versions of the sensor, one with a solid cylindrical magnet and one with a hollow cylindrical magnet, were constructed and tested. A steel plate and a superconducting YBaCuO disk were used to investigate the static response. The measurements of the dynamic behavior were carried out with rotating steel and duralumin plates. The results of the static experiments and modelling showed that the output response (change of the magnetic field) of the sensor had a hyperbolic relationship with the distance between the sensor and the measured object. This change was positive for solid cylindrical magnet design and negative for hollow cylindrical magnet design when the target was steel. In contrast, the solid magnet-based sensor produced a negative signal for the superconducting material, while the hollow cylindrical magnet sensor showed a positive signal. It was found that the main features of the dynamic response of the proximity sensors can be explained by the magnetization of steel and the induction of eddy currents in duralumin. The present study demonstrates that the proposed magnetic proximity sensor can be successfully used to search for ferromagnetic objects, investigate the properties of superconductors and detect the motion of non-ferromagnetic conductive materials and can have advantages over conventional magnetic proximity sensors.

Experimental study on effect factors of wind-induced response of flexible photovoltaic support structure

In recent years, the proportion of flexible photovoltaic (PV) support structures (FPSS) in PV power generation has gradually increased, and the wind-induced response of FPSS has gradually been noticed. In this study, the wind-induced responses of a FPSS with a single row and a single span were investigated by aeroelastic model wind tunnel tests. The effects of structural parameters of FPSS were systematically analyzed on 17 test cases (including inclinations, module spacings, initial tensions, spans and module sizes), and the variation of flutter critical wind velocities with structural parameters was obtained. The experimental results show that the most unfavorable wind direction is 180°. The static wind-induced response is mainly affected by the module inclination angle, module spacing and the structure span. The vortex-induced vibration (VIV) of the test models occurs in some specific test cases at low wind velocity, and it can be easily suppressed by changing the structural parameters. The flutter occurs at both directions of 0° and 180° when the wind velocity increases to a critical value. With the increase of module inclination angle, the flutter critical wind velocity of FPSS decreases first and then increases, and the most unfavorable module inclination is 25°. It is beneficial for suppressing the structure flutter by increasing the cable initial tension and the module spacing, and decreasing the span of the FPSS. Changing the module size will affect the aerodynamic characteristics and structural frequency of the structure, thereby affecting the wind-induced vibration of the structure.

Post-dynamic transformation from α to β phase and reverse transformation in Ti-10V-2Fe-3Al alloy during interrupted hot deformation

Interrupted hot deformation tests were carried out to study the phase transformation behavior of Ti-10V-2Fe-3Al alloy during isothermal holding after deformation. The results show that post-dynamic transformation (post-DT) from α to β phase occurred first during isothermal holding and the meta-β phase retransformed to α phase after a long holding time. This phenomenon is quite different from α+β titanium alloys in which only reverse transformation (RT, βα) took place during isothermal holding. Microstructure evolution of β-matrix was also investigated and it was found that static recovery was the main softening mechanism. Furthermore, phase transformation has a great influence on the static softening and mechanical response of interrupted hot deformation. Due to the occurrence of post-DT, the yield strength of reloading pass reduced and became lower than the initial pass when the holding time exceeds 900 s. And significant static softening was achieved. The driving and opposing force for post-DT and RT were derived and compared based on thermodynamic analysis. Since the deformation and holding temperature is close to β-transus temperature, post-DT has a lower energy barrier which can be easily overcome by stored energy. This may explain why the phase transformation direction in Ti-10 V-2Fe-3Al alloy is opposite to that in α+β titanium alloys during isothermal holding.