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Galerkin weighted residual method (GWRM) is applied and implemented to address the axial stability and bifurcation point of a functionally graded piezomagnetic structure containing flexomagneticity in a thermal environment. The continuum specimen involves an exponential mass distributed in a heterogeneous media with a constant square cross section. The physical neutral plane is investigated to postulate functionally graded material (FGM) close to reality. Mathematical formulations concern the Timoshenko shear deformation theory. Small scale and atomic interactions are shaped as maintained by the nonlocal strain gradient elasticity approach. Since there is no bifurcation point for FGMs, whenever both boundary conditions are rotational and the neutral surface does not match the mid-plane, the clamp configuration is examined only. The fourth-order ordinary differential stability equations will be converted into the sets of algebraic ones utilizing the GWRM whose accuracy was proved before. After that, by simply solving the achieved polynomial constitutive relation, the parametric study can be started due to various predominant and overriding factors. It was found that the flexomagneticity is further visible if the ferric nanobeam is constructed by FGM technology. In addition to this, shear deformations are also efficacious to make the FM detectable.

Springback is adversely affected by mechanical anisotropy in the process of sheet metal forming. In this work, an analytical method was proposed to predict the springback of the double-curved workpiece in multi-point forming process. To characterize the anisotropy of the AA7B04 aluminum plate, the plate was divided into several layers along thickness direction. And in each layer, the calculation of bending moment was done respectively based on von Mises, Hill’s 48 and Yld2004-18p yield criterion. After springback, the neutral surface curvature was calculated and the profile of the neutral surface was constructed by the Bezier surface blending method. To verify the prediction method, finite element simulation and bending experiment were performed. The results show that the predictive accuracy of the method was more accurate than that with the isotropy model. Additionally, the most accurate constitutive model to describe the in-plane anisotropy of AA7B04 aluminum was the Yld2004-18p yield criterion.

The objective of this paper is to present the study of thermal effect in the rectangular plate made of rubber, copper and glass materials using transition theory. The extension and contraction regions presented by the transition points of the differential equation in defining the deformed fields. The analysis also makes the neutral surface separating the two regions. It has been observed that with increased compressibility of materials, the value of neutral axis on the surface of tension must be concentrated on the surface compression. The value of circumferential stress has a maximum at the neutral surface of the rectangular plate made of rubber material in comparison with rectangular plate made of copper and glass materials. With the introduction of thermal effects the value of the circumference as well as radial stresses increases in temperature $$\left( {\Theta_{1} = 0^\circ F,\Theta_{2} = 1000^\circ F} \right)$$ and decreases in temperature $$\left( {\Theta_{1} = 700^\circ F,\Theta_{2} = 0^\circ F} \right)$$ . Rectangular plate made of rubber material is more comfortable than that of copper and glass materials. Numerical results are shown graphically.

This study conducted parametric analyses to investigate the influence of structural loading (pile-head loading) on the development of negative skin friction in friction single piles and friction-end-bearing single piles in consolidating ground. Numerical effective stress-based mechanical-flow analysis models were built in ABAQUS software. The appropriateness of the modeling approach was verified by applying it to simulate a field model test described in the literature. For small surcharges, pile-head loading considerably reduces the depth of the neutral plane and therefore drag load for the friction pile. Under the same pile-head loads, the reduction in total drag load for the friction-end-bearing pile is smaller than that for the friction pile. However, when the friction-end-bearing pile is subjected to larger pile-head loads, the degree of total drag load reduction is comparable to that of the friction pile. Considerable pile-head displacement occurs under the combined action of pile-head and surcharge loadings. In contrast to the friction pile, the friction-end-bearing pile, because of the greater stiffness and strength of its bearing stratum, exhibits a significant reduction in negative skin friction, no bearing failure, and a smaller pile-head displacement when it is subjected to large pile-head loading.

The instability of functionally graded material (FGM) structures is one of major threats to their service safety in widely engineering applications. This paper aims to clarify a long-standing controversy on the type of thermal instability of simply-supported FGM beams. Firstbased on the Euler-Bernoulli beam theory and von Karman geometric nonlinearitya nonlinear governing equation of simply-supported FGM beams under uniform thermal loads by Zhang’s two-variable method is formulated. Secondan approximate analytic solution to the nonlinear integro-differential boundary value problem with a thermal-induced inhomogeneous force boundary condition is obtained by using a semi-inverse method when the coordinate axis is relocated to the bending axis (physical neutral plane), and then the analytical predictions are verified by the differential quadrature method (DQM). Finallybased on the free energy theoremit is revealed that the symmetry breaking caused by the material inhomogeneity can make the simply-supported FGM beam under uniform thermal loads occur snap-through postbuckling only in odd modes; furthermorethe nonlinear critical load of thermal buckling varies non-monotonically with the functional gradient index due to the stretching-bending coupling effect. These results are expected to provide new ideas and references for the design and regulation of FGM structures.

In this paper, the bending, buckling, and vibration behaviors of bi-directional functionally graded (BDFG) nonuniform micro/nanobeams are investigated. A new Euler–Bernoulli beam model is developed for BDFG tapered micro/nanobeams using Gurtin–Murdoch surface elasticity theory and modified couple stress theory to capture the effects of surface energy and microstructure stiffening, respectively. The present formulation accounts for the physical neutral surface. The material properties of the bulk and surface continuums of the nanobeam are assumed to vary along the thickness and length directions according to power law. Also, the cross section is assumed to vary linearly along the length direction. Hamilton principle is employed to derive the nonclassical equations of motions and boundary conditions. The generalized differential quadrature method (GDQM) is employed to accurately evaluate the variable coefficients of the obtained governing equations. Then after, the Navier’s method is employed for the simply supported BDFG nanobeam for its static bending deflection, critical buckling load, and fundamental frequency. The proposed model is validated by comparing the obtained results with available literature. Effects of different geometrical and material parameters on static and dynamic behaviors of small-scale BDFG nanobeams with the simultaneous effects of microstructure and surface elasticity are comprehensively studied and discussed. Results disclose that the nonuniformity parameters, aspect ratio, dimensionless material length-scale parameter, surface stress, surface elasticity, and gradient indices have a significant effect on the bending, buckling, and free vibration responses of BDFG tapered micro/ nanobeams.

This paper investigates the nonlinear vibration characteristics of pre- and post-buckled nonuniform bi-directional functionally graded (BDFG) microbeams subjected to nonlinear thermal loading. The formulations derived herein are based on thermoelastic constitutive relations of the higher-order Reddy beam theory in conjunction with the modified couple stress theory, von Karman nonlinear strains, and physical neutral plane concept, for the first time. Power-law model is employed to describe the continuous variation of temperature-dependent thermomechanical material properties of BDFG in both the thickness and length directions. Variable microstructure length scale parameter and Poisson’s ratio in both directions are considered. The variable coefficient nonlinear governing equations and associated boundary conditions of nonuniform BDFG microbeam in the thermal environment are derived utilizing the Hamilton principle. The obtained equations are discretized using the differential quadrature method accounting for various boundary conditions, and iterative Newton’s method is adopted to solve the resulting nonlinear algebraic equations. The developed model and solution procedure are validated by comparing the predicted results with those in the available literature. To this end, extensive parametric studies are carried out to explore the influence of linear and nonlinear temperature profiles, microstructure length scale parameter ratio, microstructure length scale parameter-to-thickness ratio, gradient indices in thickness and length directions, material-temperature dependency, and taperness parameters on the nonlinear vibration response and higher-order mode frequencies of tapered BDFG microbeams accounting different boundary conditions.

The present research deals with the small and large amplitude free vibrations of thick functionally graded material (FGM) beams. Beams are resting on an elastic foundation which consists of the Winkler layer, shear layer and nonlinear springs. The effect of uniform temperature elevation is also included into the formulation. A third-order shear deformation beam theory is adopted as the basic assumption of the formulation which satisfies the traction-free boundary conditions on the top and bottom surfaces. Using two different formulations, i.e. the mid-surface-based formulation and the neutral surface-based formulation, the governing equations of motion are established. For the case of beams with immovable edges in in-plane direction and simply supported in flexure, the governing equations are given in a new presentation. These equations are solved using the two-step perturbation technique. Closed-form expressions are provided to obtain the small and large amplitude natural frequencies of the FGM beam resting on nonlinear elastic foundation and operating in thermal environment. Numerical results are given to discuss the effects of thermal environment, elastic foundation parameters, different formulations, and the geometrical parameters.

Although the time-dependent deformation behaviors of microscale materials have been investigated through experiments with uniaxial loading conditions, the influence of the strain gradient has not been clearly clarified due to the lack of appropriate testing methods. In the current study, to investigate the stress relaxation behavior of microscale single-crystal copper (Cu) at room temperature, a quantitative in situ SEM bending experiment is presented using microcantilever specimens of single-crystal Cu. The microcantilever specimens were fabricated using a focused ion beam, and a tungsten (W) layer was deposited onto the front surface to eliminate the error induced by the penetration of the stiff indenter into the metallic specimen. The yield stress of microscale single-crystal Cu is determined to be 445 MPa by a monotonic loading test, showing an apparent size effect, and no strain hardening is observed due to single-slip deformation. On the other hand, the stress relaxation behavior of the microscale single-crystal Cu consists of both a continuous stress relaxation and an abrupt stress decrease due to a strain burst. The activated volume in each dwell stage is obtained by thermodynamics theory and is found to be mainly related to the abrupt stress decrease. The value of the activated volume indicates that the continuous stress drops in the 1st and 2nd dwell stages are attributed to the evolution of dislocation structures by the single slip on system B4, while the dislocation pile-up near the neutral plane leads to the dominance of cross slip on the stress relaxation behavior in the bending plateau. The proposed microcantilever bending experiment is applicable to explore the time-dependent deformation behavior of small-scale materials.

In wearable electronics, significant research has gone into imparting stretchability and flexibility to otherwise rigid electronic components while maintaining their electrical properties. Thus far, this has been achieved through various geometric modifications of the rigid conductive components themselves, such as with microcracked, buckled, or planar meander structures. Additionally, strategic placement of these resulting components within the overall devices, such as embedding them at the neutral plane, has been found to further enhance mechanical stability under deformation. However, these strategies are still limited in performance, failing to achieve fully strain-insensitive electrical performance under biaxial stretching, twisting, and mixed strain states. Here, we developed a new platform for wearable, motion artifact-free sensors using a graphene-based multiaxially stretchable kirigami-patterned mesh structure. The normalized resistance change of the electrodes and graphene embedded in the structure is smaller than 0.5% and 0.23% under 180° torsion and 100% biaxial strain, respectively. Moreover, the resistance change is limited to 5% under repeated stretching-releasing cycles from 0% to 100% biaxial strain. In addition, we investigated the deformation mechanisms of the structure with finite element analysis. Based on the simulation results, we derived a dimensionless geometric parameter that enables prediction of stretchability of the structure with high accuracy. Lastly, as a proof-of-concept, we demonstrated a biaxially-stretchable graphene-based sensor array capable of monitoring of temperature and glucose level with minimized motion-artifacts.

A theoretical investigation is performed into the bending behavior of FOF-ACF (Flex-On-Flex bonded by Anisotropic Conductive Film) packages bonded at different positions relative to the neutral surface position. The stresses and strains produced in the upper and lower regions of the ACF layer are investigated using Mode I fracture mechanics theory. The results show that the region of the ACF layer beneath the neutral surface of the FOF-ACF package experiences a negative stress, which prevents pre-existing cracks in the conductive particles from propagating further. However, at larger distances from the neutral surface, the compressive stress increases to such an extent that it may result in crumbling of the conductive particles. By contrast, the region of the ACF layer above the neutral surface experiences a positive stress, which promotes crack tip propagation. Moreover, the tension stress (i.e., the crack propagation effect) increases with an increasing distance from the neutral surface. The optimum bonding position for the ACF layer is found to be coincident with the neutral surface since, under this condition, the stresses and strains acting on the compressed particles present their minimum values. Consequently, the risk of fracture failure is reduced and the reliability of the ACF package is correspondingly improved.

Conventional leaf springs are simple in design, utilizing multiple metallic bars (leaves) with low geometrical moment of inertia to generate an economical and linear spring rate. In its early form, the leaf-spring was manufactured using metals like steel, but, in modern applications, there exist composite leaves reinforced by advance glass and carbon fibers. Benefits of composite spring designs include: high specific strength, ability to form complex profiles, and possibility of subcomponent consolidation to reduce assembly. Due to the bending characteristics of the leaf spring, the axial load decreases through the beam thickness, reaching a minimum at the neutral surface. Given this fact, a design optimization approach for mono-composite leaf springs is developed considering a hybrid fiber-layup. Initially, a detailed topology optimization is conducted to optimize the geometry of the leaf spring based on the Tsai-Wu failure model. This process yielded a unique spring design which reduced the mass of the spring by 29% compared to the initial non-optimized spring and 80–90% compared to a steel spring. Subsequently, the design is further optimized by replacing low stress, high modulus reinforcement with lower modulus and cost-effective materials to improve overall vehicle mass, efficiency, and operation. The second stage of the optimization based on the hybrid fiber-layup approach resulted in an additional 7% mass reduction. As there is a connection between fuel efficiency and vehicle mass, the significant reduction of spring mass has a positive impact on vehicle fuel consumption and leads to suspension responsiveness gains. Moreover, the possibility of swapping up to 20% of the middle plies reinforcement with commodity plastics demonstrates the cost benefits of the hybrid fiber-layup design approach considering the high cost of carbon and other high-performance reinforcements.

Based on the nonlocal elasticity theory, the vibration behavior and wave propagation of functionally graded Euler nanobeams with axial motion are investigated. Assuming that the axial velocity of nanobeams is a constant and the graded material parameters vary along the thickness direction in terms of power index, we apply the hypothesis of neutral plane to derive the axial displacement of geometry surface caused by non-uniformity of graded materials. Effects of graded index, axial velocity and nonlocal scale parameter on natural frequencies are analyzed through numerical examples. Also, the relationship between wave propagation frequency, wave velocity and wave number is revealed. The complex mode method is utilized to solve the governing equation, and the natural frequencies and wave velocity are obtained accordingly. To solve the derived transcendental equations, the Newton iteration method is used and a detailed solution flowchart is provided. For vibration, with the increase of non-dimensional axial velocity, non-dimensional nonlocal parameter and gradient index, natural frequencies decrease. For wave propagation, with the increase of wave number, frequency of wave propagation increases. However, with the increase of wave number, velocity of wave propagation decreases. Moreover, increasing the gradient index causes a decrease in frequency and velocity of wave propagation, increasing the axial velocity causes an increase in frequency and velocity of wave propagation, and increasing the nonlocal parameter causes a decrease in frequency and velocity of wave propagation.

The paper aims to develop a theory model of clamped layered structures for parameter study of a mechanical damper. The model can be applied to many cantilever friction cases such as general shape cantilever beams, different material cantilever beams, different cross-section beams, non-uniform thickness beams, etc. The paper combined with theoretical, finite element and experimental analysis using hysteresis loop method to study a number of vital parameters such as neutral surface distance ratio of two-layer beam, in-plane friction force at the interface, concentrated load applied at the free end, tip displacement and relative slip governs the damping capacity of the two-layer beam. Under different neutral surface distance ratio of two-layer beam, the loss factor of structure increases and then decreases with further increase in the force ratio of concentrated load and in-plane friction force. When force ratio is equal to 0.133 and neutral surface distance ratio is equal to 1, the loss factor reaches maximum (0.424). The results suggest that under different neutral surface distance ratio, as force ratio reaches the best value, the loss factor achieves maximum. The work tends to assist the designers to evaluate the damping capability of beams to maximize it as per the requests in the actual application.

An analytical method considering the redistribution of residual stress in the bent plate is proposed to predict the springback of the stiffened panel when milling the panel layer by layer. Two types of stiffened panel, namely, a panel with crosswise stiffeners and a panel with lengthwise stiffeners, were selected as examples and were analyzed during the removal of each layer. Moreover, a finite-element simulation of the milling process was conducted to make comparisons with the analytical results, which demonstrates similar stress distribution and springback values. The maximum stress variation and springback value appeared when the milling depth reached the initial neutral surface. When the plate thickness decreased, the errors between analytical results and FEM results increased, and the lengthwise-stiffened panel was less affected by errors than the crosswise-stiffened panel because of a larger moment of inertia. The effects of different milling thicknesses per layer, initial plate thickness, and bending radius were also analyzed. Moreover, the milling experiment was performed to make verification. The results suggest that the analytical method can predict the springback of the stiffened panel effectively. The proposed method can also be applied to other similar forming conditions.

In the present study, a simple four-node high-order shear deformation plate bending element based on modified first-order shear deformation theory has been developed to analyze functionally graded plates subjected to both sinusoidal or uniformly distributed transversal loads. Unlike other high-order shear deformation theories, the number of unknowns has been reduced to five by using the condition of zero transverse shear stress at the free top and bottom surfaces of the FG plate and by the assumption that the transverse shear strains are quadratically distributed through the thickness. The concept of transverse shear stress-energy has been employed to improve the element performance. Furthermore, the assumed natural shear strain technique has been employed to avoid any potential locking phenomenon. Moreover, the principle of minimum total potential energy has been used to derive the elementary stiffness matrix and the loading vector. To avoid the membrane–bending coupling, the concept of the neutral plane has been introduced. The developed finite element has been validated through a set of tests available in the literature.

With the rapid development of land reclamation, a great amount of buildings are constructed on degree fill. Negative skin friction (NSF) caused by the self-consolidation of dredger fill has a significant influence on the stability of construction. Therefore, centrifuge model tests were conducted to investigate the influence of dredger fills thickness, pile top load, and piles radius on the self-consolidation of dredger fills, piles settlement, and NSF. The results show that pile top load is the main factor controlling the settlement of piles, and the settlement of piles increases with an increase of pile top load. Thickness of dredger fills has significant influence on its self-consolidation. Shaft friction increases with an increase of depth, and the increase rate is much higher when the dredger fills is thicker. Fitting formulas for maximal settlement of piles, maximal NSF, and neutral plane location in the dredger fill were also acquired, providing significant reference to practical engineering.

The transverse free vibration and wave propagation of functionally graded microbeams with an axial motion are investigated based on a nonlocal theory and the Timoshenko beam model. It is assumed the material properties of functionally graded microbeams vary along the thickness direction. The neutral plane of functionally graded materials is introduced, and the inhomogeneity of functionally graded Timoshenko microbeams is considered. The governing equations are derived using Hamilton’s principle, and the differential quadrature method is utilized to determine the first three-order natural frequencies of the microbeams with simply supported and clamped boundary conditions, respectively. The effects of gradient index, nonlocal parameter and axial velocity on natural frequencies are investigated. Moreover, the wave propagation characteristics of functionally graded Timoshenko microbeams are analyzed, and the significant influences of wave number and other variables on wave propagation frequencies and wave velocities are studied. The different influence patterns of nonlocal effect are observed in transverse vibration and wave propagation. The nonlocality shows a weakening phenomenon in transverse vibration of axially moving functionally graded Timoshenko microbeams, while it reveals both weakening and strengthening phenomena in wave propagation. Therefore, two kinds of existing nonlocal scale effects are further confirmed and this is an additional contribution of the present paper.

Recent trends in thin film encapsulations (TFEs), fabricating organic/inorganic encapsulation films are reviewed. Atomic layer deposited inorganic films have superior barrier performance and have advantages of excellent uniformity over large scales at relatively low deposition temperatures. However, organic film should be combined with a hybrid structure for improved flexibility and longer lag time. We introduce various organic deposition methods and mechanisms for enhancing barrier performance. However, stress engineering is required to achieve high performance TFEs for flexible devices, new materials and deposition methods. First, modulating the internal stress in TFEs should be considered to increase flexibility by adopting other layers that can reduce internal stress. Second, controlling the configuration of the hybrid structure can prevent degradation due to cracks. Third, the introduction of a neutral plane as the middle layer decreases the strain. The results summarize how the device can improve barrier performance under external stress. This paper can guide the improvements in barrier performance.

The problem of the nonlinear thermal buckling and post-buckling of magneto-electro-thermo-elastic functionally graded porous nanobeams is analyzed based on Eringen’s nonlocal elasticity theory and by using a refined beam model. The beams with immovable clamped ends are exposed to the external electric voltages, magnetic potentials, a uniform transverse load and uniform temperature change. For the first time, the four types of porosity distribution in the nanobeam are considered and compared in complex electric–magnetic fields. Besides, the new formula of the effective material properties is proposed in this paper to simultaneously estimate the material distribution and porosity distribution in the thickness direction. The generalized variation principle is used to induce the governing equations, then the approximate analytical solution of the METE-FG nanobeams based on physical neutral surface is obtained by using a two-step perturbation technique. Finally, detailed parametric analyses are performed to get an insight into the effects of different physical parameters, including the slenderness ratio, small-scale parameter, volume fraction index, external electric voltages, magnetic potentials, porosity coefficient and different porosity distributions, for providing an effective way to improve post-buckling strength of porous beams.

Free vibration of cracked multistep beam made of functionally graded material is studied on the basis of the Timoshenko beam theory and actual position of neutral plane of functionally graded beam. Crack model is adopted using a pair of translational and rotational springs of stiffness calculated from the same crack depth. An exact dynamic shape function is proposed and used to conduct a simplified transfer matrix for cracked uniform functionally graded beam element. Frequency equations of the cracked multistep beam established in the form of 3 × 3-dimensional determinant for different cases of boundary conditions are employed for analysis of natural frequencies in dependence on the crack position and depth, material properties and size of beam steps. It was shown that abrupt variation of beam thickness has significant effect on the sensitivity of natural frequencies to cracks. This is demonstrated by numerous results obtained for beam with three steps in different boundary condition cases.

Advanced high strength steels are widely used in the automotive industry due to their appropriate strength to weight ratio. This alloy has unique hardening behavior. In this paper, a novel analytical model is introduced to predict springback in U-shaped bending process of as-received and pre-strained DP780 dual phase steel specimens. This model is based on the Hill48 yield criterion and plane -strain condition. The effect of sheet thinning and the motion of the neutral surface is taken into account on the springback. The modified Yoshida-Uemori two surface hardening model is applied to investigate the effect of work hardening stagnation. This novel model is examined on the Numisheet 2011 benchmark 4. The effects of the blank holder force and work hardening stagnation are studied on the sheet springback phenomenon. By comparison of the present model with previous alternate models, obtaining the more accuracy is tangible. Also, it is demonstrated that the springback parameters have more changes with increasing the blank holder force. Also, the parameter of the work hardening stagnation has more effect on the pre-strained specimen as compared to the as-received sample.

The present study included the finite element analysis and optimal design of a multi-layered foldable structure (foldable display) to satisfy stress, neutral plane, and delamination requirements under a 2.5 mm radius of curvature (i.e., 2.5R) due to static bending load. Two bending types (inner folding and outer folding) were considered to accommodate the repeated bending, and their maximum stress values were evaluated. In the approximate optimization for the thickness and Young’s modulus of multiple film layers, the objective was to minimize the folding stress subjected to constraints on the positioning of the largest stress value to a neutral plane and prevention of delamination. Through the simultaneous change in thickness and Young’s modulus, the study identified the new position of a neutral axis so that a 16% improvement in the stress magnitude was obtained. A simulation-based T-peel test was also performed to analyze the fracture behavior of the adhesive, and the relation between the fracture toughness GC and separation load LP could be expressed as Lp = 12.687Gc. The optimized objective function value of von Mises stress was improved by 18% compared to an initial design, and constraints of the delamination indicator and positioning of the neutral plane were satisfied.

Within the framework of a novel shear deformation panel theory based on exponential shear stress distribution, the nonlocal continuum theory is utilized to establish an efficient size-dependent panel model to anticipate the nonlinear instability characteristics of nanoscaled panels subjected to combination of axial compressive load, lateral electric field and through-thickness heat conduction and corresponding to both the temperature-dependent (TD) and temperature-independent cases. The nanopanels contain a substrate made of functionally graded material (FGM) and surface-bonded piezoelectric nanolayers with temperature-dependent material properties. To eliminate the stretching-bending coupling terms, the physical neutral plane position related to the FGM substrate of nanopanels is taken into consideration. The nonlocal nonlinear governing equations are deduced to boundary layer-type ones and then solved via a perturbation-based solving process which results in explicit expressions for nonlocal temperature-dependent equilibrium curves. It is found that in the TD case, by heating the outer surface of nanopanel, the reductions in the values of buckling load and minimum postbuckling load are more considerable for nonlocal hybrid FGM nanopanel than those of local one.

Full-scale static loading tests on eight single test piles and hydrotests on two 50-m diameter tanks supported on 849 piles intended for storing refrigerated gas were performed at Cai Mep Industrial Park approximately 90 km southeast of Ho Chi Minh City, Vietnam. The test piles were precast concrete piles installed through 21 m of soft clay into dense sand to about 45 m depth below ground surface. Four piles were installed by driving and four by jacking. The maximum pile test loads were 3000 kN, which was well below any ultimate resistance, but showed that the tank-foundation piles (to be installed by jacking) could expect to shorten about 3 mm for the 750-kN working load. Each tank was hydro-tested to 636-MN maximum service load, which load was held constant for 1 week, while monitoring the tank settlement at benchmarks placed along the tank perimeters. The records showed the tank perimeters to settle about 15 mm in addition to an about 3-mm pile shortening. Back-analysis of the tank foundation modeled as flexible equivalent rafts at the pile toe level showed that the settlement of the tank center was about three times larger than that of the perimeter. Analysis of long-term settlements indicated that, under service loading, the tank perimeters and centers will settle an additional about 100 mm and 300 mm, respectively. Due to a 3 m thick fill placed over the site causing the clay to consolidate, the ground surface is expected to settle more than 1 m over the long-term. The general subsidence will affect the perimeter piles and transfer load to the interior piles. However, because the pile neutral plane is located in the sand below the clay, downdrag is not an issue for the piled foundation. The drag force will be well below the limit of the pile axial structural strength.

Constrained layer damping treatments are widely used in mechanical structures to damp acoustic noise and mechanical vibrations. A viscoelastic layer is thereby applied to a structure and covered by a stiff constraining layer. When the structure vibrates in a bending mode, the viscoelastic layer is forced to deform in shear mode. Thus, the vibration energy is dissipated as low grade frictional heat. This paper documents the efficiency of passive constrained layer damping treatments for low frequency vibrations of cylindrical composite specimens made of glass fibre-reinforced plastics. Different cross section geometries with shear webs have been investigated in order to study a beneficial effect on the damping characteristics of the cylinder. The viscoelastic damping layers are placed at different locations within the composite cylinder e.g. circumferential and along the neutral plane to evaluate the location-dependent efficiency of constrained layer damping treatments. The results of the study provide a thorough understanding of constrained layer damping treatments and an improved damping design of the cylindrical composite structure. The highest damping is achieved when placing the damping layer in the neutral plane perpendicular to the bending load. The results are based on free decay tests of the composite structure.

The present paper addresses the problem of free vibration in multiple cracked beams made of functionally graded material (FGM). Governing equations of the beam vibration are established using the Timoshenko beam theory, power law of material grading along the beam thickness and rotational spring model of crack. The actual position of neutral plane differed from the mid-plane due to the material properties variation is also taken into account. The frequency equation obtained in a simple form provides an efficient tool for natural frequency analysis and may also be used for solving the inverse problems such as identification of material properties or cracks in the beams from natural frequencies. Numerical examples have been carried out to validate the proposed theory and to investigate the effect of cracks, material and geometry parameters on natural frequencies of the beams.

Embedding microfluidic channel inside a microcantilever has drastically improved the sensitivity of microcantilever biosensors. The sensing principles in suspended microfluidics have been either stress induced deflections or mass based frequency variations. However, the suspended microfluidics can be designed to use flow forces as the sensing principle. In this study, a 3D suspended polymeric microfluidics (SPMF3) is designed with flow plane orthogonal to bending plane. This design innovation, enables the SPMF3 to detect physical properties of bioelements through microcantilever deflections induced by flow force variations inside the embedded suspended microfluidics. Here, the earlier approaches in design and modeling of suspended microfluidics are presented and explained in detail. First, a 2D suspended microfluidics is modeled and its sensitivity to flow forces is analyzed. Modifying the microchannel plane position with respect to cantilever neutral plane results in different microcantilever deflections and consequently biodetection sensitivity. In order to verify the concept of the 3D suspended polymeric microfluidics (SPMF3) for physical study of bioelements, first, a finite element analysis (FEA) of a sample flow inside the microfluidic system is performed. In this modeling, microfluidic-microcantilever interactions and the system sensitivity to flow forces are studied. The SPMF3 deflections with different aperture design is modeled and the sensitivity of each design is analyzed. Three different types of apertures namely, straight aperture, nozzle and diffuser have been modeled and the results show that the diffuser aperture has better sensitivity to flow forces under same working conditions. According to the FEA results, flow force can be employed as a sensing principle of 2D suspended microfluidics. However, sensitivity of the 3D suspended microfluidics is drastically increased and can be tuned for any specific biodiagnostic application using different aperture designs.

Rational reduction and tension schedules and roll profiles for 150/500×400 four-high reversing mill and 350×450 two-high reversing mill were developed and studied to increase the output of strips of high accuracy. For the 150/500×400 mill, increasing the work roll crown from +0.1 to +0.15 mm, the specific back tension from 0.12–0.16 to 0.14–0.18 МРа, and the specific front tension from 0.16–0.18 to 0.18–0.20 MPa appeared to decrease the transverse thickness deviation of strips by 10% compared with the conventional reduction and tension schedules. For the 350×450 mill, increasing the work roll crown from +(0.04–0.07) to +0.09 mm, the specific back tension from 3.3 to 8.7 MPa, and the specific front tension from 4.44 to 10.0 МРа appeared to decrease the transverse thickness deviation of 1-mm strips to 0.039 mm, which may be considered high accuracy. A mathematical model is proposed to analyze the stress-strain state of wavy strips with allowance for hardening. The numerical modeling showed that the tangential stresses are maximum on the upper and lower faces of a 0.5h1 strip, while the radial stresses are maximum in the neutral plane of the strip.

The nonlinear buckling of thin shell-type structures is sensitive to the initial geometric imperfection. In this study, the imperfection sensitivity of the nonlinear instability of cylindrical nanopanels made of functionally graded material (FGM) is addressed including surface elasticity, aiming to present a background for axial postbuckling behavior of imperfect FGM nanopanels. The material properties are supposed to be graded across the panel thickness in accordance with a simple power law function of the volume fractions of the silicon and aluminum constituents with considering the physical neutral plane position. The non-classical governing differential equations are constructed and then they are deduced to boundary layer-type ones. Afterward, a perturbation-based solution methodology is employed to extract explicit expressions for the size-dependent postbuckling equilibrium paths of FGM nanopanels with and without initial geometric imperfection and corresponding to various panel thicknesses, geometrical parameters, temperature changes and material property gradient indexes. It is displayed that through reduction of the surface elasticity effects for thicker FGM nanopanels, the influence of the initial geometric imperfection on the minimum load of the postbuckling regime increases. This pattern is more significant for FGM nanopanels with a lower value of the material gradient index.

The main purpose of the present study is to examine the axial buckling and postbuckling response of cylindrical nanoshells made of functionally graded (FG) materials in the presence of surface free energy effects. To accomplish this purpose, an efficient size-dependent shell model is introduced through combination of the classical shell theory with the well-known Gurtin–Murdoch surface elasticity theory. The volume fraction of FG nanoshells made of the mixture of aluminum and silicon is defined using a power law function. Also, in order to eliminate the stretching–bending coupling terms, the change in the position of physical neutral plane corresponding to different volume fractions is taken into account. Based upon the principle of virtual work, the non-classical governing differential equations and boundary conditions are derived. Subsequently, the governing equations are deduced to the boundary layer-type equations incorporating simultaneously the nonlinear large deflections and size effect. Finally, a perturbation-based solving process is put to use to predict the size-dependent critical buckling loads and related postbuckling equilibrium curves for FG nanoshells with various values of material property gradient index and shell thickness. It is found that the surface free energy effect is more prominent for FG nanoshell with lower shell thickness and higher material property gradient index.

Size-dependent modeling and analysis for the nonlinear postbuckling response of functionally graded (FG) cylindrical nanopanels under axial compressive load are presented based on the surface elasticity theory. The non-classical formulations are developed on the basis of the Gurtin–Murdoch elasticity theory within the framework of the classical shell theory. In order to capture the large deflections associated with the postbuckling regime, the geometrical nonlinearity is considered in von Karman sense. The material properties are supposed to be graded across the panel thickness in accordance with a simple power law function of the volume fractions of the silicon and aluminum constituents with considering the physical neutral plane position. To satisfy the balance conditions on the free surface layers, it is assumed that the bulk normal stress along the thickness direction varies linearly between those values of surface stress components at the inner and outer layers. A boundary layer theory of shell buckling is extended to the case of size-dependent FG nanopanels, and then, a singular perturbation technique is put to use to solve the nonlinear problem. It is displayed that due to the stiffening influence of surface effects, the depth of the postbuckling regime for FG nanopanels with higher material gradient index decreases, as for the metal-rich nanopanel, the snap-through phenomenon approximately diminishes.

The purpose of the current study is to address the nonlinear buckling and postbuckling response of nanoscaled cylindrical shells made of functionally graded material (FGM) under hydrostatic pressure aiming to investigate the sensitivity to the initial geometric imperfection in the presence of surface effects and thermal environments. According to a power law distribution, the material properties of the FGM nanoshell are considered change through the shell thickness. Also, the change in the position of physical neutral plane corresponding to different volume fractions is taken into account to eliminate the stretching-bending coupling terms. In order to acquire the size effect qualitatively, the well-known Gurtin-Murdoch elasticity theory is incorporated within the framework of the classical shell theory. Using the variational approach, the non-classical governing equations are displayed and deduced to boundary layer type ones. Afterwards, explicit expressions for the size-dependent radial postbuckling equilibrium paths of imperfect FGM nanoshells are proposed with the aid of a perturbation-based solution methodology. It is displayed that by moving from the ceramic phase to the metal one, the critical buckling pressure decreases, but the postbuckling stiffness increases, because in contrast to the ceramic phase, the surface modulus and residual surface stress associated with the metal phase have the same sign.

In this paper, the free vibration characteristics of smart shear deformable plates made of porous magneto-electro-elastic functionally graded (MEE-FG) materials are investigated considering various boundary conditions by using an analytical method for the first time. Porosities possibly occur inside functionally graded materials (FGMs) during fabrication because of technical problems that lead to creation of micro-voids in these materials. Magneto-electro-elastic properties of FGM plate are supposed to vary through the thickness direction according to a modified power-law model in which the porosities with even and uneven distributions are approximated. The governing differential equations of porous FGM plate under magneto-electrical field are formulated through Hamilton’s principle based on a four-variable tangential-exponential refined theory which avoids the use of shear correction factors. Influences of several important parameters such as material graduation exponent, porosity volume fraction, magnetic potential, electric voltage, various boundary conditions and plate side-to-thickness ratio on natural frequencies of the porous MEE-FG plate are investigated and discussed in detail. It is concluded that these parameters play significant roles on the dynamic behavior of porous MEE-FG plates. Presented numerical results can serve as benchmarks for future analyses of MEE-FG plates with porosity phases.

This article presents closed-form solutions for the frequency analysis of rectangular functionally graded material (FGM) thin plates subjected to initially in-plane loads and with an elastic foundation. Based on classical thin plate theory, the governing differential equations are derived using Hamilton’s principle. A neutral surface is used to eliminate stretching–bending coupling in FGM plates on the basis of the assumption of constant Poisson’s ratio. The resulting governing equation of FGM thin plates has the same form as homogeneous thin plates. The separation-of-variables method is adopted to obtain solutions for the free vibration problems of rectangular FGM thin plates with separable boundary conditions, including, for example, clamped plates. The obtained normal modes and frequencies are in elegant closed forms, and present formulations and solutions are validated by comparing present results with those in the literature and finite element method results obtained by the authors. A parameter study reveals the effects of the power law index n and aspect ratio a/b on frequencies.

An undesirable factor that affects the dimensional precision and final shape of metallic parts produced in cold forming processes is springback phenomenon. In this paper, an analytical model is introduced to predict springback in U-shaped bending process of DP780 dual-phase steel sheet. It is based on the Hill48 yielding criterion and plane strain condition. In this model, the effect of forming history, the sheet thinning, and the motion of the neutral surface on the springback of U-shaped bending process is taken into account. The anisotropic nonlinear kinematic hardening model (ANK) is used to consider the impact of complex deformation, including stretching, bending and reverse bending. This model is able to investigate the Bauschinger effect, transient behavior and permanent softening. This model is used for the Numisheet2011 benchmark U-shaped bending problem. The effect of the sheet holder force, the coefficient of friction, thickness, material anisotropy, and hardening parameters on the sheet springback is studied. It can be seen that analytical model which presented in this paper has desirable accuracy in the springback prediction, and results are close to experimental data.

Organic/inorganic multilayer structures were fabricated for extreme flexibility as well as enhanced moisturebarrier property. The organic and inorganic layers for the structures were formed by plasma polymerization and atomic layer deposition, respectively. The layers were grown alternately to form the organic/inorganic multilayer structures on a plastic substrate. To accomplish extreme flexibility of the barriers, ultra-thin aluminum oxide layers were grown by the atomic layer deposition and sandwiched by a flexible plasma-polymer layer. The moisture-barrier films were then confirmed to retain the initial barrier property even after 10,000 times of bending at a radius as small as 3mm when the barrier structure was located at a neutral plane.

In the present investigation, an analytical solution is proposed to predict the postbuckling characteristics of nanobeams made of functionally graded materials which are subjected to thermal environment and surface stress effect. To this end, a non-classical beam model on the basis of Gurtin–Murdoch elasticity theory in the framework of Euler–Bernoulli beam theory and concept of physical neutral surface is utilized which has the capability to consider the effect of surface stress and von Karman-type of kinematic nonlinearity. The size-dependent nonlinear governing equations are solved analytically for different end supports. The postbuckling equilibrium paths corresponding to various boundary conditions are given in the presence of surface stress corresponding to various beam thicknesses, material gradient indexes, temperature changes and buckling mode numbers. It is found that by increasing the values of temperature change, the equilibrium path is shifted to right and the normalized applied axial load decreases indicating that the effect of surface stress diminishes.

The location of neutral plane level (NPL) of a high-rise shaft is an important factor for the evaluation of risks of smoke spreads in high-rise buildings, where the shaft internal pressure is equal to that of the building floor at the same height. The current method to determine the location of NPL assumes uniform temperature distribution inside a shaft, which causes concerns over accuracy of the predicted NPL for high-rise shafts with non-uniformly distributed temperatures during fires. To address the effect of temperature distribution on NPL location, this paper introduces a method to calculate temperature distribution and its associated NPL location based on a coupled model of smoke temperature profile, flow rate and pressure distribution inside a shaft. The measured data from a 1/3 scale experiment is used to validate the method and used to develop two empirical equations for NPL locations in terms of dimensionless numbers: one empirical equation based on shaft top temperature and the second based on shaft bottom temperature. A sensitivity study of the empirical equations is then conducted to evaluate the applicability of the developed equations when compared to the existing NPL method. It was found that for the existing NPL equation based on uniform temperature assumption may under-/overestimate the NPL locations, and the NRMSE would be over 50%, while the NRMSE of the empirical equation is only around 6% based on the results of coupled equations. For non-adiabatic shafts, the effects of non-uniform temperature distribution on NPL should be considered and the suggested empirical equations can predict NPL locations with a reasonable accuracy.

In this paper, model tests and numerical simulations on 3 × 3 pile group embedded in consolidating soil under embankment load with different pile spacings are carried out. Single pile and 2 × 2 pile group are studied for comparative analyses. The performances of dragload versus relative displacement of pile-soil, load sequence and load rate, and the group effects of dragload and downdrag versus pile spacing are analyzed. A case study on dragload of a pile group considering with or without couple effect is also presented. It is worth pointing out that in this experimental condition, when pile-soil relative displacements reach 2 mm, dragload will reaches nearly 75-95% of the maximum values; When consolidation time reaches 240 h, the neutral plane becomes stable approximately at 0.95H (H is the thickness of compression soil). The dragload and downdrag are influenced by load sequence of pile head load versus surcharge load.

The morphologies and phase diagrams exhibited by symmetric ABC star triblock copolymer nanoparticles are investigated on the basis of real-space self-consistent field theory. The ABC star triblock copolymers were chosen to be tiling-forming with fixed polymer parameter and the spherical boundaries were modeled using the masking technique. We first study a number of examples where the ABC triblock copolymers confined in spherical cavities with neutral surface. Then, two types of spherical cavity distinct preferential surfaces are considered, including both A-block attractive and repulsive preferential surfaces. We aim at the effects due to various spherical cavity diameters and the degree of interactions between the polymer and the spherical surface. A variety of morphologies, such as ring-like structures, concentric sphere, and irregular cylinder, were identified in phase diagrams. The results show that both the degree of interactions and spherical diameters can influence the formation of morphologies so that ring-like structures and other novel structures could be obtained.

Waves occurring in cold-rolled plates or sheets can be divided into longitudinal and transverse waves. Classical leveling theories merely solve the problem of longitudinal waves, while no well accepted method can be employed for transverse waves. In order to investigate the essential deformation law of leveling for plates with transverse waves, a 2.5-dimensional (2.5-D) analytical approach was proposed. In this model, the plate was transversely divided into some strips with equal width; the strips are considered to be in the state of plane strain and each group of adjacent strips are assumed to be deformation compatible under stress. After calculation, the bending deformation of each strip and the leveling effect of overall plate were obtained by comprehensive consideration of various strips along with the width. Bending of roller is a main approach to eliminate the transverse waves, which is widely accepted by the industry, but the essential effect of bending of roller on the deformation of plates and the calculation of bending of roller are unknown. According to the 2.5-D analytical model, it can be found that, for plates, it is neutral plane offsetting and middle plane elongation or contraction under inner stress that can effectively improve plate shape. Taking double side waves as an example, the appropriate values of bending of roller were obtained by the 2.5-D analytical model related to different initial unevenness, which was applicable to the current on-line adjusting of bending of roller in rolling industry.

This paper uses a new refined beam theory based on neutral surface position for the static and free vibration analysis of functionally graded material beams. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The neutral surface position for a functionally graded beam with its material properties varying in the thickness direction is determined. Based on the present refined shear deformation beam theory and the neutral surface concept, the equations of motion are derived from Hamilton’s principle. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

A new first-order shear deformation theory is developed for bending and dynamic behaviors of functionally graded plates. Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher order shear deformation theories. The equations governing the axial and transverse deformations of functionally graded plates are derived based on the present first-order shear deformation plate theory and the physical neutral surface concept. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. To examine accuracy of the present formulation, several comparison studies are investigated. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of functionally graded plates.

A number of electric flash butt rail welds fractured vertically through the cross section of the rail. The fractures initiated in the web near the bending neutral plane in a region where high-carbon-content liquid was identified to have been produced during the welding process, resulting in a brittle cementite (ledeburite) network structure that reduced the load carrying capacity of the weld. Fracture initiation near the neutral plane was encouraged due to longitudinal stresses in the continuously welded rail from thermal contraction at colder temperatures. Additionally, residual stresses induced by flash butt welding could have contributed to fracture initiation.

Biot’s poroelastic theory has been applied for Mindlin plates to model moderately thick plates. If Mindlin’s kinematical assumptions and a power series expansion for the pore pressure in the thickness direction are considered, the original 3D problem is reduced to 2D. A truncated power series expansion with quadratic terms is considered for the pore pressure. Two functional relationships based on the given boundary conditions and one PDE are derived for the expansion coefficients. A meshless method based on the local Petrov–Galerkin approach is proposed to solve the set of governing PDE in the neutral plane of the poroelastic plate. All in-plane quantities are approximated by the moving least-squares scheme. After performing the spatial integrations, one obtains a system of ordinary differential equations for certain nodal unknowns.

Artificial modulation of electronic structures and control of the transport dynamics of carriers and excitons in CdSe nanowire are important for its application in optoelectronic nanodevices. Here, we demonstrate the aggregative flow of excitons by bending CdSe nanowires. The bending strain induces spatial variance of bandgap, and the energy bandgap gradient will result in the flow of excitons towards the bending outer edge of CdSe nanowire. The exciton emission energy shows a uniform redshift in the bending region due to the aggregative flow of excitons, and the energy redshift increases linearly with increasing the strain at the outer edge of the CdSe nanowire. Our results show an effective method to drive, concentrate, and utilize the excitons in CdSe nanowires, which provides a guide for the design of high performance and flexible optoelectronic nanodevices.

In this paper, a continuous model for flexural vibration of beams with a vertical edge crack including the effects of shear deformation and rotary inertia is presented. The crack is assumed to be an open-edge crack perpendicular to the neutral plane. A quasi-linear displacement filed is suggested for the beam, and the strain and stress fields are calculated. The governing equation of motion for the beam has been obtained using Hamilton principle. The equation of motion is solved with a modified weighted residual method, and the natural frequencies and mode shapes are obtained. The results are compared to the results of similar model with Euler–Bernoulli assumptions and finite element model to confirm the advantages of the proposed model in the case of short beams.

For light and stiff structural parts, the use of carbon-fiber-reinforced plastics (CFRPs) is currently a topic of research. However, the current manufacturing time of CFRP products is too long to enable mass production. A new sheet forming process for solidified CFRPs with dummy sheets was developed. The process can be applied to conventional press forming for mass production. It is necessary for CFRP sheets to be pressed under a tensile load because they are weak under compression load. When the neutral plane under a forming was moved inside the bending curve, the specimen could be formed under tensile load. In this study, the position of the neutral plane was moved by changing the thicknesses of dummy sheets on the inside and outside of the bending curve. Observation by microscopy, computed tomography scanning and tensile tests were performed to determine the relationship between internal defects and tensile strength.

By reformulating the governing equations of the first-order theory into those describing the interior and edge-zone problems of the plate, closed-form solutions are presented for analysis of functionally graded circular sector plates with vertex angle \({\theta_0 \leq \pi /2}\) whose radial edges are simply supported and subjected to transverse loading and heat conduction through the plate thickness. Various types of clamped, simply supported, and free-edge boundary supports are considered on the circular edge of the plate. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The effects of material property, boundary conditions, sector angle \({\theta_0}\), and boundary-layer phenomena on various response quantities in a circular sector plate are studied and discussed. Under a mechanical load, radial stress resultants in an FG circular sector plate with various clamped supports are zero, and consequently, their responses are seen to be identical. Simply supported FG circular sector plates which are immovable in radial direction do not show a neutral plane in bending, while in FG circular sector plates with other types of boundary supports this plane exists and its z-coordinate depends on the material constant. It is observed that the boundary-layer width is approximately equal to the plate thickness both in thermal and mechanical loadings with the boundary-layer effects being the strongest near a free edge.