Static Analysis of Skew Functionally Graded Plate Using Novel Shear Deformation Theory

In this article, the static response of a functionally graded material (FGM) plate is studied via hybrid higher-order shear deformation theory which uses hyperbolic and polynomial shape functions and includes the effect of thickness stretching. The composition of the plate comprises metallic and ceramic phases. The ceramic volume fraction varies gradually along with the thickness following the power law. The mechanical properties of the FGM plate are determined by the rule of mixtures and the Mori–Tanaka homogenization scheme. The displacement fields are defined to satisfy the requirement of traction-free boundary conditions at the bottom and top surfaces of the plate surface removing the need for determination of shear correction factor. A C⁰ continuity FE model is developed for the present mathematical model. Nine-node isoparametric elements with eight nodal unknowns at each node are developed. The present model comparison with existing literature is completed and found to be coherent. Inhouse MATLAB code is developed for the present work. Sinusoidal and uniformly distributed loading is analyzed in the present work. The parametric study is undertaken to explore the effect of the side-to-thickness ratio, aspect ratio, thickness, and volume fraction index on stresses and transverse displacements.     

Modeling and Solution of Large Amplitude Vibration Problem of Construction Elements Made of Nanocomposites Using Shear Deformation Theory

The main purpose of the study is to investigate the vibration behaviors of carbon nanotube (CNT) patterned double-curved construction elements using the shear deformation theory (SDT). After the visual and mathematical models of CNT patterned double-curved construction elements are created, the large amplitude stress–strain relationships and basic dynamic equations are derived using the first order shear deformation theory (FSDT). Then, using the Galerkin method, the problem is reduced to the nonlinear vibration of nanocomposite continuous systems with quadratic and cubic nonlinearities. Applying the Grigolyuk method to the obtained nonlinear differential equation, large-amplitude frequency-amplitude dependence is obtained. The expressions for nonlinear frequencies of homogenous and inhomogeneous nanocomposite construction members such as plates, panels, spherical and hyperbolic-paraboloid (hypar) shells in the framework of FSDT are found in special cases. The accuracy of the results of the current study has been confirmed by comparing them with the reliable results reported in the literature. Original analyses are carried out to examine the effects of nonlinearity, CNT patterns and volume fraction changes on frequencies in the framework of shear deformation and classical shell theories.     

Analysis of Flexural Vibrations of a Piezoelectric Semiconductor Nanoplate Driven by a Time-Harmonic Force

The performance of devices fabricated from piezoelectric semiconductors, such as sensors and actuators in microelectromechanical systems, is superior; furthermore, plate structures are the core components of these smart devices. It is thus important to analyze the electromechanical coupling properties of piezoelectric semiconductor nanoplates. We established a nanoplate model for the piezoelectric semiconductor plate structure by extending the first-order shear deformation theory. The flexural vibrations of nanoplates subjected to a transversely time-harmonic force were investigated. The vibrational modes and natural frequencies were obtained by using the matrix eigenvalue solver in COMSOL Multiphysics 5.3a, and the convergence analysis was carried out to guarantee accurate results. In numerical cases, the tuning effect of the initial electron concentration on mechanics and electric properties is deeply discussed. The numerical results show that the initial electron concentration greatly affects the natural frequency and electromechanical fields of piezoelectric semiconductors, and a high initial electron concentration can reduce the electromechanical fields and the stiffness of piezoelectric semiconductors due to the electron screening effect. We analyzed the flexural vibration of typical piezoelectric semiconductor plate structures, which provide theoretical guidance for the development of new piezotronic devices.     

Axial and Shear Buckling Analysis of Multiscale FGM Carbon Nanotube Plates Using the MTSDT Model: A Numerical Approach

The present paper investigates the axial and shear buckling analysis of a carbon nanotube (CNT)-reinforced multiscale functionally graded material (FGM) plate. Modified third-order deformation theory (MTSDT) with transverse displacement variation is used. CNT materials are assumed to be uniformly distributed, and ceramic fibers are graded according to a power-law distribution of the volume fraction of the constituents. The effective material properties are obtained using the Halpin–Tsai equation and Voigt rule of the mixture approach. A MATLAB code is developed using nine noded iso-parametric elements containing 13 nodal unknowns at each node. The shear correction factor is eliminated in the present model, and top and bottom transverse shear stresses are imposed null to derive higher-order unknowns. Comparisons of the present results with those available in the literature confirm the accuracy of the existing model. The effects of material components, plate sizes, loading types, and boundary conditions on the critical buckling load are investigated. For the first time, the critical buckling loads of CNT-reinforced multiscale FGM rectangular plates with diverse boundary conditions are given, and they can be used as future references.     

Effect of Multiple Annular Plates on Vibration Characteristics of Laminated Submarine-like Structures

A numerical model for the prediction of vibration behaviors of a laminated submarine structure consisting of spherical, cylindrical, and cone shells with multiple built-in annular plates is reported in this article. With the aid of the first-order shear deformation theory (FSDT) concerning plates and shells, the energy expressions of each substructure are derived. The displacement functions in the energy functionals are expanded by the employment of Legendre orthogonal polynomials and circumferential Fourier series. Then, the Rayleigh–Ritz procedure is performed to obtain the eigenfrequency and the corresponding eigenmode of the submarine model. The correctness of the structural model is examined by comparing the results with existing papers and the finite element method, and the maximum deviation is not more than 2.07%. Additionally, the influence of the plate’s thickness, position, inner diameter, as well as the laying angle on the intrinsic vibration characteristics of laminated submarine-like structure is determined. The results reveal that rational geometry design and assemblage benefit the vibration performance of the combination. Increasing the thickness of all the annular plates, decreasing the inner radius, and regulating the laminated scheme, make remarkable influence on structural free vibration, with the maximum relative changing rate of frequency exceeding 97%, 16%, and 23%, respectively.     

Tissue deformation spatially modulates VEGF signaling and angiogenesis

Physical forces play a major role in the organization of developing tissues. During vascular development, physical forces originating from a fluid phase or from cells pulling on their environment can alter cellular signaling and the behavior of cells. Here, we observe how tissue deformation spatially modulates angiogenic signals and angiogenesis. Using soft lithographic templates, we assemble three-dimensional, geometric tissues. The tissues contract autonomously, change shape stereotypically and form patterns of vascular structures in regions of high deformations. We show that this emergence correlates with the formation of a long-range gradient of Vascular Endothelial Growth Factor (VEGF) in interstitial cells, the local overexpression of the corresponding receptor VEGF receptor 2 (VEGFR-2) and local differences in endothelial cells proliferation. We suggest that tissue contractility and deformation can induce the formation of gradients of angiogenic microenvironments which could contribute to the long-range patterning of the vascular system.     

Formation and relaxation of erythrocyte membrane tethers in micropipettes

The red blood cell (RBC) membrane forms tethers in response to shear forces acting on tiny membrane points. Tether formation depends on viscous and elastic membrane properties and has been used as indicator of membrane fragility. A micropipette technique was used to study time dependent tether formation and tether relaxation of individual RBC. Point attached RBC were aspirated at a negative pressure of -5 mm H2O into a micropipette with an internal diameter of 7.8 microm. If tether formation occurred and the tether reached a length of approximately 16 microm, the pipette was carefully pulled back. The RBC left the orifice of the micropipette and the tether relaxed and pulled the main body of the RBC back to the attachment point. The relaxation of the tethers was exponential. The time constant for tether relaxation was 0.144 s which is similar to the time constant for recovery of entire RBC from extensional elastic deformation. Repeated tether formation and relaxation of the same RBC led to an earlier begin of tether formation and changed the behavior of tether growth, although the relaxation time did not change. We conclude that repeated tether formation decreases the resistance of the RBC membrane to form tethers upon given shear forces. Weakening of the membrane due to repeated plastic deformation may play a role in the membrane loss of circulating RBC during aging.     

On the Solution of Thermal Buckling Problem of Moderately Thick Laminated Conical Shells Containing Carbon Nanotube Originating Layers

This study presents the solution for the thermal buckling problem of moderately thick laminated conical shells consisting of carbon nanotube (CNT) originating layers. It is assumed that the laminated truncated-conical shell is subjected to uniform temperature rise. The Donnell-type shell theory is used to derive the governing equations, and the Galerkin method is used to find the expression for the buckling temperature in the framework of shear deformation theories (STs). Different transverse shear stress functions, such as the parabolic transverse shear stress (Par-TSS), cosine-hyperbolic shear stress (Cos-Hyp-TSS), and uniform shear stress (U-TSS) functions are used in the analysis part. After validation of the formulation with respect to the existing literature, several parametric studies are carried out to investigate the influences of CNT patterns, number and arrangement of the layers on the uniform buckling temperature (UBT) using various transverse shear stress functions, and classical shell theory (CT).     

Effects of Pre-Tensile Deformation on the Fatigue Fracture Behavior of Annealed 7005 Aluminum Alloy Plate

In the present study, the fatigue life and fatigue fracture characteristics of annealed 7005 aluminum alloy plates subjected to different pre-tensile deformations were investigated. The results obtained upon increasing the pre-tensile deformation of the alloy plate to 20% revealed that the second-phase particles did not show any obvious changes, and that the thickness of the thin strip grain slightly decreased. The dislocation distribution in the alloy matrix varied significantly among the grains or within each grain as the dislocation density gradually increased with increasing pre-tensile deformation. Moreover, the fatigue performance of the annealed 7005 aluminum alloy plate was significantly improved by the pre-tensile deformation, and the alloy plate subjected to 20% pre-tensile deformation exhibited an optimal fatigue life of ~1.06 × 10⁶ cycles, which was 5.7 times and 5.3 times that of the undeformed and 3% pre-stretched alloy plates, respectively. Two fatigue life plateaus were observed in the pre-tensile deformation ranges of 3–5% and 8–12%, which corresponded to heterogeneous dislocation distribution among various grains and within each grain, respectively. Moreover, two large leaps in the plot of the fatigue-life–pre-tensile-deformation curve were observed, corresponding to the pre-tensile deformation ranges of 5–8% and 16–20%, respectively.     

Large Deflections of Thin-Walled Plates under Transverse Loading—Investigation of the Generated In-Plane Stresses

Thin-walled plates subjected to transverse loading undergoing large deflection have been the topic of a large number of studies. However, there is still a lack of information about the nature and the distribution membrane stresses generated under large deflections. The purpose of this paper is to calculate and display the distribution of the generated stresses and the respective deflections on the entire rectangular plate area. Finite element analysis results for thin-walled plates with aspect ratios of 1, 2 and 5, on movable and immovable edges simply supported and clamped boundary conditions are clearly visualized. The distribution of the normal and shear stresses enables a good understanding of the plate critical points locations. It was found that strong tensile and compressive membrane stresses exist at various points near the plate edges, creating potential failure hazards.     

The effect of malonyldialdehyde on erythrocyte deformability

The addition of malonyldialdehyde (5-20 micro M) to human erythrocytes results in a marked decrease in cellular deformability as measured with a counter-rotating, cone plate Rheoscope when low shear forces (2.5-25 dynes/sq cm) are applied. At high shear forces (125-500 dynes/sq cm), malonyldialdehyde at 5 micro M had no effect on deformability, although at concentrations of 10 and 20 micro M a small but statistically significant decrease was evident. These effects of this crosslinking agent are observed in the absence of alterations in cell volume and intracellular viscosity. The results obtained are in accord with the view that the polymerization of membrane constituents may contribute to the events that lead to the removal from the circulation of either aging cells or cells exposed to peroxidation-initiating agents.     

Meshless Chebyshev RPIM Solution for Free Vibration of Rotating Cross-Ply Laminated Combined Cylindrical-Conical Shells in Thermal Environment

This paper provides a numerical solution to the vibration of a rotating cross-ply laminated combined conical-cylindrical shell in the thermal environment. Its numerical discrete solution method uses the meshless method. The combined shell assumed the temperature independence of material property is divided to the fundamental conical and cylindrical shell substructures, and the theoretical formulation for each substructure is derived based on the first order shear deformation theory (FSDT) and Hamilton’s principle. The effects of the initial hoop tension and temperature change are considered through the kinetic energy reflecting the effects of centrifugal and Coriolis forces and additional strain energy by the nonlinear part of the Green–Lagrange strains. The substructures are then assembled according to the continuity conditions. The boundary and continuity conditions are simulated by introducing artificial virtual spring technology. The displacement component in the theoretical formulation is approximated using a meshless Chebyshev-RPIM shape function. The reliability of the method is verified by comparing with mature and reliable results. The free vibration characteristics of the rotating combined conical-cylindrical shell structure under various sizes, speeds and temperatures are given by numerical examples.     

A 3D numerical study of the effect of channel height on leukocyte deformation and adhesion in parallel-plate flow chambers

The effect of channel height on leukocyte adhesion to a lower plate in a parallel-plate flow chamber is studied by direct numerical simulations in three dimensions. The numerical model takes into account deformability and viscoelasticity of the leukocyte, membrane ruffles (microvilli), and the presence of mechanically different regions inside the cell (nucleus and cytoplasm). Leukocyte adhesion is assumed to be mediated by interactions of adhesion molecules on the tips of microvilli with their counterparts on the lower plate. Results of this study indicate that an adherent leukocyte experiences much less drag than a rigid sphere due to its deformation and transient stress growth. While overall leukocyte deformation is modest at shear stresses encountered in the microcirculation, deformation in the contact region is significant. At fixed wall shear stress, the contact area of the cell membrane with the substrate increases with increasing the ratio of cell diameter to channel height, leading to greater adhesion. This suggests that in vitro flow chamber studies typically underestimate leukocyte adhesion that occurs in the microcirculation.     

Bialgebra cohomology, deformations, and quantum groups

We introduce cohomology and deformation theories for a bialgebra A (over a commutative unital ring k) such that the second cohomology group is the space of infinitesimal deformations. Our theory gives a natural identification between the underlying k-modules of the original and the deformed bialgebra. Certain explicit deformation formulas are given for the construction of quantum groups--i.e., Hopf algebras that are neither commutative nor cocommutative (whether or not they arise from quantum Yang-Baxter operators). These formulas yield, in particular, all GLq(n) and SLq(n) as deformations of GL(n) and SL(n). Using a Hodge decomposition of the underlying cochain complex, we compute our cohomology for GL(n). With this, we show that every deformation of GL(n) is equivalent to one in which the comultiplication is unchanged, not merely on elements of degree one but on all elements (settling in the strongest way a decade-old conjecture) and in which the quantum determinant, as an element of the underlying k-module, is identical with the usual one.     

Probing polymerization forces by using actin-propelled lipid vesicles

Actin polymerization provides a powerful propulsion force for numerous types of cell motility. Although tremendous progress has been made in identifying the biochemical components necessary for actin-based motility, the precise biophysical mechanisms of force generation remain unclear. To probe the polymerization forces quantitatively, we introduce an experimental system in which lipid vesicles coated with the Listeria monocytogenes virulence factor ActA are propelled by actin polymerization. The polymerization forces cause significant deformations of the vesicle. We have used these deformations to obtain a spatially resolved measure of the forces exerted on the membrane using a model based on the competition between osmotic pressure and membrane stretching. Our results indicate that actin exerts retractile or propulsive forces depending on the local membrane curvature and that the membrane is strongly bound to the actin gel. These results are consistent with the observed dynamics. After a slow elongation of the vesicle from a spherical shape, the strong bonds between the actin gel and the membrane rupture if the retractile forces exceed a critical value, leading to a rapid release of the vesicle's trailing edge.     

Dynamic Response of Angle Ply Laminates with Uncertainties Using MARS,ANN-PSO,GPR and ANFIS

In the present work, for the first time, free vibration response of angle ply laminates with uncertainties is attempted using Multivariate Adaptive Regression Spline (MARS), Artificial Neural Network-Particle Swarm Optimization (ANN-PSO), Gaussian Process Regression (GPR), and Adaptive Network Fuzzy Inference System (ANFIS). The present approach employed 2D C⁰ stochastic finite element (FE) model based on the Third Order Shear Deformation Theory (TSDT) in conjunction with MARS, ANN-PSO, GPR, and ANFIS. The TSDT model used eliminates the requirement of shear correction factor owing to the consideration of the actual parabolic distribution of transverse shear stress. Zero transverse shear stress at the top and bottom of the plate is enforced to compute higher-order unknowns. C⁰ FE model makes it commercially viable. Stochastic FE analysis done with Monte Carlo Simulation (MCS) FORTRAN inhouse code, selection of design points using a random variable framework, and soft computing with MARS, ANN-PSO, GPR, and ANFIS is implemented using MATLAB in-house code. Following the random variable frame, design points were selected from the input data generated through Monte Carlo Simulation. A total of four-mode shapes are analyzed in the present study. The comparison study was done to compare present work with results in the literature and they were found in good agreement. The stochastic parameters are Young’s elastic modulus, shear modulus, and the Poisson ratio. Lognormal distribution of properties is assumed in the present work. The current soft computation models shrink the number of trials and were found computationally efficient as the MCS-based FE modelling. The paper presents a comparison of MARS, ANN-PSO, GPR, and ANFIS algorithm performance with the stochastic FE model based on TSDT.     

Multiscale approach to link red blood cell dynamics, shear viscosity, and ATP release

RBCs are known to release ATP, which acts as a signaling molecule to cause dilation of blood vessels. A reduction in the release of ATP from RBCs has been linked to diseases such as type II diabetes and cystic fibrosis. Furthermore, reduced deformation of RBCs has been correlated with myocardial infarction and coronary heart disease. Because ATP release has been linked to cell deformation, we undertook a multiscale approach to understand the links between single RBC dynamics, ATP release, and macroscopic viscosity all at physiological shear rates. Our experimental approach included microfluidics, ATP measurements using a bioluminescent reaction, and rheology. Using microfluidics technology with high-speed imaging, we visualize the deformation and dynamics of single cells, which are known to undergo motions such as tumbling, swinging, tanktreading, and deformation. We report that shear thinning is not due to cellular deformation as previously believed, but rather it is due to the tumbling-to-tanktreading transition. In addition, our results indicate that ATP release is constant at shear stresses below a threshold (3 Pa), whereas above the threshold ATP release is increased and accompanied by large cellular deformations. Finally, performing experiments with well-known inhibitors, we show that the Pannexin 1 hemichannel is the main avenue for ATP release both above and below the threshold, whereas, the cystic fibrosis transmembrane conductance regulator only contributes to deformation-dependent ATP release above the stress threshold.     

Study on Mechanical Properties of Multi-Cavity Steel-Concrete Composite Beam

This paper proposes a new form of composite beam: a multi-cavity steel-concrete composite beam. This composite beam uses internal perforated steel plate to connect the concrete with the steel structure, and shear connectors are no longer required, which is more suitable for industrial production. The mechanical properties of a multi-cavity steel-concrete composite beam in industrial applications are studied to avoid failures. In this paper, two multi-cavity steel-concrete composite beams with a size of 2500 mm × 200 mm × 300 mm were prepared, in which the angle of internal porous steel plate was set as 60° and 75°, respectively. A full-scale static load test was conducted on the beams to research its deformation and failure modes. The finite element software ANSYS was used to perform finite element modeling of multi-cavity steel-concrete composite beams and to analyze the influence of concrete strength, steel strength, porosity, and the angle of internal porous steel plate on the mechanical properties of composite beams. The results are as follows: before the composite beam reaches its serviceability limit state, its deformation basically shows a linear change; with the increase of load, the plastic deformation is gradually obvious, which can still provide a certain bearing capacity in the failure stage; the bearing capacity of the composite beam is positively correlated with the strength of concrete and steel, while negatively correlated with the porosity and the angle of internal porous steel plate; composite beams have large bearing capacity, good ductility and integrity.     

Viscoelastic properties of erythrocyte membranes of different vertebrate animals

Using equilibrium and relaxation measurements of micropipet-aspirated membrane projections, the membrane surface “shear” moduli and surface “viscosity” coefficients were obtained for the erythrocyte membranes of selected animals from five vertebrate classes. The particular “donor” animals included: Amphiuma, frog, turkey, toadfish, snake, turtle, iguana, opossum, tree shrew, and human. The coefficients characterize the first-order, recoverable material behavior for the membrane as a viscoelastic solid. Three types of nucleated cells (amphibian, avian, and “boney” fish) exhibited similar hyperelasticity with shear moduli of 7–8 × 10^?2 dyne/cm for “stretch” ratios of up to 3:1 (finite strains of the order 400%); the surface viscosity coefficients were also similar for these three types, 6–9 × 10^?3 dyne-sec/cm. The properties of nucleated cell membranes for reptiles were higher; the shear moduli were in the range 2–3 × 10^?1 dyne/cm, and the surface viscosity was 4–10 × 10^?2 dyne-sec/cm. In contrast with the nucleated erythrocyte membranes, membranes of nonnucleated mammalian cells all exhibited lower shear moduli, 1.5 × 10^?2 dyne/cm, and surface viscosity coefficients, <10^?3 dyne-sec/cm. The pressure versus length of aspirated membrane projections of both nucleated and nonnucleated cells correlated well with the analysis of a two-dimensional, viscoelastic membrane in large deformation (at constant area). In addition, resistance to deformation was observed to increase when the cells were illuminated in the Soret band (4047 Å), or when no glucose was present in the suspending medium.