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This study investigates acoustic radiation forces on spherical objects generated by Bessel beams in a viscous fluid. Radiation forces on elastic spheres and shells of different materials are examined using viscid expression with the thermoviscous correction included, and the results are then compared with numerical simulations based on the finite element method. The Stokes drag force for zero-order Bessel waves was theoretically derived, and in turn, a practical example of negative radiation forces is proposed and investigated together with the gravity, the buoyancy, and the drag force from acoustic streaming. It is found that the negative pulling force exists even including the positive forces from the other sources; however, the parameter regions for pulling forces are reduced especially for small objects. This work helps the further study of particle manipulations by acoustic Bessel beams in viscous fluids and also guides the experimental realization of acoustic tractor beams. [ABSTRACT FROM AUTHOR]

Because of the introduction of modal coupling, discontinuous boundaries have a significant impact on the vibration characteristics of annular plates. Based on the spectral element method (SEM) and parametric equivalent method (PEM), the vibration calculation and analysis of internally perforated annular plate with discontinuous boundary are explained. Firstly, a uniform annular plate is regarded as a spectral element, and the vibration response of an annular plate with general elastic boundaries is obtained based on the motion equation of the annular plate and the virtual spring method (VSM). The displacement solution is described by the Bessel function, and a fitting method of discontinuous spring stiffness coefficient based on the weighted least square norm least square method is proposed. Based on the force equilibrium condition, the vibration response of an annular plate with a discontinuous boundary is derived, and the reasons for the change of vibration characteristics with a discontinuous boundary are explained from modal superposition. The dynamic stiffness matrix method is used to establish the vibration equation of an annular plate with a discontinuous boundary, and the influence of internal openings on the vibration characteristics of an annular plate is effectively calculated by the parametric equivalent method. Finally, a finite element simulation model is established to test the accuracy and stability of the proposed method. The influence of general discontinuous boundary conditions on structural dynamic behavior is analyzed by numerical examples, which provides useful guidance for structural vibration analysis with discontinuous boundary conditions. [ABSTRACT FROM AUTHOR]

This study aims to derive the exact stretching and bending solutions of the radially FGM annular sandwich plate subjected to either radial pressure or transverse load. The radially FGM annular sandwich plate consists of two homogeneous rings and an FGM-undercoated layer with uniform Poisson's ratio and radially graded Young's modulus based on the power function. Although the radially FGM annular sandwich plate is nonhomogeneous, the stretching and bending problems can be analyzed separately based on the elastic plate theory. Then the exact solution corresponding to the power-law graded FGM can be evaluated by solving the simultaneous equations of the boundary and continuous conditions. The theoretical results are validated through the comparison with the finite element solutions. When degenerated, our results coincide with those of the homogeneous annular plate in the literature, making the obtained solutions reliable. Using the radial-FGM as the undercoated layer makes the strains and stresses smoothly continuous at the interfaces of the layers. The effects of the material index on mechanical behavior are under investigation. [ABSTRACT FROM AUTHOR]

In the present study, author analyses the vibration of protein microtubules and its interaction with the surrounding elastic medium and electromagnetic and gravitational forces. Protein microtubules are dynamic Nano fibers found inside the cell's cytoplasm, strengthening the cytoskeleton and gives shape to the cell. When the cell undergoes deformation microtubules vibrate. Understanding the vibration of these Nano fibers within the elastic medium and along with the body forces as electromagnetic and gravitational forces is crucial. The main purpose of this study is to explore the effects of surrounding elastic medium and electromagnetic and gravitational forces on the vibration of protein microtubules. The findings reveal that the effects of surrounding medium and the external influences on the vibration of these Nano fibers are significant. The study presents the numerical values in the form of table associated with microtubules in various conditions: free, embedded, and in the presence of electromagnetic and gravitational forces. [ABSTRACT FROM AUTHOR]

Measurement of the impact process is challenging due to its short duration and high frequency response. Due to the very small strain in low-velocity impacts, the requirements for the temporal and spatial resolution of test methods are extremely high. Traditionally, strain gauges or lasers are commonly used to measure the dynamic response of a single point, or quasi-static loading is used to achieve full-field response. To finely describe the transient full-field deformation process of low-velocity impacts, a high-speed imaging system combined with 3D digital image correlation (DIC) technique is set up to investigate the instantaneous responses of impact on a polyvinyl chloride (PVC) plate at the ms and με level. The full-field deformation of the contact surface and the whole process of elastic wave propagation are measured. The measurement by DIC closely matches the measurement by strain gauges and agrees well with the numerical simulation results. The measurement reveals that the "multi-micro-impacts" phenomenon may happen during a complete impact process due to the complex strain wave propagation. This work provides a benchmark case for low-velocity impact full-field testing, and the results show that 3D DIC can accurately evaluate dynamic behaviors of low-velocity impact between flexible bodies and can accurately describe the spatiotemporal propagation characteristics of strain waves. [ABSTRACT FROM AUTHOR]

The current study investigates the effects of strong potential porous materials to absorb the transmitted energy in a dissipative device containing a wave-bearing cavity. The expansion chamber consists of horizontal as well as vertical elastic boundaries that is filled with a compressible fluid and porous media. The porous media is dealt as an equivalent fluid with complex propagation speed and density, has effects on the eigenfunctions of cavity regions. The vibrational response of the vertical elastic components having different sets of edge conditions are incorporated by mode-matching tailored-Galerkin (MMTG) approach. This approach provides displacement of vertical elastic membrane which deals with various edge conditions. The MMTG approach has point-wise convergence that is conform through generalized orthogonal relations. The MMTG solutions are used to reconstruct matching conditions and to satisfy law of conservation of energy. It confirms the validity of retained solutions and accuracy of performed algebra. It is observed from the curves of TL and P abs that by varying edge conditions the absorbed power and TL are enhanced. [ABSTRACT FROM AUTHOR]

Deployable tubular structures, designed for functional expansion, serve a wide range of applications, from flexible pipes to stiff structural elements. These structures, which transform from compact states, are crucial for creating adaptive solutions across engineering and scientific fields. A significant barrier to advancing their performance is balancing expandability with stiffness. Using compliant materials, these structures achieve more flexible transformations than those possible with rigid mechanisms. However, they typically exhibit reduced stiffness when subjected to external pressures (e.g., tube wall loading). Here, we utilize origami-inspired techniques and internal stiffeners to meet conflicting performance requirements. A self-locking mechanism is proposed, which combines the folding behavior observed in curved-crease origami and elastic shell buckling. This mechanism employs simple shell components, including internal diaphragms that undergo pseudofolding in a confined boundary condition to enable a snap-through transition. We reveal that the deployed tube is self-locked through geometrical interference, creating a braced tubular arrangement. This arrangement gives a direction-dependent structural performance, ranging from elastic response to crushing, thereby offering the potential for programmable structures. We demonstrate that our approach can advance existing deployment mechanisms (e.g., coiled and inflatable systems) and create diverse structural designs (e.g., metamaterials, adaptive structures, cantilevers, and lightweight panels). We anticipate our design to be a starting point to drive technological advancement in real-world deployable tubular structures. [ABSTRACT FROM AUTHOR]

This study investigates the mechanical response of a bi-directional functionally graded plate consisting of three distinct materials when subjected to low-velocity impact. Utilizing the New Refined Plate Theory, the research explores the mechanical behavior of the plate resting on a Pasternak elastic foundation, providing insights useful for engineering applications. The investigation examines various parameters, including initial impact velocity, projectile radius, volume fraction indices, and elastic foundation stiffness, and their effects on critical response characteristics such as contact force, indentation, lateral deflection, and projectile velocity. The theoretical predictions are validated through detailed comparisons with existing literature and numerical simulations, ensuring the reliability and applicability of the proposed methodology. This study introduces a novel approach using refined plate theory to analyze low-velocity impact on 2D-FGMs, providing practical insights for structural analysis. The findings deepen understanding of functionally graded materials and enhance the evaluation of impact-resistant structures. The research highlights the importance of diverse parameters in improving structural performance and reliability, relevant across aerospace, civil, and mechanical engineering. Detailed exploration shows that initial impact velocities and projectile radius enhance impact force and deflection, while volume fraction indices and foundation stiffness influence the dynamic response. [ABSTRACT FROM AUTHOR]

In this study the optimum topology distribution of the magnetorheological elastomer (MRE) layer in an adaptive sandwich plate is investigated. The adaptive sandwich plate consists of an MR elastomer layer embedded between two thin elastic plates. A finite element model has been first formulated to derive the governing equations of motion. A design optimization methodology incorporating the developed finite element model has been subsequently developed to identify the optimum topology treatment of the MR layer to enhance the vibration control in wide-band frequency range. For this purpose, the dynamic compliance and density of each element are defined as the objective function and design variables in the optimization problem, respectively. The method of the solid isotropic material with penalization (SIMP), is extended for material properties interpolation leading to a new MRE-based penalization (MREP) model. Method of moving asymptotes (MMA) has been subsequently utilized to solve the optimization problem. The developed finite element model and design optimization method are first validated using benchmark problems. The proposed design optimization methodology is then effectively utilized to investigate the optimal topologies of the magnetorheological elastomer (MRE) core layer in MRE-based sandwich plates under various boundary and loading conditions. Results show the effectiveness of the proposed design optimization methodology for topology optimization of MRE-based sandwich panels to mitigate the vibration in wide range of frequencies. [ABSTRACT FROM AUTHOR]

The article presents the use of the dynamic stiffness method (DSM) for analyzing the buckling and prestressed vibration of advanced composite plates subjected to uniaxial and biaxial in-plane loads. The plate consists of laminated layers reinforced with graphene platelets and the effective material properties of the plate are computed using the Halpin-Tsai micromechanical model. Through the application of Hamilton's principle, the governing differential equations (GDEs), based on the first order shear deformation theory, are obtained for the GPL-reinforced plate resting on elastic foundations. For a segment of the plate, the dynamic stiffness matrix is obtained by solving the GDEs with the Levy form of boundary conditions. Subsequently, the assembled global dynamic stiffness matrix is solved using the Wittrick-Williams algorithm to compute the buckling and prestressed vibration behavior of the plates. Convergence and comparative studies are performed to show that the DSM is efficient and produces very accurate results as it is formulated based on closed-form solutions. Several parametric studies are carried out to study the effect of different edge loads, foundation parameters, and plate boundary conditions. Results for non-uniform plate configurations are also presented to highlight the applicability and efficacy of the present DSM to fairly complex plate configurations. [ABSTRACT FROM AUTHOR]

In this paper, wave propagation in functionally graded (FG) porous plates resting on Winkler-Pasternak foundation is studied using a quasi-3D shear deformation theory. The proposed theory has a new displacement field that includes indeterminate integral terms and contains fewer unknown variables taking into account the effect of transverse shear and thickness stretching. The parameters of the elastic foundation are introduced in the present formulation following the mathematical model of Pasternak. In addition, the effect of porosity is studied. The material of the FG plate is inhomogeneous and the material properties are assumed to vary continuously in the thickness direction according to a power law of the volume fraction. The equations governing wave propagation in the plates resting on an elastic foundation are derived using Hamilton's principle. Then, the dispersion relationship between frequency and wave number is solved analytically. A comprehensive numerical result is accomplished to evaluate the effects of the volume fraction index, the porosity, thickness ratio (h/a), and the wave number on the wave propagation in functionally graded porous plates are discussed in detail. [ABSTRACT FROM AUTHOR]

Thin elastic ribbons represent a class of intermediary objects lying in-between thin elastic plates and thin elastic rods. Although the two latter families of thin structures have received much interest from the Computer Graphics community over the last decades, ribbons have seldom been considered and modelled numerically so far, in spite of a growing number of applications in Computer Design. In this article, starting from the reduced developable ribbon models [Sadowsky 1929; Wunderlich 1962] recently popularised in Soft Matter Physics, we propose a both accurate and efficient algorithm for computing the statics of thin elastic ribbons. Inspired by the super-clothoid model for thin elastic rods, our method relies on compact ribbon elements whose normal curvature varies linearly with respect to arc length s, while their geodesic torsion is quadratic in s. In contrast, however, for the sake of efficiency, our algorithm avoids building a fully reduced kinematic chain and instead treats each element independently, gluing them only at the final solving stage through well-chosen bilateral constraints. Thanks to this mixed variational strategy, which yields a banded Hessian, our algorithm recovers the linear complexity of low-order models while preserving the high-order convergence of curvature-based models. As a result, our approach is scalable to a large number of elements, and suitable for various boundary conditions and unilateral contact constraints, making it possible to handle challenging scenarios such as confined buckling experiments or Möbius bands with contact. Remarkably, our mixed algorithm proves an order of magnitude faster compared to Discrete Elastic Ribbon models of the literature while achieving, in a few seconds only, high accuracy levels that remain out of reach for such low-order models. Additionally, our numerical model can incorporate various ribbon energies, including the RibExt model for quasi-developable ribbons recently introduced in Physics [Audoly and Neukirch 2021], which allows to transition smoothly between a rectangular Kirchhoff rod and a (developable) Sadowsky ribbon. Our numerical scheme is carefully validated against demanding experiments of the Physics literature, which demonstrates its accuracy, efficiency, robustness, and versatility. Our Merci code is publicly available at https://gitlab.inria.fr/elan-public-code/merci for the sake of reproducibility and future benchmarking. [ABSTRACT FROM AUTHOR]

An elastic rod is perfectly bonded to a von Kármán elastic plate such that, except for a relative twist, no relative displacements are allowed between the rod and the plate. The deformation of the confined rod is strongly coupled to that of the flexible environment to which it has to necessarily confirm. A framework is developed where, for a given distribution of growth strains in the rod, the shape as well as the internal forces and the internal moments of the rod-plate system can be determined. The nature of mechanical interaction between the rod and the plate is discussed in detail. The boundary-value-problems, to be solved for a scalar stress function and a scalar transverse displacement field, both piecewise-smooth in the plate domain, include in-plane strain compatibility conditions and transverse force equilibrium equations on, and away from, the curve of rod-plate intersection. [ABSTRACT FROM AUTHOR]

The problems of constructing an exact or approximate solution of system of singular integro‐differential equations related to the problems of adhesive interaction between elastic thin finite or infinite nonhomogeneous patch and elastic plate are investigated. For the patch loaded with horizontal and vertical forces, the usual model of beam bending in combination with the uniaxial stress state model is valid. Using the methods of theory of analytic functions, integral transformation, or orthogonal polynomials, the singular integro‐differential equations reduced to the different boundary value problems (Karleman type problem with displacements and Riemann problem) of the theory of analytic functions or to the infinite system of linear algebraic equations. The asymptotic analysis of problem is carried out. [ABSTRACT FROM AUTHOR]

This research aims to explore the free vibration behavior of functionally graded porous (FGP) plates resting on a Kerr-type elastic foundation. This investigation employs an innovative trigonometric shear deformation (ITSD) theory with five variables. The study encompasses various plate configurations, including homogeneous FGP plates, hard-core FGP sandwich plates, and soft-core FGP sandwich plates with both regular and irregular pore structures. The ITSD theory naturally addresses shear stress concerns at the outer surfaces, while also considering the thickness stretching effect, all without the need for correction factors. To formulate the governing equations for the free vibration of such plates on an elastic foundation, Hamilton’s principle is employed. The Navier double trigonometric series approach is then utilized to solve this problem. To validate the plate theory and methodologies used in this work, a comparative analysis is conducted with existing studies. Additionally, comprehensive parametric simulations are employed to examine the impact of different factors, such as geometric properties, material characteristics, sandwich schemes, and parameters of the Kerr-type foundation, on the dimensionless natural frequencies of simply supported rectangular FGP plates. [ABSTRACT FROM AUTHOR]

Comminuted proximal humerus fractures are often repaired by metal plates, but potentially still experience bone refracture, bone “stress shielding,” screw perforation, delayed healing, and so forth. This “proof of principle” investigation is the initial step towards the design of a new plate using alternative materials to address some of these problems. Finite element modeling was used to create design graphs for bone stress, plate stress, screw stress, and interfragmentary motion via three different fixations (no, 1, or 2 “kickstand” [KS] screws across the fracture) using a wide range of plate elastic moduli (EP = 5–200 GPa). Well‐known design optimization criteria were used that could minimize bone, plate, and screw failure (i.e., peak stress < ultimate tensile strength), reduce bone “stress shielding” (i.e., bone stress under the new plate ≥ bone stress for an intact humerus, titanium plate, and/or steel plate “control”), and encourage callus growth leading to early healing (i.e., 0.2 mm ≤ axial interfragmentary motion ≤ 1 mm; shear/axial interfragmentary motion ratio <1.6). The findings suggest that a potentially optimal configuration involves the new plate being manufactured from a material with an EP of 5–41.5 GPa with 1 KS screw; but, using no KS screws would cause immediate bone fracture and 2 KS screws would almost certainly lead to delayed healing. A prototype plate might be fabricated using alternative materials suggested for orthopedics and other industries, like fiber‐metal laminates, fiber‐reinforced polymers, metal foams, pure polymers, shape memory alloys, or 3D‐printed porous metals. [ABSTRACT FROM AUTHOR]

The work presents a solution to the bending problem of an infinite piecewise homogeneous isotropic plate with an elastic circular washer and a radial through straight crack. It was assumed that under the action of an external loads at infinity, the edges of the crack are smoothly contacted on area of constant width (strip contact) on the upper base of the plate. The solution of the problem is built using the methods of the theory of functions of a complex variable and complex potentials and is reduced to a system of singular integral equations, which is numerically solved using the method of mechanical quadrature A numerical analysis of the problem is conducted and graphic dependencies of contact force, coefficients of intensity of moments and forces at various parameters of the problem were constructed. [ABSTRACT FROM AUTHOR]

This paper explores the response of a floating ice sheet to a forced, time-harmonic oscillatory pressure applied to the ice-covered surface of a uniform, finite depth fluid. The floating ice sheet is modeled as a thin elastic plate following the Euler–Bernoulli beam equation, with the additional consideration of in-plane compressive forces acting on the ice. Employing linear wave theory, the problem is presented as an initial boundary value problem and is solved using Laplace and Fourier transforms to obtain a mathematical expression for the ice sheet's deflection in terms of infinite integrals. These integrals are thereafter solved asymptotically for large time and distance using the stationary phase method. The asymptotic analysis indicates a growing response over time when the poles and stationary points of the phase functions coalesce. The deflection of the floating ice sheet is graphically presented, highlighting the effects of various non-dimensional parameters, such as flexural rigidity, compressive force, uniform current speed, and the angular frequency of the oscillatory pressure. Additionally, the group velocity and phase velocity of flexural gravity waves are derived from the dispersion relation and elucidated using diagrams. The results show that compressive force and current speed significantly influence wave amplitude, enhancing the oscillatory nature, while the flexural rigidity of the elastic plate and the angular frequency of the applied pressure have a substantial impact on the plate's deflection. [ABSTRACT FROM AUTHOR]

Interaction of nonlinear shallow water waves with a deformable seafloor represented by an infinitely long elastic sheet lying on a viscoelastic foundation is investigated. The study is motivated by damping features of muddy coastal areas on ocean waves. The mathematical model utilizes the Level I Green–Naghdi equations for the fluid flow and the thin plate theory for the elastic bottom deformations. The methodology is validated through comparisons with the linear water wave theory and available numerical data. Theoretical predictions of the coupled seafloor vertical displacement and free-surface elevation are provided for a range of the incoming wave parameters and the seafloor characteristics. The results demonstrate that the wave experiences significant decrease in amplitude and propagation speed, as a result of the interaction with the deformable seabed. An exponential decay of periodic waves with propagating distance is observed. It is found that the foundation stiffness is of dominating importance, as compared to other parameters of the deformable seafloor. It is shown that waves with shorter wavelength are dissipated strongly by the action of the deformable seafloor while the bottom conditions have less impact on long wave dissipation. Just the opposite, long waves experience significant wave diffraction when compared to the waves with shorter wavelength. Patterns of the velocity field are shown to be modulated in magnitude and wavelength contributed by the seafloor. [ABSTRACT FROM AUTHOR]

Twelve dogs below one year of age presented with a history of forelimb or hindlimb lameness, suggestive of either radius or tibia fracture were selected to study the fracture stabilisation by Elastic Plate Osteosynthesis (EPO) technique using 2.0/2.7 mm Veterinary Cuttable Plate (VCP). The implants were selected according to body weight and bone size. Post-operatively, the dogs were evaluated by clinical, radiographical and lameness grading. Primary healing was observed in eight cases and secondary healing in four cases. Fracture healing was observed by 30th post-operative day in most of the cases. The dogs regained full limb functionality by 15-30 days post-surgery. All the animals regained normal return to weight bearing early (within one month) with excellent to good limb usage. Plate removal was done in all cases on 5-8 weeks post-surgery. No major post-operative complications were observed. To conclude, the VCP used was inexpensive and the EPO technique using VCP was useful for long bone fractures of young dogs making it suitable for use in Veterinary practice and the technique resulted in early weight bearing and good functional limb out come without any complications. [ABSTRACT FROM AUTHOR]

Here, an analytical form Navier solution for higher-order micropolar theory of cylindrical shell was developed based on the CUF approach. The cases of complete linear expansion and model based on Timoshenko-Mindlin shear deformation hypothesis are considered in detail. The two-dimensional system of differential equations obtained here using the principle of virtual displacements for the theory of micropolar elastic cylindrical shell of a higher order is solved here for the case of freely supported cylindrical shell using the Navier variable separation method. Some numerical examples were performed and the influence of the rotational field, as well as the micropolar couple stress on the stress–strain state, was analyzed. The equations presented here can be used for the stress–strain calculation and for thin-walled structures modeling in macro-, micro-, and nanoscale, with considering effects of micropolar couple stress and rotation. [ABSTRACT FROM AUTHOR]

This article relates with the interaction of water waves obliquely incident on a semi-infinite submerged elastic plate of insignificant thickness. The solution is obtained using method of mode matching. Reflection coefficients under the variation of various physical parameters: submergence depth, angle of incidence, stiffness of elastic plate and Poisson's ratio, for two different edge conditions (i) pinned edge condition and (ii) sliding edge condition are discussed. Convergence and validation of results is also given. Behaviour of the velocity potentials around semi-infinite submerged elastic plate for different physical parameters are also analyzed. The consequences are explained through numerical and graphical results. More over energy balance relation is also discussed. [ABSTRACT FROM AUTHOR]

The sixth-order basic differential equation of axisymmetric bending model for modified gradient elastic Kirchhoff–Love plates (MGEKLPs) subjected to both transverse and in-plane loads in cylindrical coordinate system is derived on the basis of the simplified deformation gradient theory and general MGEKLP model in Cartesian coordinates, which incorporates two length-scale parameters related to strain gradient and rotation gradient. Using the variational method, five distinct types of axisymmetric boundary conditions (BCs) corresponding to the basic equation are simultaneously obtained. Specifically, there are two modified classical BCs and one non-classical higher-order BC for each boundary. Applying the axisymmetric MGEKLP model, we present a general solution for size-dependent bending deflection and conduct a specific analysis of axisymmetric bending examples in circular and annular thin plates under transverse loads. The study presents two types of (i.e., singly and doubly) clamped and simply supported BCs and delves into the impact of two distinct higher-order BCs on axisymmetric deflection by examining clamped and simply supported circular thin plates. In addition, based on the axisymmetric bending of an annular thin plate with simply supported inner edge and free outer edge under the action of uniform bending moment, the special case of influence of strain gradient and rotation gradient parameters on axisymmetric deflection are discussed. This study enhances the comprehensiveness of axisymmetric bending deformation of gradient elastic thin plates and can offer theoretical guidance for the microstructure design of bending materials. [ABSTRACT FROM AUTHOR]

Based on the small-amplitude water wave theory, the usefulness of a vertical porous structure extending from top to bottom of finite width to reduce the wave-induced hydrodynamics responses of an elastic plate that is floating freely on the free surface is studied. The fluid flow inside the porous structure is based on Sollitt and Cross model, and the elastic plate is modeled using the thin plate theory. A generalized code based on the eigenfunction expansion method is developed for solving the boundary value problem. Scattering coefficients and various hydrodynamic parameters related to the wave scattering, such as wave forces on the porous structure, free surface elevation, elastic plate deflection, shear force, and strain, are analyzed for various waves and structural parameters of porous structure and elastic plate. It is found that the values of the scattering coefficients are less with progressively increasing width and frictional coefficient of the porous structure. As more wave is dissipated by the porous structure with an increase in frictional coefficient, as a result, the free surface elevation, plate deflection, shear force, and strain decrease with an increase in frictional coefficient. Moreover, with the distance between the porous structure and the elastic plate, the scattering coefficients and forces on the porous structure follow a periodic and oscillatory pattern. This model is expected to be of great help in protecting different coastal assets. [ABSTRACT FROM AUTHOR]

• A coupled electromagnetic-mechanical model is built to calculate the coupling behaviors of superconducting coils. • Mechanical deformation impacts the motion of magnetic flux and changes the critical current of superconductors. • The roles of contact conditions in the superconducting coils are derived theoretically. • A mechanical homogenization model is proposed to simplify the model containing hundreds of contact pairs. Rare-earth based barium copper oxide (REBCO) superconducting coated conductors are promising candidates for the design of high field magnets. In a high magnetic field, these conductors have to withstand huge Lorentz force, which would threaten the safety of superconducting devices. Recently, researchers have found that the electromagnetic-mechanical coupling has a significant impact on the overall response of the magnet system. It has been demonstrated that mechanical deformation can lead to the movement of magnetic flux in superconductors and changes in the critical current of superconductors. To take into account the electromagnetic-mechanical coupling effects, REBCO coated conductors are modeled as deformable conductors based on continuum mechanics of electromagnetic solids. Then, a fully coupled electromagnetic-mechanical model is developed in this paper, which is verified with the experimental results. Furthermore, during the electromagnetic-mechanical coupling simulation, contact separation occurs in REBCO pancake coils. To characterize the global mechanical performance of the REBCO pancake coils (containing hundreds of contact conditions), the concept of flexural rigidity in elastic shell theory is employed. Then, a mechanical homogeneous model is proposed to simplify the model containing hundreds of contact pairs and enable the effective simulation of large-scale HTS systems. This framework can provide theoretical support to the mechanical research of high field magnets. [ABSTRACT FROM AUTHOR]

We formulate a direct theory for fiber-reinforced elastic shells. Our framework utilizes the Cosserat theory of elasticity to model both the shell-like nature of the structure and the embedded fiber response. To this end, we merge the multiple-director theory of Cosserat continua with the additional constraint that the fibers convect as material curves on the surface. The virtual power statement furnishes the equilibrium equations. We also present a coordinate-free formulation and close with a discussion of material symmetry. [ABSTRACT FROM AUTHOR]

As part of optimizing a steel composite section to determine whether longitudinal stiffeners could be omitted concerning plate buckling, a buckling tool was developed that implements both the effective width method (EWM) and the reduced stress method (RSM). These two methods are offered in addition to the finite element method in EN 1993‐1‐5 for buckling analysis. It was found that when using the formula given in EN‐1993‐1‐5 for calculating the critical buckling stress of unstiffened buckling fields, which is independent of the acting stress distribution, the ratio of the elastic critical plate buckling stress to the elastic critical column buckling stress (σcr,p/σcr,c) is underestimated if the compressive stress is not uniform. This affects the detection of column buckling behavior. The most economical variant resulting from the optimization, the buckling tool, the influence of shear deformations combined with plate buckling, and the column buckling behavior of unstiffened buckling fields are presented in this paper. [ABSTRACT FROM AUTHOR]

Thick-coal-seam with complex structures and thick-hard roof in the initial mining phase pose various challenges, including a long weighting interval, strong rock pressure, poor top coal caving performance (TCCP), and significant coal loss. These problems directly affect the safety and efficiency of the mining operations. This study employs the principles of elastic thin plates and ellipsoidal bodies to unravel the formation mechanism of strong rock pressure in thick-hard roof and the influence of parting on the TCCP. In addition, a hydraulic fracturing technique is proposed for safe-efficient recovery during the initial mining phase. The reliability of this technique is verified through numerical simulations and field experiments. The research findings reveal the following. (1) The primary causes of strong rock pressure in the mining face are attributed to a long weighting interval and wide collapse range of the main roof, and the weighting interval is primarily influenced by the thickness and tensile strength of the main roof. (2)The key factor affecting the TCCP is the cantilever beam structure formed by the fracture of the thick-hard parting, as it intersects the ellipsoidal body during coal caving. The simultaneous fracturing of both the top coal and roof can reduce the weighting interval on the working face. This process effectively decreased the strength of the thick-hard parting within the top coal, while simultaneously enhancing its load strength and eliminating the cantilever structure resulting from the parting fracture. It not only reduces the first weighting intensity but also promotes the early and proper coal release, thereby enhancing the TCCP and ensuring safe-efficient mining during the initial mining phase. (3) Aiming at the difference in the strengths of the top coal and roof, a graded hydraulic fracturing technique and system were proposed. Fracturing boreholes with a diameter of 60 mm, spacing of 10 m, and height of 20.85 m, which can economically and effectively ensure the fracturing results. Field applications have demonstrated that fractured coal and rocks in fracturing areas exhibit well-developed fractures. During the initial mining phase, the weighting interval in the working face was reduced by 20 m, resulting in a decrease in the overburden pressure and 26.9% reduction in the lumpiness of the top coal. Additionally, the recovery rate increased by 31.19%. [ABSTRACT FROM AUTHOR]

In this article, we study the numerical corroboration of a variational model governed by a fourth-order elliptic operator that describes the deformation of a linearly elastic flexural shell subjected not to cross a prescribed flat obstacle. The problem under consideration is modelled by means of a set of variational inequalities posed over a non-empty, closed and convex subset of a suitable Sobolev space and is known to admit a unique solution. Qualitative and quantitative numerical experiments corroborating the validity of the model and its asymptotic similarity with Koiter's model are also presented. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'. [ABSTRACT FROM AUTHOR]

A class of variational inequalities describing the equilibrium of elastic Timoshenko plates whose boundary is in contact with the side surface of an inclined obstacle is considered. At the plate boundary, mixed conditions of Dirichlet type and a non-penetration condition of inequality type are imposed on displacements in the mid-plane. The novelty consists of modelling oblique interaction with the inclined obstacle which takes into account shear deformation and rotation of transverse cross-sections in the plate. For proposed problems of equilibrium of the plate contacting the inclined obstacle, the unique solvability of the corresponding variational inequality is proved. Under the assumption that the variational solution is smooth enough, optimality conditions are obtained in the form of equilibrium equations and relations revealing the mechanical properties of integrated stresses, moments and generalized displacements on the contact part of the boundary. Accounting for complementarity type conditions owing to the contact of the plate with the inclined obstacle, a primal-dual variational formulation of the obstacle problem is derived. A semi-smooth Newton method based on a generalized gradient is constructed and performed as a primal-dual active-set algorithm. It is advantageous for efficient numerical solution of the problem, provided by a super-linear estimate for the corresponding iterates in function spaces. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'. [ABSTRACT FROM AUTHOR]

A circular non-touch mode capacitive pressure sensor can operate in both transverse and normal uniform loading modes, but the elastic behavior of its movable electrode plate is different under the two different loading modes, making its input–output analytical relationships between pressure and capacitance different. This suggests that when such a sensor operates, respectively, in transverse and normal uniform loading modes, the theory of its numerical design and calibration is different, in other words, the theory for the transverse uniform loading mode (available in the literature) cannot be used as the theory for the normal uniform loading mode (not yet available in the literature). In this paper, a circular non-touch mode capacitive pressure sensor operating in normal uniform loading mode is considered. The elastic behavior of the movable electrode plate of the sensor under normal uniform loading is analytically solved with the improved governing equations, and the improved analytical solution obtained can be used to mathematically describe the movable electrode plate with larger elastic deflections, in comparison with the existing two analytical solutions in the literature. This provides a larger technical space for developing the circular non-touch mode capacitive pressure sensors used for measuring the static gas pressure (belonging to normal uniform loading). [ABSTRACT FROM AUTHOR]

[Display omitted] Microcapsules with osmotically-inflated elastic shells exhibit an ultrafast release of encapsulants while mechanically stimulating the microenvironments, akin to popping balloons. To prepare elastic shells with uniform thickness and size, monodisperse water-in-oil-in-water (W/O/W) double-emulsion drops are produced in a capillary microfluidic device. The polydimethylsiloxane (PDMS)-containing oil phase is thermally cured to create the elastic shell. The elastic shells are inflated by pumping water into the lumen in hypotonic conditions. The inflated microcapsules produced undergo mechanical compression, and their release properties are studied. By controlling the osmotic pressure difference, Microballoons are inflated into a diameter of 200 μm – 316 μm and shell thickness of 7.8 μm – 0.7 µm, respectively. The inflated shell pops due to mechanical failure when subjected to mechanical stress above a certain threshold, resembling a balloon. During popping, the stretched shell rapidly retracts to the original uninflated state, resulting in an ultrafast release of encapsulants from the lumen within a millisecond. This process converts elastic potential energy stored in the shell into mechanical energy with substantial power. The microballoons mechanically stimulate the local environment, leading to the direct and rapid release of encapsulants. This has the potential to improve absorption efficiency. [ABSTRACT FROM AUTHOR]

The rational synthesis of an electrode material with a highly active and stable architecture is very critical to achieving high-performance electrochemical energy storage. Herein, N-doped carbon restricting yolk–shell CoSe2/Ni3Se4 (CoSe2/Ni3Se4@NC) flower-like microspheres were successfully synthesized from solid CoNi-glycerate microspheres using a coating technology as an anode material for lithium-ion batteries (LIBs). The unique yolk–shell CoSe2/Ni3Se4@NC microspheres with hierarchical pores can increase the contact area with the electrolyte and provide enough transfer channels for the diffusion of Li+. The carbon layer on the surface of CoSe2/Ni3Se4@NC can not only improve the conductivity of the electrode but also provide the protective effect of active nanosheets during the process of synthesis, avoiding the overall structure collapse during the charge/discharge process of LIBs. Benefiting from the high conductivity, hollow structure, and elastic NC shell bestowed by the unique architecture, the yolk–shell CoSe2/Ni3Se4@NC anode shows excellent lithium storage performances, such as an excellent reversible specific capacity of 319 mA h g−1 at a current density of 1000 mA g−1 after 500 cycles and excellent cycling stability. This synthesis strategy provides a new way to optimize the lithium storage performance of transition metal compound electrode materials, which is helpful to the design of the next generation of high-performance LIBs. [ABSTRACT FROM AUTHOR]

This paper investigates the free vibration analysis of cutout laminated composite plates resting on an elastic foundation of the Winkler and Pasternak type. An efficient isoparametric 9-noded Lagrangean C0 finite element method is developed based on five degrees of freedom (d.o.f) first-order shear deformation theory (FSDT), which has the benefit of the requirement of only one variable along the thickness to model the plate equations to obtain the numerical results from the formulation. The equation of motion of the plate is derived using the virtual work principle. The accuracy and efficiency of the current formulation are validated with established results concerning free vibration analysis of laminated composite plates on elastic foundations and plates containing cutouts. It is found that the results obtained using the present formulation have variation within ±1.5% of the established results. After sufficient validation of the present formulation, new parametric results are given for cutout laminated composite plates resting on elastic foundations with varying elastic foundation stiffness parameters, boundary conditions, cutouts, side-to-thickness ratios, and the aspect ratio of plate and fiber angle orientations. The impact of cutouts on the dynamic behavior of laminated composite plates is investigated, and interestingly, it is observed that cutouts alter the frequency response of plates when introduced to plates without elastic foundations or plates resting on elastic foundations having low stiffness parameters; however, when cutouts are introduced to plates with high elastic foundation stiffness, the cutouts have very negligible impact on the dynamic behavior of plates. It is observed that the layout and the pattern of the cutout in the laminated composite plate affect the dynamic behavior of plates at all elastic foundation stiffnesses. [ABSTRACT FROM AUTHOR]

This work analyzes the dynamic responses of plates with an elastic foundation under a concentrated moving mass. The plate is made of fluid-saturated functionally graded porous material (FFGPM). The material properties of the FFGPM plate are assumed to vary smoothly across the thickness, with symmetric, asymmetric, and uniform patterns for porosity distribution. The governing equations of the FFGPM plate are developed using Reddy's third-order shear deformation plate theory (Reddy's TSDT), Biot's poroelasticity theory, pb2-Ritz formulation, and the Lagrange equation. In the numerical results, the Newmark scheme is used to obtain the deflection response of the FFGPM plate with the traveling mass. Two approaches are considered and discussed, including moving load and moving mass. Moreover, the influences of the porosity coefficient, distribution patterns, different boundary conditions, elastic foundations, geometry parameters, Skempton coefficient, moving mass velocity, and the mass of moving mass on the dynamic characteristics of the FFGPM plate are studied. [ABSTRACT FROM AUTHOR]

The nonlinear vibration analysis of a sandwich rectangular plate is presented in this study. The layers of the plate are composed of composites reinforced with graphene nanoplatelets, while the plate's core is composed of honeycomb structures. The fundamental relations of equation motions are derived using the displacement field of first-order shear deformation theory. Furthermore, geometric nonlinearity is taken into consideration by using von-Karman nonlinear strains. The Hamilton's principle is utilized to govern the partial equations of motion. Galerkin's technique is used to simplify the equation motions into a nonlinear motion equation. The multiple scales method is then used to solve the nonlinear motion equation. The impact of many factors, including the volume percentage and dispersion of graphene nanoplatelets along thickness axes, distinct parameters of the honeycomb core, geometric attributes, and initial conditions, on the nonlinear-to-linear frequency ratio is examined. [ABSTRACT FROM AUTHOR]

In this paper, we study the Γ -limit of a properly rescaled family of energies, defined on a narrow strip, as the width of the strip tends to zero. The limit energy is one-dimensional and is able to capture (and penalize) concentrations of the midline curvature. At the best of our knowledge, it is the first paper in the Γ -convergence field for dimension reduction that predicts elastic hinges. In particular, starting from a purely elastic shell model with "smooth" solutions, we obtain a beam model where the derivatives of the displacement and/or of the rotation fields may have jump discontinuities. Mechanically speaking, elastic hinges can occur in the beam. [ABSTRACT FROM AUTHOR]

The proposed revisit to a classical problem in fluid–structure interaction is due to an interest in the analysis of the narrow resonances corresponding to a low-frequency fluid-borne wave, inspired by modeling and design of metamaterials. In this case, numerical implementations would greatly benefit from preliminary asymptotic predictions. The normal incidence of an acoustic wave is studied for a circular cylindrical shell governed by plane strain equations in elasticity. A novel high-order asymptotic procedure is established considering for the first time all the peculiarities of the low-frequency behavior of a thin fluid-loaded cylinder. The obtained results are exposed in the form suggested by the Resonance Scattering Theory. It is shown that the pressure scattered by rigid cylinder is the best choice for a background component. Simple explicit formulae for resonant frequencies, amplitudes, and widths are presented. They support various important observations, including comparison between widths and the error of the asymptotic expansion for frequencies. [ABSTRACT FROM AUTHOR]

The stress state of ice shelves using numerical modeling is studied. An ice shelf is modeled by an elastic plate floating on water and attached to the ice cover at a grounding point. Stress calculations are carried out using the FLAC3D program. The resulting stresses significantly exceed the tensile strength of the glacier during bending. The maximum tensile stresses on the lower surface of the glacier near the grounding point reach 5 × 107 Pa and significantly exceed the maximum strength values of the glacier. The mechanism of rapid transformation of a solid ice shelf into mélange is shown. During the deformation process, vertical displacements (ice ridges) can reach tens of meters. [ABSTRACT FROM AUTHOR]

The hydrodynamic stability behavior of a two-layer falling film is explored with a floating flexible plate on the top layer surface. The stress balance at the surface is modeled using a modified membrane equation. There is an insoluble surfactant at the liquid-liquid interface of the flow system. The linear instability of perturbation waves is captured by numerically solving the generalized Orr-Sommerfeld eigenvalue problem using the Chebyshev spectral collocation technique. Four different types of linear stability modes are identified: surface mode (SM), interface mode (IM), interface surfactant mode (ISM), and shear mode (SHM). The floating flexible plate has an inferior impact on all the existing modes in the longwave zone. However, a significant influence is noticed for the finite wave numbers. The surface and interface wave instabilities can be suppressed in the smaller wavenumber zone by imposing higher structural rigidity and uniform thickness of the flexible plate. The stabilizing nature of the surface mode becomes more powerful when the top layer viscosity is dominant. A new interfacial instability emerges when the top layer is less viscous than the lower one. At moderate Reynolds numbers, the behavior of interface mode is different in two different zones m r < 1 and m r > 1 , where m and r denote the viscosity and density ratio, respectively. Further, the unstable shear modes induced by the top and bottom layers are detected under the low inclination angles with a strong inertia force. The occurrence of the shear modes requires the viscosity and density of the lower layer to be much higher than those of the upper layer. The influence of characteristic parameters of the flexible plate on the lower layer shear mode is not very sensitive. Finally, the competition between the different modes for dominance of stability boundaries is also discussed. • The hydrodynamic stability of a two-layer falling film is explored with a floating flexible plate on the top surface. • The generalized Orr-Sommerfeld eigenvalue problem is solved using Chebyshev spectral collocation technique. • Four modes, known as surface, interface, interface surfactant, and shear modes are detected. • The flexible plate has an inferior impact in the longwave zone, but significant effect in the finite wave number zone. • The plate's rigidity and thickness suppress the surface and interface wave instability in the smaller wavenumber zone. [ABSTRACT FROM AUTHOR]

This paper presents an analytical study on the in-plane vibrations of a rectangular elastic lattice plate. The plane lattice is modelled considering central and angular interactions. The lattice difference equations are shown to coincide with a spatial finite difference scheme of the corresponding continuous plate. The considered lattice converges to a 2D linear isotropic elastic continuum at the asymptotic limit for a sufficiently small lattice spacing. This continuum has a free Poisson's ratio, which must be lower than that foreseen by the rare-constant theory, to preserve the definite positiveness of the associated discrete energy. Exact solutions for the in-plane eigenfrequencies and modes are analytically derived for the discrete plate. The stiffness characterising the lattice interactions at the boundary is corrected to preserve the symmetry properties of the discrete displacement field. Two classes of constraints are considered, i.e., sliding supports at the nodes, one normal and the other parallel to the boundary. For both boundary conditions, a single equation for the eigenfrequency spectrum is derived, with two families of eigenmodes. Such behaviour of the lattice plate is like that of the continuous plate, the eigenfrequency spectrum of which has been given by Rayleigh. The convergence of the spectrum of the lattice plate towards the spectrum of the continuous plate from below is confirmed. Two continuous size-dependent plate models, considering the strain gradient elasticity and non-local elasticity, respectively, are built from the lattice difference equations and are shown to approximate the plane lattice accurately. [ABSTRACT FROM AUTHOR]

Experimental tests of cross-laminated timber (CLT)-concrete composite floor panels were conducted. The tests consisted of linear-elastic tests of square CLT-concrete composite panels with a novel shear connector to determine elastic orthotropic plate properties. After the linear-elastic tests, the panels were subjected to a patch load at the center of the panel and tested to failure. To investigate load transfer across longitudinal joints between adjacent panels, nonuniform bending tests were conducted. Results from the experimentally measured orthotropic plate properties showed that the shear connector increased the bending stiffness in the weak direction of the panel compared to prior test results using conventional shear connectors. The tests to failure exhibited larger differences in behavior between the strong and weak orientations of the specimens, with both showing substantial inelastic behavior prior to failure. Numerical finite element models of the patch-load test showed good agreement with experimental results. Analytical formulas using the obtained orthotropic plate properties did not agree with experimental results for the patch-load at linear scales, suggesting the simplified method is currently not suited for CLT-concrete two-way bending. Load-transfer tests found that the reinforced concrete topping is capable of transferring load across the longitudinal joint of two parallel panels to enable two-way bending of composite timber–concrete floors and that the addition of a plywood spline with closely spaced screws enables a higher degree of force transfer. [ABSTRACT FROM AUTHOR]

A Fourier Bessel series type expansion formula is used to investigate the interaction of surface gravity wave with two arc-shaped porous breakwaters that shield a circular floating flexible structure from wave action. The flexural gravity waves result from the interaction between the surface gravity waves and the circular floating structure. Additionally, when the floating structure encounters lateral compression force, flexural gravity wave blocking occurs. Moreover, the floating structure is triggered by the interaction of three unique wave modes for every wave frequency within the confines of the blocking frequencies. The two arc-shaped permeable breakwaters significantly reduce the wave force acting on the floating structure as compared to situations where there is just one arc wall or no breakwater at all. Resonant peaks in the wave forces arising within the impermeable breakwaters diminish with the introduction of structural permeability. The hydrodynamic load on the floating structure and the pair of porous arc breakwaters exhibit removable discontinuities near the blocking frequency. Surface plots illustrate the irregular distribution of plate deflection at certain angular frequencies. Contour plots are used to ascertain the spatial configuration of fluid flow around a structure. Furthermore, several wave and structural parameters, including the position of the breakwaters and their structural dimensions, breakwater porosity, annular radius, compressive force, incident angle, and wave forces experienced by the floating structure, contribute to mitigating wave-induced structural response and wave forces experienced by the floating structure. Time-dependent simulation of the surface displacement by the incident wave demonstrates the flow features. [ABSTRACT FROM AUTHOR]

Quasicrystals (QCs) have attracted tremendous attention of researchers for their unusual properties. In this paper, an exact electric‐elastic solution of the simply supported and multilayered three‐dimensional (3D) cubic piezoelectric quasicrystal (PQC) nanoplate with the nonlocal effect is derived. Based on the basic elasticity equation of 3D QCs, we construct the linear eigenvalue system in terms of the pseudo‐Stroh formalism, from which the general solutions of the extended displacements and stresses in any homogeneous layer can be obtained. The two‐parameter foundation model is utilized to simulate the interaction between the nanoplate and elastic medium. The propagator matrices are employed to connect the field variables at the upper interface to those at the lower interface of each layer. Based on the boundary conditions of the upper and lower surfaces of the laminate and foundation model, the solutions are employed to derive from the global propagator matrix. Compared with the conventional propagator matrix method, a new propagator method is reestablished to deal with numerical instabilities of the case of large aspect ratio and high‐order frequencies for QC laminates. Finally, typical numerical examples are presented to illustrate the influence of nonlocal parameters and elastic medium coefficients on phonon, phason, and electric variables of 3D PQC nanoplates. [ABSTRACT FROM AUTHOR]

We generalize a recent theory of bending of thin micropolar plates by incorporating surface effects through the modeling of plate surfaces as adjacent two-dimensional micropolar elastic bodies. By incorporating both elastic surface effects and the micropolar elastic behavior of the plate, the proposed model is capable of taking into account the contribution of high surface-to-volume ratios as well as the influence of microstructural mechanics at micro/nano scales. We determine the fundamental solution of the resulting system of equations and establish uniqueness results for the corresponding Dirichlet and Neumann boundary value problems. Moreover, we provide a numerical example to demonstrate the efficiency of the model in representing the size-dependence arising from various factors that incorporate characteristic lengths. Furthermore, we showcase the sensitivity of the results to different types of characteristic lengths present in the model. [ABSTRACT FROM AUTHOR]

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This paper investigates the contact problem of a layered elastic halfspace with transverse isotropy under the axisymmetric indentation of a circular rigid plate. Fourier integral transforms and a backward transfer matrix method are used to obtain the analytical solution of the contact problem. The interaction between the rigid plate and the layered halfspace can be expressed with the standard Fredholm integral equations of the second kind. The induced elastic field in the layered halfspace can be expressed as the semi-infinite integrals of four known kernel functions. The convergence and singularity of the semi-infinite integrals near or at the surface of the layered halfspace are resolved using an isolating technique. The efficient numerical algorithms are used and developed for accurately calculating the Fredholm integral equations and the semi-infinite integrals. Numerical results show the correctness of the proposed method and the effect of layering non-homogeneity on the elastic fields in layered transversely isotropic halfspace induced by the axisymmetric indentation of a circular rigid plate. [ABSTRACT FROM AUTHOR]