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In this article, the numerical and experimental free vibration analyses of PLA-based composite plates with different filling geometries were carried out. Firstly, the natural frequencies and modal shapes were obtained from finite element (FE) methods to characterize the vibration behavior of the plates. The obtained results were compared with experimental testing of the three-dimensional (3D) produced plates. In the comparison, it was seen that the finite element analysis and the experimental results were quite close to each other. It was also observed that the highest frequencies are measured by a triangle, then the grid and honeycomb. Moreover, higher frequencies and lower weights are possible with the triangle pattern fill. On the other hand, it is noted that the types of filling structures do not affect the modal shapes of the 3D plates. Thus, the results of this paper are of utmost importance for getting light structure and high frequencies. [ABSTRACT FROM AUTHOR]

This study investigates the electromechanical performance of piezoelectric sandwich plates both numerically and experimentally. The effect of different inner design parameters, namely the length-to-thickness, core-to-face thickness, boundary conditions and aspect ratio on both the eigenfrequency and electric potential attributes is assessed. Moreover, vibration amplitude-dependent effects are investigated. Polymer-based, sandwich plates are additively manufactured (AM) and commercially available PZT layers are surface-bonded and experimentally probed. AM smart plates are found to yield comparable eigenfrequency properties with the ones reported for fiber-reinforced smart sandwich composites. Low length-to-thickness, low core-to-face, and rectangular rather than square designs favor the electric potential performance. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the homogenization and dimension reduction for a nonlinear elasticity problem of a textile structure. The structure is represented as a squared piece of cloth and modeled as a woven canvas made of long and thin fibers, crossing each other in a periodic pattern. The squared domain is partially clamped on the left and bottom. The fibers are assumed to be glued, a condition that allows to extend the woven structure to a non-perforate plate. The nonlinear elasticity problem is stated via minimization over the energy functional. The homogenization is made via the periodic unfolding method, with an additional dimension reduction. Since the existence of a minimum of the limit energy functional is not ensured, sufficient conditions for the existence are given by assuming that the material is homogeneous and isotropic. [ABSTRACT FROM AUTHOR]

The results are presented for impact of defects formed during one-sided friction stir welding plates made of alloy 1901 in the root part on the mechanical properties of resulting butt joints. The defects are represented by the lack of fusion and accumulations of oxide films in the root part of the joint. The defect length is 0.1–0.3 mm and the defects are detected using computer X-ray tomography and analyzing the microstructure of the joints using an optical microscope. The defects present in the root part of the plate joints made of alloy 1901T result in decrease in the welding factor from 0.85 to 0.74. The area of the joint break during a static tensile test shifts from the heat-affected zone to the stir zone. The break of the samples exposed to static tension is initiated by a lack of fusion (the areas occupied by oxide films) in the root part of the joint with a characteristic brittle fracture propagating into the stir zone. The fracture becomes ductile with islands of oxide film entering the weld during the welding process. The presence of the lack of fusion and oxide films in the root part of the joint results in a 2-fold decrease in the joint bending angle. A necessary condition for eliminating the lack of fusion in the root part of the butt joint in plates made of alloy 1901T deals with making the length of the rod (pin) of the working tool equal to the thickness of the workpieces welded, taking into account the degree of immersion of the tool shoulder in the weld metal. [ABSTRACT FROM AUTHOR]

The article combines the finite element method with the novel-type sinusoidal hyperbolic shear strain hypothesis to study the static bending response and dynamics of nanoplates subjected to simultaneous mechanical, thermal, and voltage loads. The plate equilibrium equation is developed from the concept of potential work, which takes into account the impact of the flexoelectricity effect. The formula for the electric field that is operating on the plate becomes more complicated when the new strain theory is used; nonetheless, its complexity adequately displays both the mechanical and electrical components, as well as the electromechanical components, that are acting on the nanoplate. The computational theory is also verified through comparison with previously published data. The article also investigates the influence of some material factors, temperature, and external voltage on displacement response and charge polarization of nanoplates in the case of subjecting to static and time-varying loads. The results demonstrate that the thermomechanical-electrical response of nanoplates is dependent on numerous factors, which serve as the foundation for the practical design and application of nanostructures. [ABSTRACT FROM AUTHOR]

AbstractThis article proposes a rigorous mathematical justification of the derivation of the governing equations of any beam and plate theory by the three three-dimensional (3D) elasticity equations. This is done by the application of the integration by part theorem via weight residual-like methods. The Fis polynomials (subscripts i and s denote the i-direction and the generic s-term of the displacement expansion uis, respectively) related to a given beam/plate theory are used as weight functions for each of the displacement unknown. To show how the method works a number of simple problems are discussed. These are related to the equilibrium equations and boundary conditions of bending beams according to shear deformation theory. Three methods for obtaining these equations are compared in some detail. The first two are the well-known methods used in mechanics of deformable bodies: (1) use of the Principle of Virtual Displacements; (2) use of the six cardinal ‘Newton’ equations of statics. The third method coincides with the one proposed and rigorously justified in this paper which is (3) the direct integration of the equations of 3D elasticity. Beam theories based on Lagrange polynomials are used as well. The latter makes it possible to immediately develop theories for layered beams and obtain so-called ‘layer-wise’ models, which are only applied here to the case of sandwich structures. Three appendixes discuss: A – The problem in which the derivative of one of the unknowns appears among the unknowns, as is the case with the Euler–Bernoulli theory; B – The extension to dynamics; C-Simple derivation of constitutive equations and related closed-form solution via Navier method. [ABSTRACT FROM AUTHOR]

Case: A 51-year-old woman, who had previously undergone C5-C7 anterior cervical discectomy and fusion, presented with symptomatic hardware failure and subsequently underwent instrumentation removal. Her postoperative course was complicated by an esophageal perforation. Despite initial repair using a rotational flap, the leak persisted, prompting esophageal reconstruction with a radial forearm free flap (RFFF). Conclusion: Persistent esophageal perforation is exceedingly rare and difficult to treat. This report discusses the surgical technique for RFFF, an excellent option for revising failed sternocleidomastoid rotational flaps. The decision between rotational repair and free flap reconstruction depends on factors such as defect size, vascularization, wound condition, and donor site morbidity. [ABSTRACT FROM AUTHOR]

The goal of this article was to review studies on distal humerus fracture plates (DHFPs) to understand the biomechanical influence of systematically changing the plate or screw variables. The problem is that DHFPs are commonly used surgically, although complications can still occur, and it is unclear if implant configurations are always optimized using biomechanical criteria. A systematic search of the PubMed database was conducted to identify English‐language biomechanical optimization studies of DHFPs that parametrically altered plate and/or screw variables to analyze their influence on engineering performance. Intraarticular and extraarticular fracture (EAF) data were separated and organized under commonly used biomechanical outcome metrics. The results identified 52 eligible DHFP studies, which evaluated various plate and screw variables. The most common plate variables evaluated were geometry, hole type, number, and position. Fewer studies assessed screw variables, with number and angle being the most common. However, no studies examined nonmetallic materials for plates or screws, which may be of interest in future research. Also, articles used various combinations of biomechanical outcome metrics, such as interfragmentary fracture motion, bone, plate, or screw stress, number of loading cycles to failure, and overall stiffness (Os) or failure strength (Fs). However, no study evaluated the bone stress under the plate to examine bone "stress shielding," which may impact bone health clinically. Surgeons treating intraarticular and extraarticular distal humerus fractures should seriously consider two precontoured, long, thick, locked, and parallel plates that are secured by long, thick, and plate‐to‐plate screws that are located at staggered levels along the proximal parts of the plates, as well as an extra transfracture plate screw. Also, research engineers could improve new studies by perusing recommendations in future work (e.g., studying alternative nonmetallic materials or "stress shielding"), clinical ramifications (e.g., benefits of locked plates), and study quality (e.g., experimental validation of computational studies). [ABSTRACT FROM AUTHOR]

A method for the optimization of the distribution of two materials in a thin symmetric plate is presented. The model for the plate is the Kirchhoff–Love and the optimization method is based on the small amplitude, or low contrast, approximation for homogenization. Numerical results are presented for compliance minimization, i.e., maximizing the global stiffness of the plate, and for minimizing the integral of an even power of the deflection in a subset of the plate. The method arrives at classical designs without the need of penalization, which allows evaluating the exact performance of the proposed shapes and the comparison with some simple intuitive designs. This also gives insight in how small the contrast needs to be for the method to give designs which are better than some intuitive designs. [ABSTRACT FROM AUTHOR]

Aim Acetabular fractures are complex articular fractures with a big challenge for orthopaedic surgeons. Surgically managed displaced fractures carry favorable outcomes, especially if the articular surface is reduced accurately. This study aims to assess the clinical outcomes of surgical-ly fixed displaced acetabular fractures with central dislocation using combined anterior and medial plating.Methods We have retrospectively evaluated sixteen patients, who had surgically managed dis-placed acetabular fractures with central dislocation at our institute. All patients underwent open reduction and internal fixation using combined anterior and medial plating via the Kocher-Langenbeck, the ilioinguinal, or the Stoppa approach. The functional outcome was assessed using the Harris Hip score.Results Our study includes sixteen patients (12 males, 4 females) with a mean age of 35 years (range: 15-53 years). The mean follow-up was 7.8 years (range: 5-13 years). Functional outcomes were good to excellent in 12 (80%) patients and fair in 3 (20%) patients. At the final follow-up, the solid union had been achieved in all fractures, the mean HHS was 88.84 ± 7.61.Conclusion Early reduction and surgical fixation of dis-placed acetabular fractures with central dislocation using combined anterior and medial plates appear to have good clinical outcomes.

Introduction. Improving the calculation methods of mechanical engineering facilities is an urgent and in-demand task. This fully applies to the techniques of calculating the strength of all-welded gastight boiler structures. Normative calculation techniques are based on simplified models that give limited possibilities for optimizing these structures. The low calculation accuracy inherent in such techniques is unacceptable under real design conditions, when an engineer is faced with the task of developing competitive structures in a short time, i.e., reducing metal consumption while providing the strength of these structures with limited development time. The use of simplified models was justified in the past, under conditions of insufficient development of computer technology. Application of the most advanced techniques based on computer modeling makes it possible to increase the accuracy of calculations, provide the optimization of such structures, and improve the quality of design. The objective of this study was to develop a new special procedure for calculating the strength of all-welded gastight structures based on computer modeling, using the most advanced methods of modeling the membrane wall and factors affecting it. The accompanying task was to verify the developed procedure based on comparing the results of calculations using the developed technique and the normative method.Materials and Methods. The developed technique is based on the replacement of the membrane wall with an orthotropic plate or shell. Computer modeling was used applying the finite element method of all-welded gastight structures, and the impacts to which they were subjected during operation, as well as an effective method for assessing the technical condition of these structures.Results. A new two-stage technique for calculating the strength of increased accuracy of all-welded gastight boiler structures was developed and patented. The calculation results were compared according to the proposed procedure and the normative method. It was shown that the proposed technique made it possible to increase the accuracy of modeling and calculation. The error in calculating all-welded gastight structures of a high-power boiler was reduced by more than 30% for the recommended steps between stiffeners. For specially reinforced membrane walls with steps exceeding the permissible values, the error reduction reached 70% or higher.Discussion and Conclusion. The developed technique is used in the modeling and calculation of all-welded gastight structures. Its application makes it possible to optimize the step between the stiffeners of the structure of the support and connecting nodes of gastight membrane walls. Based on the results of the application of the two-stage calculation procedure, new designs were developed and patented. The developed technique has been used in the real design of boilers since 2014.

Currently, bending deformations of lithospheric plates are calculated based on Kirchhoff's theory of bending of thin plates, which was formulated about 170 years ago. This paper examines the possibility of refining these calculations based on the theory of bending of thick plates developed by Timoshenko and Reissner. A new unified derivation is presented of the Timoshenko equations for 2D bending of beams and the Reissner equations for bending of slabs by direct transformation of the general elasticity equations with a simple approximate replacement of power-cubic functions with effective linear ones. This allows a more detailed and clearer understanding of the differences between the equations and the sense of the simplifications made in these theories. By comparing the analytical solutions of the Timoshenko and Reissner equations with the known test analytical solutions of the exact elasticity equations, quantitative estimates of the accuracy of these theories are given. [ABSTRACT FROM AUTHOR]

The production of homogeneous Ti–10Nb–(1–3)Mo (at %) alloys in the form of semifinished products (plates) was studied through multiple remeltings and homogenization annealing. Metallographic studies of the resulting materials in cast, rolled, and annealed states were carried out. The effect of annealing and composition on the structure, phase composition, and mechanical properties of the Ti–10Nb–(1–3)Mo alloy was revealed. Homogeneity after smelting was achieved by annealing at a temperature of 950°C for 12 h. An increase in the Mo content in the Ti–10Nb–(1–3)Mo alloy led to an increase in the strength of the alloys, while the ductility decreased. The achievement of high strength characteristics in selected alloys was associated with the development of annealing parameters after plastic deformation, namely, controlling the size of recrystallized grains and separating the α and β phases. In addition to α-Ti and β-Ti, the samples contained small amounts of ω-Ti, which led to a sharp increase in the hardness of the samples. [ABSTRACT FROM AUTHOR]

We propose a new implicit–explicit scheme to address the challenge of modeling wave propagation within thin structures using the time‐domain finite element method. Compared to standard explicit schemes, our approach renders a time marching algorithm with a time step independent of the plate thickness and its associated discretization parameters (mesh step and order of approximation). Relying on the standard three dimensional elastodynamics equations, our strategy can be applied to any type of material, either isotropic or anisotropic, with or without discontinuities in the thickness direction. Upon the assumption of an extruded mesh of the plate‐like geometry, we show that the linear system to be solved at each time step is partially lumped thus efficiently treated. We provide numerical evidence of an adequate convergence behavior, similar to a reference solution obtained using the well‐known leapfrog scheme. Further numerical investigations show significant speed up factors compared to the same reference scheme, proving the efficiency of our approach for the configurations of interest. [ABSTRACT FROM AUTHOR]

In the present study, experimental and numerical investigations are carried out on Vanadium dioxide (VO2)-UHMWPE composite plates while considering the temperature across phase change. VO2 is known for semiconducting to metallic transition along with structural changes from monoclinic to tetragonal during heating above 68°C, which enhances structural stiffness. For the experimentation, VO2-UHMWPE composite samples are fabricated by employing the Hot-Press method. These samples are further utilized to perform the compression test in order to find Young's moduli at room temperature (RT) and 75°C (temperature across phase change) using a Universal Testing Machine (UTM). Based on the experimentally computed Young's moduli, the numerical investigations in terms of free vibration and bending analyses, are performed. For structural kinematics, a C0-continuous higher-order shear deformation theory (HSDT) is employed, and the governing equations are derived using the Lagrange model. The numerical results, that is, natural frequencies and center deflection, are assessed using the finite element method (FEM). The convergence and comparison studies are accomplished to ensure the performance and competence of the present numerical model within the framework of MATLAB and ABAQUS. The influence of temperature, thickness ratio, boundary conditions, etc. on the frequency and deflection of the bare UHMWPE polymer and VO2-UHMWPE plates, is discussed in detail. Based on the results, it can be concluded that the VO2 reinforcement to the UHMWPE polymer improves structural stiffness at a temperature of 75°C. Moreover, VO2-UHMWPE composite can be utilized for structural applications, wherein lightweight and high-temperature resistive material is desired. Highlights • The fabrication of the VO2-UHMWPE composite samples is accomplished through the Hot-Press method. • Young's moduli of the VO2-UHMWPE composites at RT and 75°C are assessed utilizing UTM. • The finite element method is employed to analyze the behavior of the bare UHMWPE polymer and VO2-UHMWPE plates in free vibration and bending. • The effect of influencing parameters such as temperature, thickness ratio, boundary conditions, etc., on natural frequency and deflection of the plates are explored. [ABSTRACT FROM AUTHOR]

The solution of the nonlinear (NL) vibration problem of the interaction of laminated plates made of exponentially graded orthotropic layers (EGOLs) with elastic foundations within the Kirchhoff–Love theory (KLT) is developed using the modified Lindstedt–Poincaré method for the first time. Young's modulus and the material density of the orthotropic layers of laminated plates are assumed to vary exponentially in the direction of thickness, and Poisson's ratio is assumed to be constant. The governing equations are derived as equations of motion and compatibility using the stress–strain relationship within the framework of KLT and von Karman-type nonlinear theory. NL partial differential equations are reduced to NL ordinary differential equations by the Galerkin method and solved by using the modified Lindstedt–Poincaré method to obtain unique amplitude-dependent expressions for the NL frequency. The proposed solution is validated by comparing the results for laminated plates consisting of exponentially graded orthotropic layers with the results for laminated homogeneous orthotropic plates. Finally, a series of examples are presented to illustrate numerical results on the nonlinear frequency of rectangular plates composed of homogeneous and exponentially graded layers. The effects of the exponential change in the material gradient in the layers, the arrangement and number of the layers, the elastic foundations, the plate aspect ratio and the nonlinearity of the frequency are investigated. [ABSTRACT FROM AUTHOR]

An analysis of the influence of applied loads on free vibrations of plate and shell panels made of functionally graded materials is analyzed in the present work. Formulations for the static analysis considering geometrically nonlinear behavior, as well as linear buckling and free vibrations analyses are considered. A calculation of the through-thickness stress distribution is also performed. The finite element model is based on a higher order shear deformation theory using a non-conforming flat triangular plate/shell element with three nodes, and eight degrees of freedom per node is used in the numerical implementation. The results obtained with this numerical model are presented, discussed, and compared with alternative solutions published by other authors in some benchmark applications. [ABSTRACT FROM AUTHOR]

Purpose: In comparison to traditional, constant stiffness laminates, variable stiffness composite laminates (VSCL) with curvilinear fibres represent an extra analysis effort. It is the purpose of this work to present and test a relatively simple optimisation procedure, in order to find the maximum fundamental frequency of vibration in bending and in in-plane vibrations. It is also intended to explain why certain fibre paths lead to higher frequencies. Methods: The optimisation is performed using a genetic algorithm (GA), which is described in detail. The bending and the in-plane plate models are based on the p-version Finite Element Method. Each model requires a small number of degrees of freedom, an important feature because applying the GA involves the solution of a large number of eigenvalue problems. In order to support the physical interpretation of the optimal designs, mode shapes and stress fields corresponding to some optimal solutions are illustrated. Results: Single- and multi-layer plates with different boundary conditions and fibre path types are studied. Fibre paths that lead to maximum fundamental frequencies are found and justified. The consequences that maximising the first frequency has on the higher-order modes of vibration are studied. Conclusion: The proposed optimisation and modelling methods are effective. Curvilinear fibres with the characteristics considered led to the maximum first natural frequency of vibration in a few cases, but not all. Particularly in in-plane vibrations, curvilinear fibres can provide major gains in comparison to straight fibres. The increase in the vibration frequency is accompanied by, overall, larger stresses. [ABSTRACT FROM AUTHOR]

The design of thin-walled structures is commonly based on the solutions of linear boundary-value problems, formulated within well-developed theories for elastic plates and shells. However, in modern appliances, especially in MEMS design, it is necessary to take into account non-linear mechanical effects that become decisive for flexible elements. Among the substantial non-linear effects that significantly change the deformation properties of thin plates are the effects of residual stresses caused by the incompatibility of deformations, which inevitably arise during the manufacture of ultrathin elements. The development of new methods of mathematical modeling of residual stresses and incompatible finite deformations in plates is the subject of this paper. To this end, the local unloading hypothesis is used. This makes it possible to define smooth fields of local deformations (inverse implant field) for the mathematical formalization of incompatibility. The main outcomes are field equations, natural boundary conditions and conservation laws, derived from the least action principle and variational symmetries taking account of the implant field. The derivations are carried out in the framework of elasticity theory for simple materials and, in addition, within Cosserat's theory of a two-dimensional continuum. As illustrative examples, the distributions of incompatible deformations in a circular plate are considered. [ABSTRACT FROM AUTHOR]

In the present work, attention is paid to the nonlinear vibrations and chaotic dynamic behaviors of rotating graphene platelets reinforced metal foams (GPLRMF) blades operating in a thermal environment. Considering three different distribution patterns of graphene platelets (GPL) and foams, the improved Halpin–Tsai model, mixing rules and Maxwell-Eucken model are applied to obtain the physical parameters of rotating GPLRMF plates. The motion equations of GPLRMF rotating plates are established through higher-order shear deformation theory (HSDT), in which the centrifugal force, Coriolis force and heat conduction are included. Under the cantilever and simply supported boundary conditions, the nonlinear ordinary differential equation (ODE) of the system is obtained by Galerkin method. The amplitude-frequency response, bifurcation curve, and chaotic motion of the rotating GPLRMF blades are analyzed with the aid of the methods of multi-scale and Runge–Kutta. Furthermore, comprehensive investigations into the effects of temperature, presetting angle, GPL distribution mode, foam distribution mode, volume fraction, porosity coefficient, rotational speed, damping coefficient, and excitation force on the nonlinear dynamics of rotating plates are performed through numerical analyses. [ABSTRACT FROM AUTHOR]

We consider elastic thin shells without through-the-thickness shear and depict them as Gauss graphs of parametric surfaces. (We use the term shells to include plates and thin films therein.) We consider an energy depending on the first derivative of the Gauss map (so, it involves curvatures) and its second-rank minors. For it we prove existence of minimizers in terms of currents carried by Gauss graphs. In the limiting process we adopt sequences of competitors that satisfy a condition that prevents self-penetration of matter.

Purpose: The aim of this study was to evaluate the results of distal femoral fracture fixation of two different methods, lateral locking plate (LP) or an Intra-medullary nail (IMN), in patients managed in our institution. More specifically, to assess: (a) if there was a difference in functional outcomes between the LP and IMN groups; (b) whether the rate of complications was different between the two groups. Methods: Between January 2009 and December 2018 adult patients with distal femoral fractures managed in our unit with either LP or IMN for extra and intra-articular fractures were eligible to participate. Demographic details, fracture type, procedures performed, time to union, complications and functional scores (Oxford Knee Score) were recorded and analysed. The mean follow up was 4 years (12–120 months). Results: Out of 193 patients who met the inclusion criteria, 93 received an IMN whereas 100 patients were treated with LP. Mean age was 64.2 (18–99) and 70.1 (18–100) for the IMN and LP groups respectively. Overall, the two groups had similar demographics and there was no significant difference in the type of fractures sustained (p > 0.05). The Oxford Knee Score was highest for patients fixed with LP, mean 37.3 (6–48, SD 7.3) versus 28.4 (3–48, SD 14.4), (p = < 0.02) compared to the IMN group. In terms of complications, the rate of non-union was higher in the LP group 8.6% versus 4% in those patients treated with an IMN, p value < 0.01. Conclusion: While the rate of non-union was higher in the LP group and the functional results were superior in the plating group. [ABSTRACT FROM AUTHOR]

An interior penalty discontinuous Galerkin method is devised to approximate minimizers of a linear folding model by discontinuous isoparametric finite element functions that account for an approximation of a folding arc. The numerical analysis of the discrete model includes an a priori error estimate in case of an accurate representation of the folding curve by the isoparametric mesh. Additional estimates show that geometric consistency errors may be controlled separately if the folding arc is approximated by piecewise polynomial curves. Various numerical experiments are carried out to validate the a priori error estimate for the folding model. [ABSTRACT FROM AUTHOR]

The use of column-tree connections is common in controlled shop environments due to their cost-effectiveness in achieving ductile welds. Field bolts are also easy to install and inspect. However, there is currently no prequalification available for these connections, their performance is not fully understood, and the cost of aftermath repairs is still a major concern for owners. In this research, analytical and numerical studies were performed to assess the cyclic behavior considering the effects of the bolted splice location, bolt slippage, and splice plate thickness. Fourteen numerical models using the finite element method in ANSYS software were analyzed to evaluate the nonlinear behavior of moment connection configurations in terms of the strength, stiffness, ductility, energy dissipation, and overall cyclic response. The results showed that appropriately proportioned bolted splice connections can meet the requirements for prequalified moment connections. The models complied with the criteria established in AISC 358 and achieved flexural resistance that was higher than 80% of the beam plastic moment at 4% of the interstory drift ratio. The weakened plates concentrated the inelastic action, which allowed us to prevent the brittle behavior and damage to the column, welding, and other components of the moment connection. Complex geometries or specially fabricated parts were not required, providing a cost-effective way to control seismic-related damage. Also, required repairs are based on the replacement of standard parts, reducing operational detentions in facilities. Finally, the moment connection studied is classified as partially restrained (PR) according to the requirements established in AISC 360. [ABSTRACT FROM AUTHOR]

The paper is dedicated to the modeling of the elasticity problem for a textile structure. The textile is made of long and thin fibers, crossing each other in a periodic pattern, forming a woven canvas of a square domain. The textile is partially clamped. The fibers cannot penetrate each other but can slide with respect to each other in the in‐plane directions. The sliding is bounded by a contact function, which is chosen loose. The partial clamp and the loose contact lead to a domain partitioning, with different expected behaviors on each of the four subdomains. The homogenization is made via the periodic unfolding method, with an additional dimension reduction. The macroscopic limit problem results in a Leray–Lions problem with only macroconstraints in the plane. [ABSTRACT FROM AUTHOR]

In this present study, we are interested in the use of a precise theory of shear deformation for the buckling analysis of plates with functional gradation simply supported such as the refined theory of plates with four variables. Several parameters of comparison have been used, dimensional and nondimensional. The displacement field is compatible with this study, the nonuse of shear correction factors is satisfied, and the choice of material is very precise in such a way are variable according to the thickness of the plate and on the other hand to make comparison with other researcher and confirms that this study gives precise results and converges. The transverse shear stresses vary through the thickness, the results found is also studied and discussed. [ABSTRACT FROM AUTHOR]

We consider elastic thin shells without through-the-thickness shear and depict them as Gauss graphs of parametric surfaces. (We use the term shells to include plates and thin films therein.) We consider an energy depending on the first derivative of the Gauss map (so, it involves curvatures) and its second-rank minors. For it we prove existence of minimizers in terms of currents carried by Gauss graphs. In the limiting process we adopt sequences of competitors that satisfy a condition that prevents self-penetration of matter. [ABSTRACT FROM AUTHOR]

We give a new full explanation of the Tacoma Narrows Bridge collapse, occurred on November 7, 1940. Our explanation involves both structural phenomena, such as parametric resonances, and sophisticated mathematical tools, such as the Floquet theory. Contrary to all previous attempts, our explanation perfectly fits, both qualitatively and quantitatively, with what was observed that day. With this explanation at hand, we set up and partially solve some optimal control and shape optimization problems (both analytically and numerically) aiming to improve the stability of bridges. The control parameter to be optimized is the strength of a partial damping term whose role is to decrease the energy within the deck. Shape optimization intends to give suggestions for the design of future bridges.

In this study, the linear free vibration of intact and cracked functionally graded material plates is investigated numerically and experimentally. The experimental work is limited to the isotropic materials. The numerical work is based on finite element, where a code is developed to obtain the natural frequencies of intact plates based on the first-order shear deformation theory (FSDT) using MATLAB software. Also, a model of through-cracked FGM plate is developed using ANSYS Workbench with the help of APDL coding. The material properties of the plates under study are graded in one, two, and three directions. The novelty of this study emerges through its examination of the synergistic impacts resulting from variations in FGM material properties, crack length, crack orientation, and crack location. These effects are comprehensively discussed in the results section. The result of the present model shows that the use of three-directional FGM reduces the natural frequency compared with the other cases of two-directional and unidirectional FGM. Also, the results show that the effect of FGM gradient on the frequency of intact and cracked plate is high when the gradient index n < 3. The present paper results are useful for the design of FGM plates especially when cracks exist. [ABSTRACT FROM AUTHOR]

An analysis of industrial operation of EGAV 1-19-15-6-2 electrostatic precipitators designed for purifying non-aggressive non-explosive process gases and aspiration air from dust was carried out. The nonuniformity of flow distribution at the inlet to the working volume of electrostatic precipitators was revealed. This non-uniformity can lead to efficiency deterioration, increased energy consumption, and frequent cleaning of precipitation electrodes. The authors proposed constructive improvements of electrostatic precipitators supported with calculations. [ABSTRACT FROM AUTHOR]

The interaction of a sprocket with the links of a drive gear chain is studied by graphical analysis. In gear chains with rolling hinges, the contact pitch of the chain is increased on chain engagement with the sprocket. The contact pitch is changed when the sprocket turns through two angular increments. Change in the contact pitch is undesirable, because it results in nonuniform chain motion. Recommendations are made for decreasing the dynamic loads in a drive with gear chains. [ABSTRACT FROM AUTHOR]

Objective: Periodic configuration of mechanical and civil structures has shown great potential for noise and vibration reduction. However, the use of Cartesian coordinates in studying periodicity effects in elastic structures overlooks the benefits of radially periodic configurations when dealing with wave propagation in large flexible plates disturbed by a small source area. This paper presents an easy-to-use numerical approach to predicting bandgap characteristics in polar coordinates. Methodology: To demonstrate the vibration-attenuation effect, we consider a circular radially periodic plate model. We use an adapted Wave Finite-Element method in numerical experiments to demonstrate the existence of the attenuation effect. To verify the numerical results, we apply an adapted Floquet theory to polar coordinates. Results and Conclusions: Our findings indicate that theoretical and numerical results are in excellent agreement considering a new parameter that introduces the distance from the origin. The adapted Wave Finite-Element approach and Floquet theory presented here demonstrate their potential to model more complex structures in polar coordinates. [ABSTRACT FROM AUTHOR]

The structure, phase composition, and mechanical and corrosion properties of plates made of a structural aluminum Al–Cu–Mg alloy are studied in its various states. The results obtained are compared with the properties of its commercial analog (AK4-1 alloy). The alloy under study is found to surpass its analog in strength properties at room and elevated (up to 175°C) temperatures by 9–12%. The impact toughness KCU of the Al–Cu–Mg alloy is twofold that of the AK4-1 alloy. The increase in the strength and corrosion properties of the alloy after operational heating is shown to be explained by the phase composition and morphology of intermetallic phases, including transition-metal phases, which form in the surface layers of samples in small quantities. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this historical review is to illustrate the progression and evolution of treatment for distal femur fractures. Methods: Scientific literature was searched for descriptions of treatment for distal femur fractures to provide an in-depth overview of the topic, with emphasis on the evolution of surgical constructs used to treat these fractures. Results: Prior to the 1950s, distal femur fractures were treated nonoperatively, resulting in considerable morbidity, limb deformity, and limited function. As principles of surgical intervention for fractures emerged in the 1950s, surgeons developed conventional straight plates to better stabilize distal femur fractures. Angle blade plates and dynamic condylar screws emerged out of this scaffolding to prevent post-treatment varus collapse. Meanwhile, intramedullary nails, and later, in the 1990s, locking screws, were introduced to minimize soft tissue disruption. Treatment failure led to the development of locking compression plates with the advantage of accommodating either locking or nonlocking screws. Despite this advancement, the rare but significant incidence of nonunion has not been eliminated, leading to the recognition of the biomechanical environment as important for prevention and the development of active plating techniques. Conclusion: Emphasis for the surgical treatment of distal femur fractures has incrementally progressed over time, with initial focus on complete stabilization of the fracture while the biological environment surrounding the fracture was ignored. Techniques slowly evolved to minimize soft tissue disruption, allow more ease of implant placement at the fracture site, and attend to the systemic health of the patient, while simultaneously ensuring appropriate fracture fixation. Through this dynamic process, the desired results of complete fracture healing and maximization of functional outcomes have emerged. [ABSTRACT FROM AUTHOR]

The solution of the nonlinear (NL) vibration problem of the interaction of laminated plates made of exponentially graded orthotropic layers (EGOLs) with elastic foundations within the Kirchhoff–Love theory (KLT) is developed using the modified Lindstedt–Poincaré method for the first time. Young’s modulus and the material density of the orthotropic layers of laminated plates are assumed to vary exponentially in the direction of thickness, and Poisson’s ratio is assumed to be constant. The governing equations are derived as equations of motion and compatibility using the stress–strain relationship within the framework of KLT and von Karman-type nonlinear theory. NL partial differential equations are reduced to NL ordinary differential equations by the Galerkin method and solved by using the modified Lindstedt–Poincaré method to obtain unique amplitude-dependent expressions for the NL frequency. The proposed solution is validated by comparing the results for laminated plates consisting of exponentially graded orthotropic layers with the results for laminated homogeneous orthotropic plates. Finally, a series of examples are presented to illustrate numerical results on the nonlinear frequency of rectangular plates composed of homogeneous and exponentially graded layers. The effects of the exponential change in the material gradient in the layers, the arrangement and number of the layers, the elastic foundations, the plate aspect ratio and the nonlinearity of the frequency are investigated.

An analysis of the influence of applied loads on free vibrations of plate and shell panels made of functionally graded materials is analyzed in the present work. Formulations for the static analysis considering geometrically nonlinear behavior, as well as linear buckling and free vibrations analyses are considered. A calculation of the through-thickness stress distribution is also performed. The finite element model is based on a higher order shear deformation theory using a non-conforming flat triangular plate/shell element with three nodes, and eight degrees of freedom per node is used in the numerical implementation. The results obtained with this numerical model are presented, discussed, and compared with alternative solutions published by other authors in some benchmark applications.

The design of thin-walled structures is commonly based on the solutions of linear boundary-value problems, formulated within well-developed theories for elastic plates and shells. However, in modern appliances, especially in MEMS design, it is necessary to take into account non-linear mechanical effects that become decisive for flexible elements. Among the substantial non-linear effects that significantly change the deformation properties of thin plates are the effects of residual stresses caused by the incompatibility of deformations, which inevitably arise during the manufacture of ultrathin elements. The development of new methods of mathematical modeling of residual stresses and incompatible finite deformations in plates is the subject of this paper. To this end, the local unloading hypothesis is used. This makes it possible to define smooth fields of local deformations (inverse implant field) for the mathematical formalization of incompatibility. The main outcomes are field equations, natural boundary conditions and conservation laws, derived from the least action principle and variational symmetries taking account of the implant field. The derivations are carried out in the framework of elasticity theory for simple materials and, in addition, within Cosserat’s theory of a two-dimensional continuum. As illustrative examples, the distributions of incompatible deformations in a circular plate are considered.