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Finite Element Analysis (FEA) combining with the concepts of Linear Elastic Fracture Mechanics (LEFM) provides a practical and convenient means to study the fracture and crack growth of the materials. 2-D finite element model is developed for two different geometries; a rectangular plate with cracks emanating from a circular hole and Double Edge Notched Plate (DENT). Both geometries are in tensile loading and under mode I conditions. In this paper, a displacement extrapolation technique is employed particularly, to predict the crack propagations directions and to, calculate the Stress Intensity Factors (SIFs). Therefore, verification of the predicted SIF and crack trajectory are validated, with the relevant numerical and analytical results obtained by other researchers. [ABSTRACT FROM AUTHOR]

The transverse vibrations of a rectangular plate with theKelvin type boundary conditions at four corners are investigated. The plate is modeled as being attached to four lumped spring-damper systems at the corners. An analytical procedure is proposed based on the modal analysis. The completely free case of the plate is first studied. The expressions for the eigenfrequencies and eigenfunctions of the plate are obtained by utilizing the separation of variables. Then, the case in which the stiffness and the viscous damping as external forces acting at the corners of the plate is studied. Following the modal analysis procedure, the general solution for the equation of motion of the rectangular plate is derived. Some numerical results are presented. [ABSTRACT FROM AUTHOR]

Thermoelastic damping (TED) in a simply supported functionally graded material (FGM) micro rectangular plate is investigated analytically based on the higher-order shear deformation plate theory. The equations of motion for the thermo-elastic coupled transverse free vibration and the heat conduction equation coupled are derived based on the Levinson plate theory and the one-way coupled heat conduction theory. A semi-analytical solution of the heat conduction equation with variable coefficients is obtained by using a layer-wise homogenization approach. The complex frequency of the micro plate including TED is determined in terms of the frequency of the corresponding isothermal homogenous Kirchhoff plate by using the mathematical similarity between the eigenvalue problems for the two types of plates. The effects of the shear deformation, the material gradient and the geometry on the TED are examined in detail for the FGM micro plate made of ceramic–metal constituents with the power-law gradient profile. The numerical results show that the TED evaluated by the Levinson plate theory is smaller than that by the Kirchhoff plate theory. Therefore, for a thick or moderately thick micro plate the Levinson plate theory can provide a more accurate prediction of the TED than the Kirchhoff plate theory. [ABSTRACT FROM AUTHOR]

• A novel optimal design method of DVA suitable for the vibration suppression of complex structure with high mode density is proposed; • A dimension reduction method is proposed to simplify a multi-mode dominated response to a response dominated only by one excitation-dependent representative basis; • A new relationship between the DVA design of single-mode primary system and that of a SDOF primary system is developed. Dynamic Vibration Absorber (DVA) design methods based on one vibration mode have poor performance on controlling the resonant vibrations of complex flexible structures. A mathematical formulation for the DVA design which is suitable for suppressing the structural vibration characterized by multiple natural modes is proposed. An Excitation-Dependent Representative Basis (EDRB) for the structural vibration response characterized by multiple natural modes is derived via the dimensional reduction method proposed in modal space, based on which the DVA design method for one vibration mode can be directly used for the case when the vibration of structures is characterized by multiple natural modes. A new relationship between the optimal design of DVAs on a single-degree-of-freedom system and that on a single-mode system is also established, which enables the fixed-points theory or min-max optimization method to be directly applied on the DVA design for complex flexible structures with the derived EDRB. Numerical simulation on a simply-supported square plate is firstly conducted to verify the proposed method. Results show that the proposed method has better performance on vibration suppression than the existing method when the structural vibration is characterized by natural modes associated with the same natural frequency. The application on a complex fairing structure is presented to prove that the proposed method can effectively control the resonant vibrations of complex flexible structures with only one optimized DVA. [ABSTRACT FROM AUTHOR]

• Nonlinear (NL) vibration of multilayer shell-type structures with double curvature is studied. • Multilayer shell-type structures (ML-STSs) are consisted of CNT patterned layers. • FSDT is generalized on the NL vibration of ML-STSs with double curvature. • NL basic relations and dynamic equations for ML-STSs in finite deflections are derived. • Applying Galerkin and semi-inverse methods frequency-amplitude relationship is obtained. In this article, the nonlinear vibration of moderately thick multilayer shell-type structural elements with double curvature consisting of carbon nanotube (CNT) patterned layers is investigated within different shell theories. The first order shear deformation theory has been generalized on the motion for moderately thick multilayer shell-type structural elements with double curvature consisting of CNT patterned layers for the first time. Then, by applying Galerkin and semi-inverse perturbation methods to motion equations, and the frequency-amplitude relationship is obtained. From these formulas, the expressions for nonlinear frequencies of multilayer spherical and hyperbolic-paraboloid shells, rectangular plate and cylindrical panels patterned by CNTs within shear deformation and classical shell theories are obtained in special cases. The reliability of obtained results is verified by comparison with other results reported in the literature. The effects of transverse shear strains, volume fraction, sequence and number of nanocomposite layers on nonlinear frequency are discussed in detail. [ABSTRACT FROM AUTHOR]

In the design of cantilevered balconies of buildings, many stability problems exist concerning vertical plates, in which reaching a critical load plays an important role during the stability analysis of the plate. At the same time, the concrete forming vertical plate, as a typical brittle material, has larger compressive strength but lower tensile strength, which means the tensile and compression properties of concrete are different. However, due to the complexities of such analyses, this difference has not been considered. In this study, the variational method is used to analyze stability problems of cantilever vertical plates with bimodular effect, in which different loading conditions and plate shapes are also taken into account. For the effective implementation of a variational method, the bending strain energy based on bimodular theory is established first, and critical loads of four stability problems are obtained. The results indicate that the bimodular effect, as well as different loading types and plate shapes, have influences on the final critical loads, resulting in varying degrees of buckling. In particular, if the average value of the tensile modulus and compressive modulus remain unchanged, the introduction of the bimodular effect will weaken, to some extent, the bending stiffness of the plate. Among the four stability problems, a rectangular plate with its top and bottom loaded is most likely to buckle; next is a rectangular plate with its top loaded, followed by a triangular plate with its bottom loaded. A rectangular plate with its bottom loaded is least likely to buckle. This work may serve as a theoretical reference for the refined analysis of vertical plates. Plates are made of concrete or similar material whose bimodular effect is relatively obvious and cannot be ignored arbitrarily; otherwise the greater inaccuracies will be encountered in building designs. [ABSTRACT FROM AUTHOR]

Thin-walled structures are extensively used in aerospace, automotive and mechanical engineering applications due to their high strength- and stiffness-to-weight ratios. However, the performance of these structures tends to be heavily influenced by localised features such as manufacturing defects or design details included for non-structural reasons, e.g. inspection cut-outs. Understanding the sensitivity of structural performance to these nominal stiffness variations, and especially their spatial distribution through the volume of the structure, is important to the designer. We propose a new methodology, the Localised Nominal Stiffness method, to quantify the sensitivity of buckling performance to the distribution of nominal stiffness variations across the structure. The underpinning idea involves reducing the stiffness in small localised regions of the structure and quantifying the ensuing variation in linear buckling capacity before returning the stiffness to its original value. The process is repeated for all locations ensuring coverage of the entire structural domain, which leads to a sensitivity map. In practice, each location corresponds to an element in a finite element mesh. Focusing on structures subject to buckling constraints, and with the aim of using highly efficient structural analysis, we identify sensitivities using the hierarchical Unified Formulation. The resulting sensitivity contour maps can be used to identify regions of the structure where defects or removal of material (for lightweighting) would not significantly affect buckling and post-buckling performance. The effectiveness of the method is tested through three examples: a simply-supported plate; a simply-supported, thin-walled box-section column; and a thin shell with simply-supported and clamped boundary conditions. In all cases, the buckling performance of structures can be maintained with reduced structural weight. • A novel localised nominal stiffness method is proposed. • Improved structural efficiency of thin-walled structures in buckling. • Unified Formulation framework to improve the computational performance. [ABSTRACT FROM AUTHOR]

A new concept of an electrical shunt with two rectangular holes in a copper plate (ESRP) has been developed to be used for measuring a large current with a short-duration steep wave in a high-voltage field. The ratio of the input current to the output current is 106, as obtained from a DC voltage test circuit. The electrical shunt has a special configuration. To verify the shunt current ratio of ESRP in a real application, the shunt current was connected to a sphere-to-sphere electrode breakdown test circuit with a 10 mm gap to measure the large damping current (8.4 kA) of a DC breakdown voltage. The voltage signal from the shunt was transmitted to excite two light-emitting diodes (max. 50 mA, 4 V), which were reverse-connected in series. The light-emitting diodes operated properly and were illuminated, which validated the capability of the newly designed electrical shunt. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

It is experimentally established that gas-permeable inserts arranged in front of a finite rectangular step can reduce the characteristic size of the recirculation region for oncoming flow with Mach numbers within M = 2-5. [ABSTRACT FROM AUTHOR]

In this paper, a new analytical approach is proposed for free vibration and buckling analysis of a rectangular Mindlin plate resting on the Winkler–Pasternak foundation of varying stiffness. According to Mindlin theory, there are three independent governing differential equations. Thus, three Fourier series expansions along with auxiliary polynomial functions are employed to represent the plate's deflection and rotation angle functions. The process of making a set of equations is then completed satisfying the corresponding equilibrium equations and boundary conditions. The proposed method incorporates general elastic supports for all plate's edges, and subsequently can deal with all possible boundary conditions including classical ones as well as uniform or non-uniform elastic constraints. The natural frequencies and buckling loads of several examples are determined to merely show the accuracy of the presented approach. • A novel mathematical approach for analysis of Mindlin plates is proposed. • The natural frequencies as well as buckling loads of the plate are determined. • The plate is laid on the Winkler–Pasternak elastic foundation. • The foundation is of variable translational and rotational stiffness. • The proposed solution can deal with any arbitrary boundary condition. [ABSTRACT FROM AUTHOR]

In this paper, analytical solutions for the buckling loads of thin rectangular plates with internal supports and different boundary conditions are derived. The analytical method presented herein is based on the development of a static solution for a plate. The physical meaning of buckling is the loss of stiffness, and it is found as the value of the in-plane loading intensity at which a zero force on the plate surface will generate infinite displacement. The solution is obtained in a series form, and the coefficients are solved to match the edge conditions. For every internal support in the plate domain we add one equation enforcing zero deflection at that point. By using this new method, exact buckling loads and buckling modes of many new cases of plates with various boundary conditions and several internal supports are obtained. The optimal location for placing an additional support is shown for several cases of square plates. Results are given for several cases of uni-directional and bi-directional loading. • Static analysis is used to find the exact buckling loads of plates. • Point supports are inserted within the plate domain. • Exact buckling loads for plates with many combinations of boundary conditions. • The optimal location for adding a support is identified for several cases. [ABSTRACT FROM AUTHOR]

Results of investigation of buckling behaviour of an orthotropic composite plate resting on elastic orthotropic foundation with nonlinear change of transverse displacement over the thickness, using the Ritz method are reported in the paper. The foundation has the form of a parallelepiped with the fully fixed bottom plane. A model of the foundation, linking its transverse displacement with the plate deflection, is developed in this work. According to this model, the transverse displacement of the foundation varies nonlinearly over the thickness as opposed to the traditional Winkler-Pasternak model. The proposed method of calculation of critical buckling load is based on a one-dimensional minimisation procedure with respect to the parameter characterising the decay of the transverse displacement of the foundation over its thickness. Using this method, the effects of plate and foundation thicknesses, and moduli of elasticity of the foundation material on the critical buckling load are analysed. It is found that the values of critical loads calculated using the proposed model are lower than those calculated based on the Winkler-Pasternak model. The verification of the results obtained based on the different models of deformed foundation is performed using the finite element method. The finite-element model was composed of three-dimensional elements. The analysis confirmed the validity of the calculations of critical load. The study has shown that the model of the foundation deformation developed in this work enables more accurate calculations of the critical load to be performed compared with those based on the conventional Winkler-Pasternak model. [ABSTRACT FROM AUTHOR]

In current structural steel design specifications, the local buckling of cross-sections is typically treated on an element-by-element basis, with the boundary conditions along the adjoined longitudinal edges of the individual plates assumed to be simply-supported. In reality, cross-sections buckle locally as a whole and the individual plate elements interact. As a result, the boundary conditions along the adjoined longitudinal edges of the critical isolated plate (i.e. that with the lowest elastic local buckling stress) lie between lower and upper bounds of simply-supported and fixed, respectively. Based on this concept, explicit formulae to predict the elastic local buckling stress of full cross-sections of common profiles, including I-sections, have recently been developed (Gardner et al., 2019) [1]. In the present paper, the formulae for single I-sections set out in Gardner et al. (2019) [1] are extended to cover the case of three-flanged cross-sections that arise in longitudinally-stiffened plate girders and in the haunch and apex regions of portal frames. The geometry and loading of the studied cross-sections are assumed to remain constant along the member length, i.e. the influence of tapering and moment gradients on local buckling are not considered herein, but has been evaluated in parallel work (Quan et al., 2020) [2]. The proposed formulae are calibrated against results from finite strip analysis performed using CUFSM v4.05 (Li and Schafer, 2010) [3] on a range of three-flanged sections, and provide predictions of elastic local buckling stresses that are typically within 5% of the numerically obtained values. • Elastic local buckling behaviour of three-flanged cross-sections has been investigated. • Formulae for calculating the elastic local buckling stress of three-flanged cross-sections have been developed. • Accuracy of predictions using the developed formulae has been confirmed against results obtained from finite strip analysis. • The predictions using the developed formulae have also been compared with results calculated on an element-by-element basis. [ABSTRACT FROM AUTHOR]

The present paper proposes a comparison between two different computational techniques to evaluate the natural frequencies of some selected structural components. More specifically, three case studies are investigated: i) Isotropic circular and elliptical cylindrical shells; ii) Non-homogeneous circular cylindrical shell sectors; iii) Homogeneous and non-homogeneous rectangular beams. The 1D-Hierarchical Ritz Formulation (HRF) with 3D capabilities and the 2D-Generalized Differential Quadrature (GDQ) formulation (both in a weak- and a strong-form) are assessed by using a Finite Element Method (FEM) software. For both computational methodologies the Method of Power Series Expansion of the Displacement Components (MPSEDCs) has been employed. A parametric investigation is performed to study the sensitivity of the natural frequencies to some significant parameters, namely, the boundary conditions, the length-to-thickness ratio, as well as some material and geometrical properties. The main advantages of the proposed solution techniques are discussed in terms of convergence and accuracy, for each selected case study. [ABSTRACT FROM AUTHOR]

• An exact spectral element model is proposed for a rectangular Kirchhoff plate. • The general solution and boundary conditions are represented in the spectral forms. • An FFT algorithm can be applied for the calculation of spatial spectral coefficients. • The SEM model is derived by the projection method and force–displacement relations. • The high accuracy and efficiency of the proposed SEM model are numerically verified. As an extension of the previous work on membranes by Kim and Lee (2020), an exact frequency-domain spectral element model is proposed for the transverse vibrations of a rectangular Kirchhoff plate, based on the following procedure. First, in the frequency-domain, the general solution of a finite rectangular plate element is derived in the spectral form in the spatial domain, after removing all the trigonometric terms that vanish at the four boundary edges. Second, as an important theoretical improvement, the boundary functions that represent the boundary conditions at the four boundary edges are also expressed in the spectral forms in the spatial domain. Next, by using the projection method based on the orthogonality of trigonometric functions, the spatial-domain spectral coefficients of the general solution are related to those of the boundary functions. Finally, from the force-displacement relationships, the spectral element matrix (or dynamic stiffness matrix) is formulated for a finite rectangular plate element. As both the general solution and boundary functions are expressed in the spectral forms in both the temporal and spatial domains, a fast Fourier transform (FFT) algorithm can be applied to efficiently simulate the vibration responses and waves in a plate. The accuracy and computational efficiency of the proposed SEM are evaluated by comparison with the exact theory, modal analysis method, and the commercial finite-element-analysis software ANSYS. Image, graphical abstract [ABSTRACT FROM AUTHOR]

This paper aims at investigating the optimum positions and the required flexural rigidity (γ rq) of a single and two longitudinal web stiffeners of unsymmetric plate girders subjected to pure bending by using gradient-based optimization algorithms. The optimization procedure is performed into two steps: The first step is to maximize the bend-buckling coefficient k b generated from eigenvalue buckling analyses, and then the second step aims to minimize the flexural rigidity of the stiffeners (γ). This procedure is implemented using the Abaqus2Matlab toolbox which allows for the transfer of data between Matlab and Abaqus and vice versa. Based on this research, the optimum locations of the stiffeners are recommended for the unsymmetric plate girders under pure bending. Additionally, equations are suggested to determine γ rq of the longitudinal web stiffeners of the unsymmetric plate girders. These proposed equations are more realistic in the practical designs than those recommended by AASHTO LRFD specifications and several works in the literature in which γ rq of the longitudinal web stiffeners is determined based on the simply supported plates but not the unsymmetric plate girders under bending. • The optimum stiffener location of the plate with a single stiffener and two stiffeners is at around 0.42 D c and around 0.25 D c and 0.56 D c , respectively, regardless of the asymmetry of the girder section. • γ rq obtained according to the AASHTO LRFD requirements is too conservative in cases ϕ > 1.0 but not conservative in cases of ϕ ≤ 1.0. • The formulas for determining the minimum flexural rigidity requirement of a single and two stiffeners are suggested for practical design purposes. [ABSTRACT FROM AUTHOR]

• Symplectic superposition method for buckling of side-cracked plates is developed. • New analytic buckling solutions of side-cracked rectangular plates are obtained. • Comprehensive benchmark numerical and graphical results are presented. • The present method provides a rational approach to exploring analytic solutions. Exploring new analytic buckling solutions of cracked plates is of much importance for providing benchmark results and implementing preliminary structural designs based on explicit parametric analysis and optimization. However, the governing higher-order partial differential equations as well as the geometric discontinuity across a crack essentially complicate the problems, make it more intractable to seeking analytic solutions. This paper presents a first attempt to extend an up-to-date symplectic superposition method to linear buckling of side-cracked rectangular thin plates. The problems are introduced into the Hamiltonian system, and a side-cracked plate is then divided into several sub-plates that are analytically solved by the symplectic superposition method, where the symplectic eigenvalue problems are formulated, followed by the symplectic eigen expansion. Some elaborated mechanical quantities are imposed on the edges of each sub-plate, with multiple sets of constants determined by the actual boundary conditions of the cracked plate, free edge conditions along the crack, and interfacial continuity conditions among the sub-plates. The final analytic solution of a side-cracked plate is obtained by integration of the solutions of the sub-plates. Comprehensive benchmark results are tabulated and plotted for buckling loads and mode shapes of typical plates with a side crack from a simply supported edge, a clamped edge, or a free edge. The crack length effect is also investigated by the analytic solutions obtained. Due to the rigorous mathematical derivations without predetermination of solution forms, the present method provides a rational approach to exploring more analytic solutions. Image, graphical abstract [ABSTRACT FROM AUTHOR]

The problem of interaction between a floating ice cover and an engineering structure is considered, in which the ice–structure contact forces are caused by an increase in ice temperature due to solar radiation in situations, when the lateral thermal expansion of ice is constrained. The focus is on the determination of the maximum thermally-induced horizontal force exerted on a structure wall, assuming that the magnitude of this force is bound by the smallest force capable of fracturing the ice cover due to its buckling. The ice cover is modelled as a rectangular plate of uniform thickness, with its four edges being constrained by vertical rigid walls, and it is assumed that ice deforms, and eventually fails, by the mechanism of viscous creep buckling. The plate is subjected to in-plane axial compressive stresses developing in ice to prevent its thermal expansion due to solar heating, and is transversely (vertically) bent by the forces caused by the reaction of underlying water. The floating ice is treated as a material whose elastic and viscous properties depend on temperature and the ice porosity, and therefore they vary with time and the depth of ice. The results of numerical simulations, conducted for a variety of the ice plate horizontal dimensions, thicknesses and daytime temperature-change scenarios, illustrate the evolution of the plate deflection surface prior to its failure, and show the time variation of the maximum forces exerted by ice on a structure wall as functions of the ice thickness and maximum daytime temperature rise at the top surface of ice. • Sea ice – structure interaction problem is analysed in which stresses in ice are due to its constrained thermal expansion. • Sea ice cover is modelled as a rectangular plate of uniform thickness which deforms by the mechanism of creep buckling. • Results illustrate evolution and maximum values of thermally-induced forces exerted by ice on constraining walls. [ABSTRACT FROM AUTHOR]

In the version of the article originally published [1], Eqs. (19)–(21) and (31) were shown incorrectly. The corrected equations are the following. [ABSTRACT FROM AUTHOR]

In this paper, Reddy's higher-order and Mindlin's first-order plate theories are used for buckling analysis of porous rectangular plates subjected to various types of mechanical loading. The condition of the internal pores is considered to be either free of or saturated by fluid. Biot's theory of poroelasticity is thereby employed to model the behaviour of fluid. Distribution of pores is assumed to vary through the thickness according to an asymmetric distribution. For each displacement field considered, five highly coupled partial differential equations are derived by means of variational principle. These systems of equations are first decoupled through an efficient method, and then solved analytically for Levy-type boundary conditions. Accuracy of the approach is examined by comparing the obtained results with those available in literature. Eventually, comprehensive parametric studies are provided to investigate the effects of geometrical parameters, boundary conditions, loading conditions, porosity coefficient and pore fluid compressibility on the buckling response of the system. The results suggest that a structure with higher equivalent rigidity is met, when its corresponding internal pores are saturated by fluid. The results of the current work can be considered as a benchmark for future studies. [ABSTRACT FROM AUTHOR]

• An exact and 3D method for in-plane/out-of-plane frequency analysis of transversely isotropic/ isotropic FG circular plates is presented. • Material properties vary in the thickness direction according to exponential and second-order law. • Contrary to plate theories, all boundary conditions are satisfied in a three-dimensional manner and surface-constraint form. • There is no ad-hoc assumption, and thus the obtained solution is applicable to any thickness ratios. • As the thickness ratio increases (thick FGM plate), the effects of gradient factor, grading pattern and elasticity constants are more significant. This paper presents a simple and effective analytical method based on displacement potential functions for solving the 3D free vibration problem of the functionally graded circular plates with surface boundary conditions consisting of a transversely isotropic linearly elastic material. Material properties vary in the thickness direction according to exponential law and a special power law. Using the potential function method, the coupled governing equations are decomposed into two linear partial differential equations of fourth and second-order, and each equation solved independently by using the separation of variables with exact satisfaction of the two special boundary conditions in a pointwise manner. In addition, the analytical solutions are degenerated for two particular cases, including FG isotropic material and axisymmetric vibration. Also, the in-plane shear vibration has been discussed separately without considering the coupling of transverse and plane displacements. As an advantage of the proposed method, contrary to plate theories, all boundary conditions have been applied in a three-dimensional manner and surface-constraint form. Moreover, obtained solutions are applicable to any thickness ratio. In-plane/out of plane frequencies and mode shapes with nodal patterns are presented for different material properties and different thickness ratios. The results are compared with other analytical works as well as a 3D finite element (FE) solution obtained from the ABAQUS software, which demonstrates the effectiveness and high accuracy of the present method. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

• The discrete stiffness parameters are employed to yield the theoretical optimal ply orientation that corresponds to the maximum critical buckling load of simply supported orthotropic plates at a layer level, then, the optimal stacking sequence are obtained with the derived optimal ply orientation and a sign vector. • Two laminate optimal design problems are addressed: the critical buckling load with fixed thickness is maximized, and the thickness with buckling constraint is minimized. • The derived maximum critical buckling load can be extended to the symmetric and antisymmetric angle-ply laminated plates with small coupling stiffness B 16 and B 26. • The theoretical optimal ply orientations exhibiting a range of load ratios and aspect ratios are presented. The buckling characteristic of rectangular orthotropic plates under axial compression with simply supported boundary has been extensively studied. To enhance the structural efficiency, the stacking sequence of laminate should be optimized to maximize the critical buckling load. In this study, the discrete stiffness parameters are employed to yield the theoretical optimal ply orientation corresponding to the maximum critical buckling load at a layer level, and the buckling mode shapes are calculated analytically. Subsequently, the derivation is performed based on optimal ply orientation to derive the optimal stacking sequence of the laminate, in which a sign vector is adopted to minimize the bending-twisting coupling effects. As a result, two laminate optimal design problems are solved: maximizing critical buckling load with fixed thickness, as well as minimizing the thickness with buckling constraint. Two numerical examples are adopted to verify the yielded optimal solutions. Lastly, the theoretical optimal ply orientations exhibiting different load ratios and aspect ratios are presented. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Using the ideas of variational differential quadrature and finite element methods (VDQ and FEM), a novel numerical approach is developed in this paper to investigate the postbuckling behavior of plates with arbitrary shape under the action of thermal load within the framework of higher-order shear deformation theory (HSDT). It is considered that the plates are made of functionally graded carbon nanotube reinforced composite (FG-CNTRC). By the proposed approach, the thermal postbuckling behavior of plates with arbitrary-shaped cutout can be modeled. The rule of mixture is utilized to obtain the effective material properties of nanocomposite which are considered to be temperature-dependent. To implement the proposed method that can be named as VDQFEM, the variational temperature-dependent formulation of problem is first developed. This formulation is presented using novel vector-matrix relations with the aim of utilizing in programming in an efficient way. In the context of VDQFEM, the space domain of plate is first transformed into a number of finite elements. In the next step, the VDQ discretization technique is implemented within each element. Then, the assemblage procedure is performed to derive the set of matricized governing equations which is finally solved by means of the pseudo arc-length continuation algorithm. One of the main novelties of present approach is proposing an efficient way based on mixed-formulation to accommodate the continuity of first-order derivatives on the common boundaries of elements for the used higher-order shear deformable plate model. Quadrilateral plate, skew plate, annular plate, square plate with rectangular hole and rectangular plate with circular hole under different boundary conditions including CCCC, SSSS, CSCS and CCSS (S: simply-supported, C: clamped) are considered in the numerical example. First, validation studies are presented in terms of critical buckling temperature of CNTRC rectangular plates with various CNT distribution patterns. It is shown that the proposed method has the advantages of standard VDQ technique including fast convergence rate, being locking-free and simple implementation. Moreover, it is capable of considering polygon and concave domains. Also, the effects of geometrical properties, volume fraction and distribution pattern of CNTs and temperature-dependency of material properties on the thermal postbuckling of plates are studied. [ABSTRACT FROM AUTHOR]

In this paper, the problem of the stability of functionally graded thin plates with a microstructure is presented. To analyse this problem and take into consideration the effect of microstructure, tolerance modelling is used. The tolerance averaging technique allows us to replace the equation with non-continuous, tolerance-periodic, highly oscillating coefficients of the system of differential equations with slowly-varying coefficients, which describes also the effect of the microstructure. As an example, the buckling of a microstructured functionally graded plate band on a foundation is investigated. To obtain results, the tolerance model and the asymptotic model combined together with the Ritz method are used. It is shown that the tolerance model allows us to take into account the effect of microstructure on critical forces. [ABSTRACT FROM AUTHOR]

The nonlinear mechanical response of highly flexible plates and shells has always been of primary importance due to the widespread applications of these structural elements in many advanced engineering fields. In this study, the Carrera Unified Formulation (CUF) is used in a total Lagrangian framework to analyze the large-deflection and post-buckling behavior of isotropic rectangular plates based on different nonlinear strain assumptions. The scalable nature of the CUF provides us with the ability to tune the structural theory approximation order and the strain–displacement assumptions opportunely. In this work, the Newton–Raphson linearization scheme with a path-following constraint is used in the framework of the 2-D CUF to solve the geometrically nonlinear problems to draw important conclusions about the consistency of many assumptions made in the literature on the kinematics of highly flexible plates. In this regard, the effectiveness of the well-known von Kármán theory for nonlinear deformations of plates is investigated with different modifications such as the thickness stretching and shear deformations due to transverse deflection. The post-buckling curves and the related stress distributions for each case are presented and discussed. According to the results, the full Green–Lagrange nonlinear model could predict the nonlinear behavior of plates efficiently and accurately, whereas other approximations produce considerable inaccuracies in the case of thick plates subjected to large rotations and deflections. • This paper proposes a unified theory for nonlinear metallic plates. • Large deflection and post-buckling analyses are considered. • The effect of different nonlinear approximations is evaluated. • It is found that von Kármán approximation is inappropriate for thick plates and large rotations. [ABSTRACT FROM AUTHOR]

Understanding the mechanical response of structures such as plates and thin-walled extrusions subjected to cutting and tearing by hardened wedges (blades) is of great interest to scientists and engineers. This complex problem arises in a plethora of disciplines, including but not limited to the broad spectrums of manufacturing, construction and engineering design. Furthermore, studying this topic is a comprehensive endeavor which incorporates advanced concepts within stress analysis and materials science. Despite these challenges, a multitude of advancements were achieved through extensive physical testing, followed by the subsequent development of theoretical explanations and modeling efforts. This paper reviews the major contributions in recent decades towards understanding cutting-induced plastic deformation through experimental, analytical and numerical modeling techniques. The plate tearing problem was historically of interest to the ocean engineering community as an approximation for ship grounding incidents. More recently, the potential for cutting to serve as a means of energy dissipation for enhanced vehicular safety was identified due to the characteristic near-constant force response. Experimental studies were conducted from quasi-static to high rate blast loading conditions (V > 100 m/s). Numerical modeling with Eulerian mechanics and meshfree element formulations were identified as the most accurate techniques, although these schemes are computationally expensive. Analytical solutions are highly sought after since they provide valuable information almost instantaneously. Early modeling efforts yielded purely empirical relationships with gradual improvement, followed by the development of fully analytical formulations which rely upon approximations of the strain fields in combination with the principle of virtual power to obtain resultant forces. Image 1 • Cutting and tearing of thin-walled plates and extrusions by rigid wedges. • Deformation mode useful for disaster reconstruction from ship raking to WTC attacks. • Recognized as a novel means of ideal energy absorption for improved vehicle safety. • Experimental testing from quasi-static crushing up to 168 m/s blast impacts. • Broad analytical and numerical modeling efforts, Eulerian mechanics most successful. [ABSTRACT FROM AUTHOR]

This paper presents simulation and experimental results on the implementation of a velocity feedback control unit with a new flywheel inertial actuator, which can be used to reduce flexural vibration of distributed structures. The actuator incorporates a classical coil–magnet linear transducer and a flywheel element such that both linear and rotational inertia effects are generated by the moving components of the actuator. The additional rotational inertia effect shifts to lower values the fundamental resonance frequency of the actuator without increasing the static deflection of the suspended masses. Therefore, this actuator can be conveniently used to implement feedback control units, which are robust to shocks, have enhanced stability properties and, thus, improved vibration control effects. To illustrate the key features of the proposed actuator, the characteristic electro-mechanical response functions of a classical actuator and of the flywheel actuator are first presented. Then, the stability and flexural vibration control performance of velocity feedback loops with a classical and the flywheel inertial actuators are contrasted considering a thin rectangular plate hosting structure. [ABSTRACT FROM AUTHOR]

This paper investigates the buckling behaviors of thin rectangular functionally graded carbon nanotubes reinforced composite (FG-CNTRC) plate subjected to the arbitrarily distributed partial edge compression loads. Three distribution types of carbon nanotubes (CNTs) are considered and the effective material properties of carbon nanotube reinforced composite are given according to the extended rule of mixture, in which the distribution uncertainty of CNTs is also taken into account. Based on the differential quadrature method (DQM) and work equivalent method, the pre-buckling in-plane stress distribution of thin rectangular FG-CNTRC plate are determined firstly. Then the accurate critical buckling loads and buckling modes of FG-CNTRC plate are consequently obtained. By comparing with the results in published literatures, the feasibility and accuracy of present numerical method are validated. Finally, the systematic parametric studies are carried out to elaborate the effects of distribution type, volume fraction and distribution uncertainty of CNTs as well as the distribution width, position and distribution type of partial edge compression loads on the buckling behaviors of thin rectangular FG-CNTRC plate for the first time. • A numerical method for buckling analysis of thin rectangular FG-CNTRC plate under arbitrarily distributed partial edge compression loads is developed. • The influence of CNTs distribution uncertainty in the matrix of FG-CNTRC plate is considered and discussed in details. • Effects of partial edge compression loads on the buckling behaviors of FG-CNTRC plate are studied for the first time. [ABSTRACT FROM AUTHOR]

• Effects of shapes of splitter are studied in a PPFHS numerically. • Numerical results are validated with experimental data obtained by a fabricated setup. • Highest heat transfer enhancements are recorded for models equipped indirect splitters. • Maximum value of performance index can be 1.36 for AF model at Re = 50. Previous studies Razavi et al. (2015) and Sajedi et al. (2016) have shown that the use of thin straight plates connected to pin-fins as splitters can weaken the flow separation and decrease the pressure drop through plate-pin-fin heat sinks (PPFHSs). In the current study, two new configurations of splitter, namely arched and wavy, are proposed to improve the overall hydrothermal performance of PPFHSs. In addition to the forward arrangement studied previously, the backward arrangement of splitters is also investigated here. The case under the consideration to implement the current idea is a PPFHS equipped with rectangular plate-fins and square pin-fins. Hence, six enhanced models are examined, and the obtained results are evaluated as compared with the smooth case. The working fluid is water in the Reynolds number range from 50 to 250. This analysis is carried out using 3D-numerical simulations, and the results are validated by the obtained experimental data as well as previously proposed correlations. It is found that the shape and arrangement of splitters affect considerably temperature contours and flow fields of the fluid through the PPFHS. Further, indirect splitters with forward arrangement lead to lower base temperature of the PPFHS in comparison with the straight one, however, an inverse trend is seen for the backward arrangement. The minimum base temperature is detected for the model having arched splitters with forward arrangement. At the studied range, the best overall hydrothermal performances are also reported for this model. For instance, the maximum value for one performance index is reported to be 1.36 at the minimum Reynolds number of 50. [ABSTRACT FROM AUTHOR]

In this research we present a new analytical solution for finding the buckling loads of thin isotropic and orthotropic rectangular plates in which all four corners are supported. This new solution is also capable of solving all cases where few or all the edges are supported. The methods that are currently known in the literature for finding the buckling loads of plates are mainly numerical. Although some plates with specific boundary conditions have analytical solutions, a comprehensive analytical method providing analytical solutions that fit all possible combinations of boundary conditions is lacking. The solution method in this study is based on the development of a static solution for a plate. The physical meaning of buckling is the loss of stiffness, and it is found as the value of the in‐plane loading intensity at which a zero force on the plate surface will generate infinite displacement. The solution is obtained in series form, and the coefficients are solved to match the edge conditions. Using this new method, exact buckling loads and buckling modes of many new cases of classical boundary conditions are found. Results are given for several stiffness ratios in both directions of the plate, and for uni‐directional and bi‐directional loading. [ABSTRACT FROM AUTHOR]

The evacuation of crowds in a building has always emerged as a vital issue in many accidents. The geometrical structure of a room, especially the exit design has a great influence on crowd evacuation under emergency conditions. In this paper, the effect of exit location of a room on crowd evacuation in an emergency is investigated with mice. Two different exits are set in a rectangular chamber. One is located in the middle of a wall (middle-exit) and the other is at the corner of the chamber (corner-exit). Arching and clogging are observed in the flow of mice. The result based on the escape trajectories of mice shows a dynamic balance in the arch near the exit wherever the exit is located. We demonstrate that the occupant position in the arch has an effect on the escape sequence of mice. At a low stimulation level, the narrow middle-exit is more effective in increasing the flow rate of mice than the narrow corner-exit. However, the opposite result appears when the exit becomes wider. At a high stimulation level, the effect of exit location on flow of mice tends to be weakened. The results suggest that the specific level of stimulation needs to be taken into account when optimizing the evacuation efficiency of a crowd through the geometrical structure of a room. [ABSTRACT FROM AUTHOR]

Objective The aim of this study was to evaluate the impact of oxygen and argon/oxygen low-pressure plasma on the shear bond strength (SBS) between dental PEEK compounds and veneering composites as a function of plasma process time. Methods Of an unfilled PEEK (“Juvora”) and two pigment powder filled PEEK compounds (“DC4420”, “DC4450”), 273 rectangular plates were prepared and polished up to 1200 grit. Afterwards the samples were sandblasted and randomly assigned to five different surface pre-treatment groups (1. No plasma (control); 2. O 2 plasma for 3 min; 3. O 2 plasma for 35 min; 4. Ar/O 2 plasma for 3 min; 5. Ar/O 2 plasma for 35 min). Surface roughness and water contact angles were recorded using three samples of each PEEK compound for each of the plasma treatment groups. An adhesive (visio.link, Bredent GmbH & Co KG, Senden, Germany) was applied onto the specimen surfaces and light cured. A mold was used to shape three different veneering composites (a) Vita VM LC, “Vita” (Vita Zahnfabrik, Bad Säckingen, Germany); (b) GC GRADIA, “Gradia” (GC Europe, Leuven, Belgium); (c) GC GRADIA DIRECT Flo, “Gradia Flo” (GC Europe, Leuven, Belgium)) into a cylindrical form on the sample surface before light curing. SBS was measured using a universal testing machine after 24 h of incubation in distilled water at 37 °C. Results The two pigment filled PEEK compounds treated with O 2 plasma and veneered with Gradia Flo showed the highest SBS values (34.92 ± 6.55 MPa and 34.2 ± 1.87 MPa) followed by the combination of the unfilled PEEK material with Gradia Flo (29.57 ± 3.71 MPa). The SBS values of the samples veneered with Gradia were lower, but not significantly so. The SBS values of the specimens with Vita were for the most part associated with significantly lower results. Significance A low-pressure plasma process using oxygen plasma for a duration of 35 min, preceded by sandblasting, seems to be the most effective in increasing shear bond strength between veneering composites and PEEK materials. [ABSTRACT FROM AUTHOR]

The magnetohydrodynamic (MHD) flow of a third grade fluid through a rectangular channel, considering the effect of aspect ratio, has been investigated. The flow considered is steady, laminar, incompressible and hydro-dynamically fully developed. The equation, describing the flow, is a highly non-linear partial differential equation (PDE) with remote possibility of having an exact solution and even numerical solution also is very difficult to obtain. A combination of the homotopy perturbation method (HPM) and integral method (IM) has been employed to solve the non-linear PDE which is scarce in open literature. The results of the present study are compared with the results obtained by the least square method (LSM) of the MHD third grade fluid flow through a rectangular channel, without the effect of aspect ratio and are found to be in close agreement. The results indicate that the flow field is significantly affected by the aspect ratio which should be considered for practical applications. In all the available literatures of the third grade fluid flow, the aspect ratio effect is neglected and this simplifying assumption reduces the highly complicated non-linear PDE to a non-linear ordinary differential equation (ODE). The novelty of the subject work lies in the inclusion of the effects of aspect ratio in the governing equation describing the flow of a third grade fluid through a channel and solving this by a combined analytical method (HPM and IM). Further, the effects of the Hartmann number and non-Newtonian third grade fluid parameter on the flow filed are discussed. [ABSTRACT FROM AUTHOR]

Previous work covers building a tower from a stack of homogeneous rectangular plates, each with a maximum shift in displacement. We suggest using plates shaped as curvilinear triangles bounded by segments of power-law functions. The masses of the plates and the position of their center of mass are calculated and measured experimentally after cutting them out from cardboard and aluminum sheets. A computer simulation of the displacement towers is combined with their live building. Individual maximum shifts of the plates in the stack prove to be much bigger the higher the power coefficient of the boundary curves. The resulting total overhang of such a displacement tower may exceed that of a stack of traditionally used homogeneous rectangular cards. [ABSTRACT FROM AUTHOR]

The wavelength-tunable rectangular mode-locking operation is demonstrated in an all-fiber laser based on semiconductor saturable absorber mirror. As the dissipative soliton resonance signature, the pulse duration varies from 580 ps to 2.1 ns as a function of the increasing pump power. Correspondingly, the maximum pulse energy is 9.11 nJ. Moreover, it is found that the wavelength tunable operation with a range of approximately 10 nm could be obtained by properly adjusting the polarization controllers. The characteristics of the rectangular pulses at different wavelengths are similar to each other. The demonstration of the wavelength tunable rectangular pulses would be beneficial to some applications for many fields such as spectroscopy and sensing research. [ABSTRACT FROM AUTHOR]

In this paper we show the interaction of a composite of a periodic or aperiodic signal and intrinsic electrochemical noise with the nonlinear dynamics of an electrochemical cell configured to study the corrosion of iron in an acidic media. The anodic voltage setpoint (V0) in the cell is chosen such that the anodic current (I) exhibits excitable fixed point behavior in the absence of noise. The subthreshold periodic (aperiodic) signal consists of a train of rectangular pulses with a fixed amplitude and width, separated by regular (irregular) time intervals. The irregular time intervals chosen are of deterministic and stochastic origins. The amplitude of the intrinsic internal noise, regulated by the concentration of chloride ions, is then monotonically increased, and the provoked dynamics are analyzed. The signal to noise ratio and the cross-correlation coefficient versus the chloride ions' concentration curves have a unimodal shape indicating the emergence of an intrinsic periodic or aperiodic stochastic resonance. The abscissa for the maxima of these unimodal curves correspond to the optimum value of intrinsic noise where maximum regularity of the invoked dynamics is observed. In the particular case of the intrinsic periodic stochastic resonance, the scanning electron microscope images for the electrode metal surfaces are shown for certain values of chloride ions' concentrations. These images, qualitatively, corroborate the emergence of order as a result of the interaction between the nonlinear dynamics and the composite signal. [ABSTRACT FROM AUTHOR]

A lift formula for a wing in a rectangular control volume is given in a very simple and physically lucid form, providing a rational foundation for calculation of the lift of a flapping wing in highly unsteady and separated flows at low Reynolds numbers. Direct numerical simulations on the stationary and flapping two-dimensional flat plate and rectangular flat-plate wing are conducted to assess the accuracy of the lift formula along with the classical Kutta-Joukowski theorem. In particular, the Lamb vector integral for the vortex force and the acceleration term of fluid for the unsteady inertial effect are evaluated as the main contributions to the unsteady lift generation of a flapping wing. [ABSTRACT FROM AUTHOR]