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This article first introduces a novel optimization-driven reduced order model (ROM) to the dynamics of plates utilizing isogeometric analysis (IGA). The proposed paradigm uses an iterated improved reduced system (IIRS) technique to condense the system's dynamic properties. This model takes account of inertia items, the consistent mass matrix is therefore preserved. Moreover, master degrees of freedom (DOFs) defined at control points of the IGA in ROM are optimized via the derivative-free adaptive hybrid evolutionary firefly algorithm (AHEFA). Accordingly, the accuracy and the correlation of high-order shape modes can be improved. The Galerkin discretization is employed to establish the IGA-based ROM for the plate's dynamic analysis with proportional damping. In which, its weak form relied upon a generalized shear deformation theory (GSDT) is derived from the Hamilton's principle. Consequently, the reduced IGA can deal with both thick and thin plates without shear correction coefficients and the shear locking phenomenon. The Newmark- β method is then employed to achieve time-history responses of the reduced dynamic equation system. Several numerical examples are tested to illustrate the reliability and efficiency of the present methodology. Obtained outcomes have shown their useful and potential applications to the structural health monitoring (SHM) field, especially when the number of sensors is limited. • A novel optimization-based ROM using IGA is proposed for the dynamics of plates. • IIRS is utilized to condense dynamic properties with consistent mass conservation. • Master DOFs defined at control points are optimized by AHEFA. • Examples of plates' transient analysis with proportional damping are investigated. [ABSTRACT FROM AUTHOR]

Abstract The paper investigates the effects of the geometrical imperfections in buckling analyses of plated steel elements at elevated temperatures and provides an alternative branch-switching procedure to perform post-buckling analyses without introducing initial imperfections into the model. This procedure is appealing since the choice of appropriate imperfections in classical analyses is not straightforward, above all at elevated temperature. Several numerical analyses show that the choice of the imperfections is not trivial and that the buckling mode may vary with temperature. They also show that the proposed branch-switching procedure is an interesting preliminary tool to understand the instability behaviour of steel structural members. Highlights • Buckling of compressed steel plated elements at elevated temperatures is studied. • A branch-switching procedure performed without introducing imperfections is proposed. • The procedure is an interesting preliminary tool to study the post-buckling behaviour. • Linear buckling analyses may not capture the buckling mode at high temperature. • Imperfections based on modes at ambient temperature do not always give safe results. [ABSTRACT FROM AUTHOR]

Load paths represent the load flow in structures and are used to identify how the load is transferred throughout the structure from points of application to support. The load function method is used in this paper for identification and visualization of load paths in plate and shell structures. Authors previously proposed a load function method to calculate the load paths in plane elasticity problems. This work extends the previous formulation to plates and shells. The significant difference from previous work is that the plates and shells equilibrium equations are not divergence free. Therefore, Helmholtz decomposition is used to decompose the stress field to divergence and curl free components to calculate the load function and find load paths. Mathematical formulations are presented to support the proposed method. Numerical and analytical examples show the application of this method. [ABSTRACT FROM AUTHOR]

Modern structures and components may require advanced materials whose properties vary continuously not only in one specified direction, but also different other directions. In particular, the bi-directional functionally graded materials (2D-FGMs) introduced are expected to have more effective properties, consequently eliminating commonly awkward problems such as local stress concentrations and delamination. In this paper, buckling and bending behaviors of 2D-FGM plates, which are of great importance in the design and development of engineering applications, are numerically analyzed by a finite element model. The plate kinematics are described using a new third-order shear deformation plate theory (TSDT), without the need for special treatment of shear-locking effect and shear correction factors. The present TSDT theory based on rigorous kinematic of displacements, which is shown to be dominated over other preceding theories, is derived from an elasticity formulation, rather by the hypothesis of displacements. The materials are assumed to be graded in two directions and their effective properties are computed through the rule of mixture. The accuracy of the proposed approach assessed on numerical results is confirmed by comparing the obtained results with respect to reference published solutions. The effects of some numerical aspect ratios such as volume fraction, boundary conditions, thickness to length ratio, etc. on static deflections and critical buckling are numerically studied. The investigation of results confirms that such aforementioned aspect ratios have significant effects on the mechanical behaviors of plates. [ABSTRACT FROM AUTHOR]

Natural fibres such as flax, jute and hemp have been utilised for thousands of years, however have only recently been considered for fibre-resin composites. A major motivation for such an application is their superior sustainability attributes compared with traditional building materials. Population rise continues to place increasing demands for new infrastructure. Meanwhile, public concerns about the environment, climate change, energy consumption and greenhouse gas emissions, place increasing demands for the use of sustainable materials in infrastructure. While there is a wealth of knowledge in the materials aspects of natural fibre composites, relatively few studies have investigated their potential for structural applications. This paper presents an experimental and analytical study of natural fibre composite plates and channel sections consisting of flax, jute and hemp fibres and subjected to pure compression. The intrinsic mechanical properties are shown to be relatively modest. However, the buckling and post-buckling responses are shown to be stable, the ultimate condition is reached in a stable and predictable manner, and failure ensues in a gradual and ductile process. These characteristics show promise for the use of natural fibre composite sections in light structural applications such as in the residential and light commercial markets. Additionally, the analytical effective width mechanics model shows promise for use as a design technique for estimating their compression strength. [ABSTRACT FROM AUTHOR]

The behaviour of Carbon Fibre Reinforced Polymers (CFRP) reinforced mild steel isolated plate (strut) under uniform axial compression is not well understood because there is a lack of experimental research. This paper presents experimental results for a series of struts reinforced with CFRP sheets subjected to uniform axial compression. The main parameters examined were the thickness of the steel plates, and the location and the number of the CFRP sheets. Three different thicknesses of steel plates were examined, namely, 2, 3 and 4 mm. The testing program included 21 struts with three different width-to-thickness ratios of 50, 66.7, and 100. The CFRP sheets were adhesively bonded where the fibres were aligned in the longitudinal direction parallel to the direction of the applied force. The results showed that the debonding failure strain in the compression face occurred in the range of 0.3–0.6% for all the composite specimens. It was found that the amount of permanent damage in the composite strut identified by the residual displacement is significantly less than that of the bare strut. Experimental results showed a global increase in strength, energy absorption and ductility for all test specimens where the greatest percentage increases were 452%, 259% and 107%, respectively. The 2 and 3 mm composite specimens showed greater percentage increases than the 4 mm composite specimens due to the relative thickness of the carbon fibre sheets verses steel. All experimental specimens failed by overall buckling, achieving maximum capacity at the end of their elastic range showing that the specimens were successfully bonded and acting as composites within such range. An existing rigid plastic theory considers initial imperfections (defects) was modified and used to predict the response of the struts. Experimental and theoretical curves showed consistency where initial defects controlled the elastic-inelastic behaviour and the load bearing capacity of the strut. In general, specimens with initial defects produced a smooth elastic-plastic curve, while specimens with little to no initial defects showed a sharp peak at the buckling load. The rigid plastic theory well predicted the response of the bare specimens whereas it reasonably predicted the plastic collapse curve of the composite struts. [ABSTRACT FROM AUTHOR]

Open-hole details have gained widely application in bolted connections subjected to fatigue loading. Although the use of carbon fibre reinforced polymer (CFRP) can be efficient in strengthening critically stressed tension area, its benefit in improving the fatigue life of open-hole details has not been extensively evaluated. This paper presents the results of an experimental and finite element analytical study on the fatigue behaviour of CFRP strengthened open-hole steel plates. The merits resulted from CFRP strengthening are investigated and compared with some others from referred open-hole fabrication methods and these with artificial initial cracks or notches as reported in the literature. Typical failure modes, local strain evolution and stiffness degradation behaviour of the test open-hole details are reported. The fatigue life results are evaluated and compared against the design curves of the AASHTO. The results show that the use of single and triple layered CFRP strengthening results in fatigue life enhancement of nearly 20% and 60% respectively in contrast to bare steel open-hole plates. Incorporating the stress ratios allowing for fibrous rupture and steel-adhesive interface failure, the fatigue life of CFRP strengthened specimens can be properly evaluated. Finally, the geometric and configuration parameters of CFRP on the stress concentration of the open-hole details are studied based on finite element modelling. It is demonstrated that the studied stress concentration can be reduced with the increase of the modulus of carbon fibre and the number of CFRP layers. The contribution of the effective width of CFRP to the decrease of stress concentration is also discussed [ABSTRACT FROM AUTHOR]

This paper aims to investigate the linear elastic behavior of composite sector plates with rectilinear orthotropy in terms of displacement and stress fields determination. This variety of plates presents layers reinforced with unidirectional fibers organized along straight directions that make a variable angle with the generic radial direction. The fundamental equations for rectilinear orthotropic composite sector plates are obtained according to the Classical Lamination Theory. The mid-surface deflection of the sector plates is derived on the basis of an original analytical approach that combines the principle of virtual works with the Ritz method. Different boundary conditions in terms of displacement constraints are taken into account and, accordingly, the relative discretized forms of the displacement field are written as a linear combination of expressly obtained approximation functions. Commonly employed symmetrical stacking sequences are considered to demonstrate the accuracy and reliability of the proposed method in the final test cases. • A new method for the linear elastic analysis of composite sector plates was obtained. • Original approximation functions for the Ritz method were derived. • The effect of the boundary conditions on the stress field was determined. • The outcomes were successfully compared with reference FEA outcomes. [ABSTRACT FROM AUTHOR]

Damage modelling is essential in preliminary structural design and non-destructive damage detection. This paper investigates changes in natural frequencies of plates due to an arbitrarily aligned crack. A novel hybrid method couples an exact strip model for the intact part with a finite element model for the cracked part. The crack is modelled as a rotational spring with additional rotational freedoms being added to the finite element nodes. The method is validated against published results for through-the-depth cracks. Cracks with varying direction, location, depth and length are used to study the effects of changing the crack parameters. [ABSTRACT FROM AUTHOR]

This paper presents and analytical study to investigate the local buckling behaviour of structural steel I-section columns at elevated temperatures. An inelastic stability model is developed that accounts for the reduction in stiffness and strength of the steel when subjected to elevated temperatures. Using the model, a comprehensive parametric study is conducted to investigate the effect of each of the parameters of the column. Based on the results of the parametric study, expressions for the local buckling capacity of steel I-section columns are given in which all the parameters are reflected including the interaction between the flange and the web. [ABSTRACT FROM AUTHOR]

This paper presents a bending and free vibration analysis of functionally graded plates (FGPs) resting on elastic foundation by using an original first shear deformation theory (FSDT). This theory contains only four unknowns, which is even less than the classical FSDT. The elastic foundation follows the Pasternak (two-parameter) mathematical model. The governing equations for the bending and free vibration analysis are obtained through the principle of virtual work and Hamilton's principle, respectively. The original displacement field allows obtaining interesting governing equations. These equations are solved via Navier-type, closed form solutions. The accuracy of the current solution is verified by comparing it with 3D and other closed form solutions available in the literature. [ABSTRACT FROM AUTHOR]

This paper presents an analytical study to investigate the effect of flange–web interaction on local buckling of welded steel I-sections subjected to bending. An inelastic local buckling stability model is presented that accounts for all the geometric and material variables of the problem. The deformation theory of plasticity was used to describe the behavior of steel beyond the elastic limit. The model results were verified through comparison with finite element model results and published experimental ones. A parametric study was conducted to investigate the effect of flange–web interaction on the width to thickness limits. Using the parametric study results, new width to thickness limits were proposed in which all the parameters of the section are reflected. [ABSTRACT FROM AUTHOR]

Steel plates may be classified as slender, moderate, and stocky based on their distinctive behavior characterized by geometrical buckling and material yielding. Slender plates undergo elastic buckling first and then yield in the post-buckling stage, while stocky plates yield first and then undergo inelastic buckling. Moderate plates, on the other hand, buckle and yield simultaneously. The development of low yield point (LYP) steel enables the application of steel plates with improved buckling and energy absorption capacities as lateral force-resisting and energy dissipating elements in structures. On this basis, buckling and yielding behavior of LYP steel plates with various support and loading conditions is studied in this paper from the point of view of their application in steel plate shear wall (SPSW) systems. The limiting thicknesses of standalone plates corresponding to concurrent geometrical buckling and material yielding are determined theoretically and verified through detailed numerical simulations. Effects of using LYP steel and plate aspect ratio parameter on the required limiting plate thickness as an effective parameter in seismic design of SPSW systems are investigated as well. In addition to the studies on the performance of plates with two and four restrained edges and also applicability of some extrapolation techniques for predicting the critical buckling load of moderate plates, detailed studies are performed on determination of the limiting plate thickness in code-designed SPSW systems. Based on the findings of this study, some practical recommendations are provided for efficient seismic design of SPSW systems with LYP steel infill plates. [ABSTRACT FROM AUTHOR]

Cuboid explosives are usually offered in the military and civilian market. Whilst, the plates are widely used in engineering structures. Plates subjected to blast loads generated by cuboid explosives were numerically investigated in this study. The LS-DYNA was used to create the numerical models, which were then validated using experimental data. The height-to-length ratio (h / a) was used to define the shape of the cuboid explosives in the study, and the effects of h / a on dynamic responses and plate damage were explored. The maximum displacement of the center point and the global damage level of plates increased as the h / a decreased. When the identical mass explosives were utilized, the deformation geometries of stiffened and unstiffened plates were remarkably correlated to the h / a of the explosives. Cuboid explosives with significant h / a can cause an inner dome in the plate, and the smaller the h / a , the smoother the deformation. The bottom length (a) of the explosive had a significant impact on the deformation shapes. Explosives with the same bottom length may lead to similar deformation shapes. Finally, the study aimed to equivalent cuboid explosives (1/4 ≤ h / a ≤ 4) to cubic explosives (h / a = 1) with the same mass. The equivalent cubic shape coefficients (η i) of the cuboid explosives were evaluated and calculated using the maximum central displacements and damage level as indexes. Furthermore, the study presented four coefficients (η 1 – η 4), and the applicability of the coefficients was demonstrated through instances. • The numerical model was validated by experimental results. • Influences of the h / a of cuboid explosives on plates' responses and damages were discussed. • The influence factors of deformation shapes of plates were revealed. • The equivalent cubic shape coefficients were proposed. [ABSTRACT FROM AUTHOR]

This paper introduces two semi-analytical models developed for the nonlinear analysis of stability of isotropic and orthotropic plates under uniaxial compression. The possibility of considering fully free in-plane displacements at longitudinal edges (or unloaded edges) is the innovation of these models over existing models, where these displacements are always assumed constrained to remain straight. Contributions for the large deflection theory of plates related to the derivation of analytical solutions for the Airy stress function which satisfy Marguerre?s equations for isotropic and orthotropic plates are presented. Namely, the extension of the Coan and Urbana solution for isotropic plates in order to consider all the terms of the unknown amplitudes of the out-of-plane displacements and the derivation of a solution for orthotropic plates. Comparisons between the semi-analytical model and nonlinear finite element model results are presented in order to discuss the effect of in-plane displacement boundary conditions on behaviour and strength of plates similar to bottom flanges used in steel box girder bridges. This study shows that the semi-analytical models have a clear potential to provide accurate solutions, requiring only a short computer time. It is also shown that the in-plane displacement boundary conditions for the unloaded edges significantly influence the behaviour and strength of plates and this problem cannot be neglected in the definition of the design rules. [ABSTRACT FROM AUTHOR]

Abstract: Stowell's solution [1] for the buckling behaviour of flange elements in compression was premised on the assumption that the element was fixed against flexural rotations at the ends, a condition representing relatively thick elements for which the thickness dimension is adequate to prevent rotations. This paper presents a solution similar to Stowell's which is applicable to pin-ended flange elements. Aspects not considered in Stowell's work, such as the use of elliptic functions to describe the gradual change of mode shape from sinusoidal to essentially linear, and the gradual and asymptotic changes in axial rigidity in the post-buckling range are described in the paper. The paper also presents comparisons between the behaviour of pin-ended and fixed-ended flange elements. Finally, simple strength equations for flange elements in uniform compression based on the first yield criterion are derived. [Copyright &y& Elsevier]

Abstract: Buckling and postbuckling behavior of metal plates is governed by their slenderness parameter. Using nonlinear finite element simulations, unstiffened mild carbon steel, stainless steel and aluminum plates under the action of axial compression are first classified into slender, moderate and stocky plates. Then the effects of initial imperfection amplitude on each plate type and material is studied via sensitivity analyses. The results show that the transition from slender to stocky plates, regardless of material type, occurs at the slenderness parameter of 2. Empirical equations for evaluating the buckling and postbuckling capacities of imperfect plates are drawn out. It is observed that the increase of imperfection amplitude decreases the buckling load of slender plates, but their postbuckling reserves and ultimate capacities are unaffected. In contrast, the ultimate strength of stocky plates is highly affected by initial imperfections. [Copyright &y& Elsevier]

Abstract: This study presents detailed and rigorous numerical analysis for a parametric series of unstiffened aluminium plates typical of those used in lightweight ships and equivalent thin walled stiffened structures. The study is undertaken with a nonlinear finite element analysis procedure using ABAQUS. The strength behaviour of the plates under a progressively increasing longitudinal in-plane load are shown to be affected by a number of parameters including the alloy, geometric imperfection shape, heat affected zone distribution, level of heat softening and residual stress distribution. The comparative influences of these various factors, some of which are specific to welded aluminium structure, are explored to determine which must be accounted for in the development of a parametric series of design curves. [Copyright &y& Elsevier]

Abstract: The objective of this work is to analyze the initial and post-collapse plate deflections based on measurement records of the experiments of three corroded box girders subjected to pure vertical bending loading inducing a compressive stress on deck. The effect of initial imperfections and corrosion degradation on the final post-collapse deformation shape has been investigated and a relationship between different loading responses, shape of initial imperfections and plate slenderness has been derived. Analyzing initial imperfections, plate slenderness and final post-collapse deformations, a slenderness criterion has been established to predict the post-collapse deformation shape. [Copyright &y& Elsevier]

Abstract: This work presents the dynamic analysis of three-dimensional plate and shell structures based on an improved meshless method, the Natural Neighbour Radial Point Interpolation Method (NNRPIM) using a shell-like formulation. In the NNRPIM, the nodal connectivity is imposed using the natural neighbours concept. An integration background mesh is constructed, totally node-dependent, and used in the numerical integration of the NNRPIM interpolation functions, which possess the delta Kronecker property. Several dynamic plate and shell problems are studied to demonstrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents two modifications to the spline finite strip method (SFSM) for plate and thin-walled beam buckling and free vibrations; these being augmenting of the flexural buckling displacements with Legendre polynomials which represent additional bubble modes, and a modification of the dedicated amended splines that are conventionally needed to handle boundary conditions. A simple matrix technique to remove the need for amended splines is described, and the efficacy of the method is demonstrated in which it is shown that inclusion of the Legendre polynomials enhances the performance of the SFSM significantly when benchmarked against other techniques. [Copyright &y& Elsevier]

Abstract: An analytical stability model for the local buckling of pultruded fiber reinforced polymer (FRP) structural shapes subjected to eccentric compression is presented. The model is based on considering each of these shapes as being composed of a group of orthotropic plates that are linked together. The differential equations that describe the buckling behavior of each of the plates comprising the shape were defined and solved using the Levy''s solution. The presented model was used to conduct a parametric study to investigate the effect of the main parameters governing the local buckling behavior of such shapes. [Copyright &y& Elsevier]

Abstract: Buckling behavior of slender and compact carbon steel, stainless steel and aluminum plates under the action of in-plane shear is investigated. Unstiffened shear plates with respect to their slenderness parameter and buckling behavior are qualitatively and quantitatively divided into slender, moderate and stocky categories. Accordingly, slender plates have a low buckling capacity, followed by a large postbuckling reserve. Their ultimate load coincides with the formation of inclined yield bands. Stocky plates yield before buckling. They have some post-yield capacity, buckle plastically and their ultimate and critical loads are equivalent. Moderate plates have concurrent material yielding and geometrical buckling followed by a sudden loss of stiffness. They neither have post-yield nor postbuckling reserves. Since the proportional limit stress is observed to be the cause of bifurcation in stocky plates, it is suggested that in dealing with the slenderness parameter, the yield stress be replaced by the proportional limit stress. [Copyright &y& Elsevier]

Abstract: This paper discusses the use of the theory of elasticity to determine the post-buckling strength of uniformly loaded square simply supported thin (steel) plates with sinusoidal-shaped initial imperfections and longitudinal edges free to wave in plane. Based on the findings from a FEM parameter study two main types of failure are distinguished: edge failure and center failure. The parameters determining which failure mode occurs are explained using a simple two-strip model. To determine the elastic post-buckling behavior of plates a modified far post-buckling solution is proposed, which is simpler to use than the existing far post-buckling solutions reported in the literature, giving results with engineering accuracy for loads up to about three times the buckling load. It is shown that determining the post-buckling strength as the elastic load corresponding to first membrane yield (as is done in the effective width method) paradoxically gives reasonable results for plates failing by center failure, but very conservative results for plates failing by edge failure. For plates failing by edge failure a more accurate strength prediction is obtained by deriving empirical expressions for a fictitious elastic strain at failure. [Copyright &y& Elsevier]

Abstract: Equations for the elasto-plastic large deflection non-axisymmetric response of discretely stiffened circular plates are presented. Plastic strains within the plate and stiffener are modelled using the Ilyushin full-section and modified Von Mises yield criteria and the associated flow rule. The equations are discretised using finite differences for solution by the DR iterative procedure. The analysis is used to study the large deflection response of uniformly loaded plates stiffened by a diametral stiffener of rectangular cross-section. Dimensionless graphs of centre deflection, etc., versus pressure are presented for stocky and slender simply supported and clamped plates with shallow and deep stiffeners. [Copyright &y& Elsevier]

Abstract: When carrying out vibration health monitoring (VHM) of a structure it is usually assumed that the structure is in the absence of fluid interaction and that any environmental effects which can cause changes in natural frequency either remain constant or are negligible. In certain cases, this condition cannot be assumed and therefore it is necessary to extract values of natural frequencies of the structure for the condition with no fluid interaction from those values measured. This paper considers the case of a thin circular plate in contact with a fluid cavity giving rise to strong structural/fluid vibration interaction. The paper details the free vibration analysis of the coupled system and through consideration of modal energy, illustrates how the affined modes of vibration of the plate and the fluid can be qualitatively described. The paper then introduces a method by which the natural frequencies of the plate in the absence of fluid interaction can be obtained from those of the plate in interaction with the fluid. [Copyright &y& Elsevier]

Abstract: This work is related to the bending problem of thick rectangular Levy plates. Series solution for the Mindlin (thick) plate model is obtained and represented as a sum of the Kirchhoff (thin) plate model solution, the “shear terms” and the “boundary layer terms”. Hard- and soft-simple supported, hard- and soft-clamped and free boundary conditions are considered. In order to detect plate regions where Kirchhoff model is good enough, and plate regions where Mindlin model should be used, a model error indicator is introduced. Several examples are presented, illustrating the difference between the Mindlin and the Kirchhoff results, the strengths of boundary layers for different boundary conditions, accuracy of several possible model error indicators and dependence of results on plate thickness. [Copyright &y& Elsevier]

Abstract: Some aspects of buckling behaviour of structural elements made of nonlinear materials with strain hardening, for which the stress–strain law has no yield plateau (stainless steels, aluminium alloys and others) are discussed. Considering compressed bars and plates made of materials with linear and nonlinear strain hardening, on the basis of tangent modulus theory and the deformation theory, we show that there exists a “threshold” value of the hardening factor below which the hardening does not influence the limit load. But if the hardening factor exceeds the threshold value then the hardening significantly increases the limit load and this increasing is not properly accounted for in some worldwide design codes. [Copyright &y& Elsevier]

Abstract: This paper shows that a simple two-strip model can be used to describe the post-buckling behaviour of simply supported rectangular plates subjected to uni- and biaxial compression, provided the ratio of the post-buckling to pre-buckling stiffness of the perfectly flat plate is known. The formulas for this two-strip model are derived in two ways: by using a force method, and by using an energy method. The two-strip model is compared to other available solutions in literature and it is shown that the model can be regarded as a modification of the lower bound plate analysis method. [Copyright &y& Elsevier]

Abstract: A solution for the elastic buckling of flat rectangular plates with centerline boundary conditions subjected to non-uniform in-plane axial compression is presented. The loaded edges are simply supported, the non-loaded edges are free, and the centerline is simply supported with a variable rotational stiffness. The Galerkin method is used to establish an eigenvalue problem and a series solution for plate buckling coefficients is obtained by using combined trigonometric and polynomial functions that satisfy the boundary conditions. It is demonstrated that the formulation approaches the classical solution of a plate with a clamped edge as the variable rotational stiffness is increased. The variation of buckling coefficient with aspect ratio is presented for various stress gradient ratios. The coupling between plate aspect ratio, centerline rotational stiffness, and gradient of applied compressive stress is illustrated and discussed. The solution is applicable to stiffened plates and I-shaped beams that are subjected to biaxial bending or combined flexure and torsion, and is important to estimate the reduction in elastic buckling capacity due to stress gradient. [Copyright &y& Elsevier]

Abstract: A differential quadrature (DQ) procedure is developed for free vibration analysis of variable thickness moderately thick plates with edges elastically restrained against translation and rotation. The governing equations are based on the first order shear deformation theory and the rotary inertia effects are considered. Comparisons with known thin plate and uniform thickness Mindlin plate solutions are carried out to verify the applicability and accuracy of the analysis. Plates with linear or nonlinear varying thickness in one or two directions can be considered. It is demonstrated that using this DQ procedure, classical boundary conditions such as simply supported, clamped and free edges for variable thickness, thin as well as moderately thick plates can be simulated without any numerical difficulties. The effects of different combinations of constraints at edges, aspect ratio, thickness-to-length ratio, and stiffness parameter values on accuracy and convergence behaviors of the plates are presented. Some new results are presented for bi-linearly variable thickness plates with elastically restrained edges. [Copyright &y& Elsevier]

Abstract: The mechanics of the compressional behaviour of stub columns fabricated from Grade 350 steel plates welded to very high strength (VHS) circular tubes are investigated in this paper. In the investigations comparisons of experimental load-axial shortening curves are made with the results of a postulated design analysis set up to examine the complete load-shortening behaviour of such members. Ramberg-Osgood type stress–strain equations are set up for the plate and tube materials. A procedure is described to evaluate the loads in individual plate and tube elements as the axial shortening is increased until the 0.2% proof strain for the VHS tube material is attained. Upon reaching this strain it is assumed that failure ensues as the result of a simple plastic mechanism occurring in the tubes. Comparisons of the load-axial shortening curves given by this analysis and experimental results indicate good agreement. [Copyright &y& Elsevier]

The finite difference method was used to solve differential equations of motion of free vibration of composite plates with different boundary conditions. The effects of shear deformation and rotary inertia on the natural frequencies of laminated composite plates are investigated in this paper. Four cases are studied: neglecting both shear deformation and rotary inertia, considering only rotary inertia, considering only shear deformation, and considering both. Solutions were obtained for symmetric and angle-ply laminated plates. The factors that affect natural frequencies of different composite plates, such as span-to-depth ratio, aspect ratio, angle-ply, and lamination sequence were also investigated. Results were found to agree well with exact and approximate solutions reported in literature. Shear deformation showed a considerable effect on the natural frequencies for composite plates, whereas the rotary inertia effect was found to be negligible. [Copyright &y& Elsevier]

This paper deals with the structural shape optimization of prismatic folded plates under buckling load consideration. Buckling loads are determined using linear, quadratic and cubic, variable thickness, C(0) continuity, Mindlin-Reissner finite strips. The whole structural optimization process is carried out by integrating finite strip analysis, cubic spline shape and thickness definition, semi analytical sensitivity analysis and mathematical programming algorithm. The objective is either the maximization of the critical buckling load or minimization of the cross-section of the prismatic folded plate with constraints on the volume and buckling loads. Several examples are included to illustrate various features of the optimization algorithm, including plates and stiffened panels. [Copyright &y& Elsevier]

A brief examination of some of the research on the post-buckling analysis of plates and plate structures is outlined. Only a very superficial examination has been carried out. The behaviour of plates and sections under eccentric load or eccentric compression is considered, and the application of plate analysis to strut, beam and column design is discussed. [Copyright &y& Elsevier]

In this paper a simple method of deriving lower bound limit loads for thin plates is presented. This method is based on the method of elastic compensation, an iterative elastic technique, which has recently been extended to allow the analysis of structures using thin shell finite element analysis using generalised yield criteria. Here the method is modified to allow analysis of plates, including the effects of transverse shear. The elastic compensation method, combined with generalised yield criteria, is implemented using the finite element numerical analysis technique. Convergence studies are carried out and limit loads are obtained for a range of geometries, boundary conditions and loading. The calculated limit loads are compared with results available in the literature and with new elasto-plastic results and show that the method can be used to quickly obtain practical results. [Copyright &y& Elsevier]

A brief examination of some of the research on the post-buckling elastic and plastic behaviour of plates and plate structures is outlined. This field is so wide ranging that only a very superficial examination of the early research has been carried out, and the writer has concentrated on some specific aspects of the general field of study. A very limited examination of some of the early research on rectangular cross-section tubes is also given. [Copyright &y& Elsevier]

This research investigates a concept for cut-out resonators that exploit a small area of active mass of a host plate structure for sake of tuned, low frequency vibration attenuation. Integrated computational and experimental studies reveal that embedding the resonators at locations offering high bending moment gradient and arranging the central resonator beam along a nodal line of bending moment best excite the first resonator eigenmode for targeted vibration suppression. These results are independent of plate boundary conditions and do not require periodic resonators to achieve notable vibration suppression outcomes. These design concepts may guide the development of resonators for vibration absorption of plates with arbitrary boundary conditions. • Moment-coupled built-in resonators proposed. • Computational and experimental studies demonstrate working mechanisms. • Vibration attenuation of plates is functional regardless of plate boundaries. • Absorption mechanism does not require periodic resonator placement. [ABSTRACT FROM AUTHOR]

Polyurea has been used in armor applications for over a decade. Its ability to mitigate shock waves and survive after experiencing large deformations makes it suitable for structural protection purposes. One of the many uses of polyurea coatings is in maritime structures, in which polyurea is not only a mechanical armor but can also serve as chemical protector against corrosion due to its high resistance to environmentally aggressive conditions. To further implement such applications, one must understand the effect of polyurea coatings on the overall structural response to hydrodynamic shocks. An experimental investigation of high-pressure shock-loaded polyurea coated aluminum plates is presented. These experiments add to previous experiments that are described in detail in Rijensky and Rittel (2016) [1]. The present experiments reveal the effects of polyurea coating on the fluid structure interaction taking place between shocked water and aluminum plates. This interaction can be the result of numerous scenarios ranging from violent blasts in water to relatively milder loads like wave slamming. Emphasis is put on the selection of the coated side of the aluminum plate, considering those different interactions and their influence on the structure. The presented setup is also an interesting experimental physics case study as the deformation under shock process involves soft materials, fluid-structure interaction and conventional engineering materials deforming all together and affecting one another. Whereas weak shock mitigation was found to favor polyurea on the wet side of the plate, the present work reveals that for strong shocks, polyurea must now be applied on the dry side, thereby revealing a dependence of the optimal placement of the protective layer on the shock intensity. • An apparatus for creating strong hydrodynamic shock loads plates is presented. • Hydrodynamic bulge tests of polyurea-coated 6061 aluminum alloy plates were conducted. • Measurements were conducted using 3D DIC technique on images obtained via fast photography. • PU coating side for protection against hydrodynamic shocks should be determined by the strength of the anticipated threat. [ABSTRACT FROM AUTHOR]