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The application of Topology Optimisation (TO) to help in the manufacture of metallic components in highly technological industries has increased recently. To equally benefit from TO, the construction industry must address its specific issues, such as adherence to code requirements and challenges in using cutting-edge software packages in complex joints with non-linear behaviour. To assist in such a challenge, the current study offers a methodology proposal to synthesise code and structural behaviour requirements into geometrical constraints for the optimisation problem of laminar steel parts under compression while integrating Non-linear Finite Element Analyses (NLFEA) that ensure the safety of the solution. It has been found that, for a real case-study, the initial volume of a connection's cover-plate can be decreased by up to 40% while maintaining the connection's original capacity and that a 30% volume decrease may be achieved while keeping the original plate capacity. In both cases, the plate's ultimate deformation capacity was enhanced. Evidence has been found that Linear Elastic TO may not provide safe-sided solutions for parts with an intrinsic non-linear behaviour. With the attained volume reductions, less raw materials may be consumed, assembly and transportation will be facilitated, and the goals of the sector's decarbonisation, energy intensity and sustainability will be favoured. [ABSTRACT FROM AUTHOR]

This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams. The analyses include three models for porosity distribution and two scenarios for thermal distribution. The material properties are assessed under two conditions, i.e., temperature dependence and temperature independence. The theoretical framework for the beams is based on the higher-order shear deformation theory, which incorporates shear deformations with higher-order polynomials. The governing equations are established from the Lagrange equations, and the beam displacement fields are approximated by the Chebyshev polynomials. Numerical simulations are performed to evaluate the effects of thermal load, slenderness, boundary condition (BC), and porosity distribution on the buckling and vibration behaviors of metal foam beams. The findings highlight the significant influence of temperature-dependent (TD) material properties on metal foam beams' buckling and vibration responses. [ABSTRACT FROM AUTHOR]

The stability of axially functionally graded (AFG) heavy columns was analyzed. Consideration in stability analysis of the column is given to the free vibration and bucking problems. The mass density and Young's modulus of the AFG heavy column vary along the column axis through a power-law function. Unified modeling of the differential equations with the associated boundary conditions governing the deformed shape of the free vibrations and buckling of the column was developed. Using a combination of direct numerical integration method and numerical solution method of nonlinear equation, differential equations were solved to calculate the natural frequency and the critical buckling load. Calculation results for the natural frequency and buckling load compare well with the FEM results. As a result of numerical experiments, the effects of material and geometric properties on the natural frequency and the buckling load were reported and discussed in detail. [ABSTRACT FROM AUTHOR]

This paper investigates the instability and buckling characteristics of a porous microplate under the influence of electrostatic fields, taking into account the implications of the intermolecular Casimir forces. Employing the modified couple stress theory, this research formulates equations that encapsulate the interplay between electrostatic and Casimir forces within porous plates. The analysis integrates distributed support loads, employing both Galerkin mode summation and finite element methods to solve static deformation equations and determine pull-in instability voltages and buckling loads. A novel approach is introduced, and equilibrium relationships are derived with respect to displacement to determine both the buckling load and instability voltage. This study effectively compares classical and non-classical theories, scrutinizing the effects of dimensionless length scale parameters and porosity ratios on maximum displacement, pull-in instability voltages, and buckling loads. The results demonstrate that the analytical method converges swiftly and aligns with the findings of the finite element method. The method for deriving equilibrium relationships proves to be accurate in predicting both instability voltage and buckling load. Additionally, the instability voltage exhibits an almost linear relationship with variations in the percentage of porosity, and similarly, the buckling load undergoes linear changes with alterations in porosity percentage. Hence, formulas for the linear relationships are calculated for both of these associations. [ABSTRACT FROM AUTHOR]

This paper presents the analytical process of porous functionally graded graphene-reinforced truncated conical shells subjected to hydrostatic pressure and axial tension. Three types of graphene platelet (GPL) dispersion and three patterns of porous distribution were considered. A modified model, in which the volume fraction of the pores is regarded as the essential parameter, was built to evaluate the material properties. The static stability equations of the shells, coupled with the effect of the combined forces, were derived. The Galerkin integrate technique was employed to obtain the critical buckling hydrostatic pressure and axial tension. After the present method was validated, the influences of pores, GPLs, and shell geometrical characteristics were investigated in the parametric studies. The results show that the critical hydrostatic pressure and axial tension can be elevated by increasing the porous coefficient, semi-vertex, and length–thickness ratio. On the contrary, the critical pressure and tension are decreased with the rise of GPL mass fraction. [ABSTRACT FROM AUTHOR]

A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication. The expression of the geometric stiffness matrix is derived, the finite element linear buckling analysis is conducted, and the sensitivity solution of the linear buckling factor is achieved. For a specific problem in linear buckling topology optimization, a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells. The aggregation function method is used to consider the high-order eigenvalues, so as to obtain continuous sensitivity information and refined structural design. With cyclic matrix programming, a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted. To maximize the buckling load, under the constraint of the given buckling load, two types of topological optimization columns are constructed. The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm. The vertex method and the matching point method are used to carry out an uncertainty propagation analysis, and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance. Finally, the differences in the structural topology optimization under different reliability degrees are illustrated by examples. [ABSTRACT FROM AUTHOR]

In the current research, we delve into the intricate realm of bifurcation analysis for Föppl–von Kármán plates, employing a precise numerical tool. This innovative numerical approach melds the power of spectral discretization with the prowess of a high-order continuation method-based Taylor series development (HODC). It is worth noting that combining the high-order continuation method with such discretization techniques offers an efficient path-following approach, complete with adaptive step lengths, capable of tackling a wide array of nonlinear problems. Despite the extensive applications of nonlinear elasticity, the spectral method remains relatively uncharted territory within this context. However, our deep-rooted understanding and expertise in the field drive us to embrace this method alongside high-order development continuation for bifurcation analysis of Föppl–von Kármán plates. The governing equations governing thin elastic plates experiencing significant elastic deflections manifest as a pair of coupled nonlinear differential equations, famously known as the von Kármán (vK) equations, presented in a strong form with two principal unknowns: deflection (w) and the Airy stress function (F). Leveraging Chebyshev decomposition matrices, we approximate these fourth-order elliptic nonlinear partial differential equations. Subsequently, we harness high-order development continuation techniques to morph these nonlinear systems into linear ones. Our rigorous evaluation and validation of this numerical approach's precision and performance come to fruition through a comprehensive buckling analysis encompassing multiple illustrative examples. [ABSTRACT FROM AUTHOR]

Interest in components with detailed structures increased with the progress in advanced manufacturing techniques. Parts with lattice elements can provide improved global buckling stability compared to solid structures of the same weight. However, thin features are prone to local buckling. We present a two-scale optimization approach that simultaneously improves the local and global stability of parametrized graded lattice structures. Elastic properties and local buckling behavior are upscaled via homogenization based on geometric exact beam theory. To reduce computational effort, we construct a worst-case model for the homogenized buckling load factor, which acts as a safeguard against local buckling. We briefly discuss advantages and limitations by means of numerical examples. [ABSTRACT FROM AUTHOR]

Based on the shell and plate theory, this paper uses the divide-and-combine method (DCM) to derive an analytical out-of-plane compression buckling limit expression of the basic unit of the core layer of a grid beetle elytron plate (GBEP); the accuracy of expression and the mechanism of GBEP unit buckling are investigated through experiments and finite element (FE) simulation. The results show that: (1) the theoretical expression of the out-of-plane compression buckling limit of a GBEP unit obtained by DCM is applicable and is closer to the test results than the classical solution of the out-of-plane compressive buckling of a cylindrical shell and the theoretical result of Flügge. Based on this, a modified expression of the theoretical result of Flügge's compressive buckling limit load is proposed. (2) Given the significant differences between the theoretical values obtained in this paper and the experimental values, the out-of-plane compressive buckling resistance of the GBEP unit and its mechanism are investigated from the viewpoints of structural parameters η (the ratio of the radius of the trabeculae to the width of the element) and deformation process; the synergistic mechanism of the honeycomb-trabeculae structure is also studied. This paper contributes to improving the bionic system derived from the beetle's forewing. [ABSTRACT FROM AUTHOR]

Recent advancements in additive manufacturing (AM) have opened new possibilities for fabricating highly complex lattice structures with enhanced mechanical properties, particularly hybrid and functional gradient structures. Most of the conducted research focused on linear/longitudinal designs for both hybrid and functional gradient structures. This study focuses on designing and evaluating novel functionally graded radially hybridized structures, combining different unit cells from beam-based and surface-based structures. The research introduces a cylindrical/radial hybridization approach, incorporating three distinct unit cells: body-centered cubic (BCC), face-centered cubic (FCC), and octet from beam-based structures, and diamond, gyroid, and split-p from surface-based structures. Polylactic acid (PLA) was selected as the material, and fused filament fabrication (FFF) was employed for fabrication. Quasi-static compression tests were conducted to assess the influence of hybridization and functional gradience on compressive modulus, ultimate strength, specific energy absorption, and failure properties. Both experimental and numerical results demonstrated that functionally graded lattice structures, whether surface-based or beam-based, exhibited improved mechanical performance. The surface-based functionally graded lattice structures showed the highest compressive modulus (71%), ultimate strength (36%), and specific energy absorption (19%). On the other hand, the beam-based functionally graded structures displayed a higher compressive modulus (50%), ultimate strength (11%), and specific energy absorption (19%). However, it should be noted that the beam-based functionally graded structures exhibited a decrease in these properties due to factors such as unit cell size, volume fraction, and structural buckling. Overall, the findings highlight the superior mechanical properties of functionally graded lattice structures compared to hybrid lattice structures. [ABSTRACT FROM AUTHOR]

The mechanical properties of soft tissues are driven by their complex, heterogeneous composition and structure. Interestingly, studies of soft tissue biomechanics often ignore spatial heterogeneity. In our work, we are therefore interested in exploring the impact of tissue heterogeneity on the mechanical properties of soft tissues. Therein, we specifically focus on soft tissue heterogeneity arising from spatially varying thickness. To this end, our first goal is to develop a non-destructive measurement technique that has a high spatial resolution, provides continuous thickness maps, and is fast. Our secondary goal is to demonstrate that including spatial variation in thickness is important to the accuracy of biomechanical analyses. To this end, we use mitral valve leaflet tissue as our model system. To attain our first goal, we identify a soft tissue-specific contrast protocol that enables thickness measurements using a Keyence profilometer. We also show that this protocol does not affect our tissues' mechanical properties. To attain our second goal, we conduct virtual biaxial, bending, and buckling tests on our model tissue both ignoring and considering spatial variation in thickness. Thereby, we show that the assumption of average, homogeneous thickness distributions significantly alters the results of biomechanical analyses when compared to including true, spatially varying thickness distributions. In conclusion, our work provides a novel measurement technique that can capture continuous thickness maps non-invasively, at high resolution, and in a short time. Our work also demonstrates the importance of including heterogeneous thickness in biomechanical analyses of soft tissues. [ABSTRACT FROM AUTHOR]

Steel circular hollow section (CHS) bridge piers have been widely used in the engineering practices. However, end corrosion is one of the most common damages to steel bridge piers, leading to degradation of seismic performance and changing of failure modes. This paper investigates the seismic performance of the chloride corroded steel CHS bridge piers and proposes a method to predict its lateral ultimate strength under the transverse cyclic loads. Firstly, the multi-scale finite element (FE) models of the CHS steel bridge pier are developed considering both the local buckling and the end corrosion, which are calibrated against the previous test results. Subsequently, the effects of the characteristic parameters (i.e., the corrosion conditions and the column parameters) on the failure modes and the horizontal ultimate strengths of the corroded steel CHS bridge piers are investigated, and then the sensitivity of the parameters is quantified using the Sobol method. Finally, a method is presented for estimating the ultimate strength of the end corroded steel CHS bridge piers under the horizontal cyclic loads. Results show that the end corroded bridge piers exhibit more significant stress concentration when comparing with the uncorroded bridge piers. The buckling half-wavelength is influenced by corrosion parameters, and the buckling position changes. The ultimate strengths of end corroded bridge piers are reduced, which is more sensitive to the corrosion rate. The proposed theoretical method to predict the ultimate strengths of corroded steel CHS bridge piers is accurate enough with errors less than 10%. [ABSTRACT FROM AUTHOR]

During seismic events, cyclic demands exceeding the elastic limit load and buckling of steel reinforcing bars significantly impact the global response of thin and lightly reinforced concrete (TLRCW) wall buildings. This study evaluates the cyclic response of low-diameter steel reinforcing bars commonly used in thin RC walls. The experimental program of the study comprises the characterization and reversed cyclic tests of 60 specimens obtained from steel reinforcing bars grade 60 (420 MPa) with nominal diameters of 9.5 and 12.7 mm. An increasing, symmetrical strain protocol was used during the cyclic tests. The study analyses the stress–strain curves obtained in the cyclic tests of steel reinforcing bars and assesses the effect of parameters such as the slenderness ratio, bar diameter, and yield stress on the cyclic response of bars. The onset of buckling and its effects on the cyclic response of steel reinforcing bars, such as pinching and stress reduction in compression are also examined. The degradation of the mechanical properties of steel reinforcing bars obtained during cyclic tests was evaluated and compared to that obtained during monotonic tests. The study shows that low-diameter steel rebars under cyclic loading exhibit lower ductility and premature hardening in tension when compared to bars subjected to monotonic loading. Finally, fundamental properties of low-diameter steel reinforcing bars subjected to cyclic loads were established, such as ductility and hardening capacity. These properties will contribute to enhancing the understanding of the seismic behavior of TLRCW buildings. [ABSTRACT FROM AUTHOR]

This paper proposes a three-dimensional (3D) Maltese cross metamaterial with negative Poisson's ratio (NPR) and negative thermal expansion (NTE) adopted as the core layers in sandwich plates, and aims to explore the relations between the mechanical responses of sandwich composites and the NPR or NTE of the metamaterial. First, the NPR and NTE of the metamaterial are derived analytically based on energy conservation. The effective elastic modulus and mass density of the 3D metamaterial are obtained and validated by the finite element method (FEM). Subsequently, the general governing equation of the 3D sandwich plate under thermal environments is established based on Hamilton's principle with the consideration of the von Kármán nonlinearity. The differential quadrature (DQ) FEM (DQFEM) is utilized to obtain the numerical solutions. It is shown that NPR and NTE can enhance the global stiffness of sandwich structures. The geometric parameters of the Maltese cross metamaterial significantly affect the responses of the thermal stress, natural frequency, and critical buckling load. [ABSTRACT FROM AUTHOR]

The paper aims to develop a unified modeling to analyze the free vibrations and buckling of laterally functionally graded material columns. The columns of rectangular cross-section, in which the mass density and Young's modulus vary along the depth as a power-law function, were considered. The differential equation governing a mode shape of a deformed column was derived with the relevant boundary conditions, including the effect of rotatory inertia. The computation results for the natural frequencies and buckling load were compared well with those available in the open scientific literature. The effects of geometrical and material properties on natural frequencies and buckling loads with the mode shapes are highlighted. [ABSTRACT FROM AUTHOR]

The stability behaviour of unsymmetrical laminated structures made of fibre-reinforced plastics is significantly influenced by bending–extension coupling and the comparatively low transverse shear stiffnesses. The aim of this work is to improve the analytical stability analysis of unsymmetrically laminated structures. With the discrete plate theory, the stability of laminated structures can be reduced to single laminated plates. The structure is divided into individual segments, and the surrounding structure is modelled by rotational elastic restraints. The governing equations for single plates under specific boundary conditions can be solved exactly with Lévy-type solutions. In this study, Lévy-type solutions for the mentioned boundary conditions under biaxial compressive load is described for the classical laminated plate theory, the first-order shear deformation theory and the third-order shear deformation theory (TSDT). In addition to transverse shear, bending–extension couplings of unsymmetrical cross-ply and antisymmetrical angle-ply laminates are considered. For the implementation of boundary conditions for the rotational restraints in the context of TSDT, a new set of conditions is formulated. The investigation shows very good agreement of the buckling load with comparative finite element analyses for different layups. [ABSTRACT FROM AUTHOR]

Interest in components with detailed structures increased with the progress in advanced manufacturing techniques in recent years. Parts with graded lattice elements can provide interesting mechanical, thermal, and acoustic properties compared to parts where only coarse features are included. One of these improvements is better global buckling resistance of the component. However, thin features are prone to local buckling. Normally, analyses with high-computational effort are conducted on high-resolution finite element meshes to optimize parts with good global and local stability. Until recently, works focused only on either global or local buckling behavior. We use two-scale optimization based on asymptotic homogenization of elastic properties and local buckling behavior to reduce the effort of full-scale analyses. For this, we present an approach for concurrent local and global buckling optimization of parameterized graded lattice structures. It is based on a worst-case model for the homogenized buckling load factor, which acts as a safeguard against pure local buckling. Cross-modes residing on both scales are not detected. We support our theory with numerical examples and validations on dehomogenized designs, which show the capabilities of our method, and discuss the advantages and limitations of the worst-case model. [ABSTRACT FROM AUTHOR]

Background: The modelling of the sheet metal forming operations requires accurate and precise data of the material plastic behaviour along non-proportional strain paths. However, the buckling phenomenon severely limits the compressive strain range that could be used to deform thin metal sheets. Objective: The main aim of this paper was to propose an effective device, that enables to determine of accurate stress-strain characteristics of thin metal sheet specimens subjected to axial deformation without buckling and with a special emphasis on friction correction. Methods: In this paper, an anti-buckling fixture was proposed to assess the deformation characteristics of X10CrMoVNb9-1 (P91) power engineering steel, and DP500 and DP980 dual-phase steels, under compression loading. The fixture enables monitoring of the friction between the specimen and supporting blocks during the test, and thus the precise stress response of the material could be determined. Results: The effectiveness of the fixture was evaluated under tension–compression cyclic loading and during the compression tests in which high-strength thin metal sheets were successfully deformed up to 10% without specimen buckling. Furthermore, the successful determination of a friction force variation between supporting blocks and the specimen during tests enabled to determine an actual force acting on the specimen. Conclusions: The proposed testing fixture was successfully assessed during the compression and cyclic tension–compression of high-strength thin metal sheets as no buckling was observed. Its advantage lies in adapting to change its length with specimen elongation or shrinkage during a test. The friction force generated from a movement of both parts of the device could be effectively monitored by the special strain gauge system during testing and thus its impact on the stress-strain characteristics could be successfully eliminated. [ABSTRACT FROM AUTHOR]

Context: The discovery of graphene gave way to the search for new two-dimensional structures. In this regard, octa-graphene is a carbon allotrope consisting of 4- and 8-membered rings in a single planar sheet, drawing the research community's attention to study their inorganic analogs. Considering the promising properties of octa-graphene-like structures and the role of GaAs and GaP in semiconductor physics, this study aims to propose, for the first time, two novel inorganics buckled nanosheets based on the octa-graphene structure, the octa-GaAs and octa-GaP. This work investigated the structural, electronic, and vibrational properties of these novel octa-graphene-based materials. The octa-GaP and octa-GaAs have an indirect band gap transition with a valence band maximum between M and Г points and a conduction band minimum at Г point with energy of 3.05 eV and 2.56 eV, respectively. The QTAIMC analysis indicates that both structures have incipient covalent in their bonds. The vibrational analysis demonstrates the occurrence of ΓRaman = 6Ag + 6Bg and ΓRaman = 12A′ + 12B″ for octa-GaP and octa-GaAs, respectively. The symmetry reduction of octa-GaAs leads to activating inactive modes observed in the octa-GaP structure. The frontier crystalline orbitals are composed by Ga(px) and P(py and pz) orbitals for octa-GaP and Ga(px and py) and As(s, py, and pz) for octa-GaAs in the valence bands while in the conduction bands by Ga(py, pz, and s) for both compounds and P(px and pz) and As(py). The phonon bands demonstrate the absence of the negative frequency modes and the structural stability of these new nanosheets. This report aims to reveal the fundamental properties of both newfound materials for stimulating experimental research groups in the search for synthesis routes to obtain this structure. Methods: This work used the DFT/B3LYP approach implemented in the CRYSTAL17 computational package. Ga, As, and P atomic centers were described by triple-zeta valence with polarization (TZVP) basis set. The vibrational analysis was carried out via coupled-perturbed Hartree–Fock/Kohn Sham (CPHF/KS) method, and the chemical bonds were evaluated via the quantum theory of atoms in molecules and crystals (QTAIMC). [ABSTRACT FROM AUTHOR]

A hot stamping process of quenchable steel tubes using a mandrel reinforced with eco-friendly fibers was developed to produce ultra-high strength steel hollow parts having enhanced lightweighting and crashworthiness. High internal pressure was generated to improve the die quenchability and shape accuracy of the formed parts by the fiber reinforcement. Wood sawdust, shredded copy paper, and plant fiber made of recycled toilet paper were chosen as the fibers, and not only the strength was evaluated from a uniaxial compression test but also the melting behavior of the mandrel was examined. The influence of the fiber reinforcement on the shape accuracy and die quenchability of hot-stamped parts was investigated. The generated internal pressure with the fiber-reinforced ice mandrel was higher than that with the pure ice mandrel without the reinforcement, and thus, the shape accuracy and die quenchability of hot-stamped parts were significantly improved even for a comparatively small change in internal volume of tubes. [ABSTRACT FROM AUTHOR]

This paper studies the snap-back of the buckled triangular structure, which consists of three clamped-clamped elasticas. Here the rotation control is applied at one vertex, where the slopes of two clamped-clamped elasticas at the vertex are controlled. The deformation of the buckled triangular structure is obtained by the stiffness-curvature curves of three clamped-clamped elasticas. In this way, the relation between the external moment and rotation at the vertex of the buckled triangular structure is obtained. The critical points where snap-back occurs under rotation control are identified with three branches of the moment-rotation curve, including two saddle-node bifurcation points and two boundary points. Removing the external moment after the snap-back, the buckled triangular shape is still symmetrical, but the symmetry axis after the snap-back changes. In addition, the chiral shape is found to be unstable based on the moment-rotation curve, but the chiral shape can possibly become stable when more constraints exist such as in the cellular structure. The study in this paper can provide insight into the snap-back of the elasticas with several constraints. [ABSTRACT FROM AUTHOR]

In this study, an analytical solution based on the first-order shear deformation theory was performed for free vibration and buckling analysis of functionally graded porous beams (FGM-P) subjected to various boundary conditions. Also, this problem is solved by using finite element (FEM) and artificial neural network (ANN) methods. Here a Ritz-based analytical solution is used, and different polynomial series functions are proposed for each boundary condition. Lagrange's principle was used while deriving the equations of motion. A power-law rule describes the variation of the beam's materials in volume. The normalized fundamental frequencies and critical buckling loads are obtained for various boundary conditions, power-law index (k), slenderness (L/h), porosity coefficient (e), and porosity distribution (FGM-P1, FGM-P2). The polynomial series functions used in this study were verified with the literature, and the numerical results obtained were compared with FEM and ANN. The results obtained are quite compatible with each other. [ABSTRACT FROM AUTHOR]

It is known that the famous theoretical formula by Koiter for the critical buckling load of circular cylindrical shells under axial compression does not coincide with the experimental data. Namely, while Koiter’s formula predicts linear dependence of the buckling load λ (h) of the shell thickness h ( h > 0 is a small parameter), one observes the dependence λ (h) ∼ h 3 / 2 in experiments; i.e., the shell buckles at much smaller loads for small thickness. This theoretical prediction failure is believed to be caused by the so-called sensitivity to imperfections phenomenon (both, shape and load). Grabovsky and the first author have rigorously proven in (J Nonlinear Sci 26(1):83–119, 2016) , that in the problem of circular cylindrical shells buckling under axial compression, a small load twist leads to the buckling load scaling λ (h) ∼ h 5 / 4 , while shape imperfections are likely to result in the scaling λ (h) ∼ h 3 / 2. In this work, we prove that in fact the buckling load λ (h) of cylindrical (not necessarily circular) shells under vertical compression depends on the curvature of the cross section curve. When the cross section is a convex curve with uniformly positive curvature, then λ (h) ∼ h , and when the cross-sectional curve has positive curvature except at finitely many points, then C 1 h 8 / 5 ≤ λ (h) ≤ C 2 h 3 / 2 for h small thickness h > 0. [ABSTRACT FROM AUTHOR]

This paper presents a hyperbolic shear deformation theory and discusses its application to investigate the bending and buckling behavior of functionally graded carbon nanotubes-reinforced composite (FG-CNTRC) beams. The proposed theory satisfies the parabolic variation of shear stress distribution throughout the thickness and fulfills the zero condition of shear stress on the upper and bottom surfaces of the FG-CNTRC beams. Therefore, there is no need to use any correction factor concerning conventional equivalent single-layer theories. Five different types of CNTs reinforcement distribution are considered for the analysis while assuming a power-law function variation of the material properties in the thickness direction. The governing equations are solved using a finite element method, where several new numerical results are presented to demonstrate the robustness and reliability of the proposed model. The compartive study shows that the proposed element model is: (a) accurate and comparable with the literature; (b) of a faster rate of convergence to the reference solution; (c) excellent in terms of numerical stability; (d) valid for both symmetric and non-symmetric FG-CNTRC beams. Results also show the validity of the proposed formulation for both thin and thick FG-CNTRC beams. In addition, the effect of various material and geometric parameters such as the CNTs volume fraction, distribution patterns of CNTs, boundary conditions, and the length-to-thickness ratio is investigated on the bending and buckling responses of FG-CNTRC beam structures. Several new referential results are also reported for the first time, which will serve as a benchmark for future studies in a similar direction. [ABSTRACT FROM AUTHOR]

In the present research, the optimum paths and orientations for curvilinear and straight fibers of variable-and constant-stiffness composite cylindrical shells subjected to an external hydrostatic pressure and bending were found. For this purpose, a linear variation in the fiber orientation was considered for the curvilinear fibers. A genetic algorithm program written in the Python language was developed and linked to the ABAQUS finite-element code and used in an optimization process. The optimization was performed for several aspect ratios of the length-to-diameter of composite cylindrical shells. The buckling pressure of the variable-stiffness composite cylindrical shell increased by about 30℅ in comparison with that of the constant-stiffness composite cylindrical shell under an external hydrostatic pressure. The gaps and overlaps were modeled using a Pythonbased program and the ABAQUS software to investigate their effects on the buckling load of variable-stiffness cylindrical shells under external pressure loads. [ABSTRACT FROM AUTHOR]

Typically, the columns of the prefabricated reinforced concrete (RC) industrial buildings and warehouses with large clear storey heights are very slender, with aspect ratios (shear span to width) larger than 10. In addition to supporting the gravity loads, the columns also provide strength, stiffness, dissipation and displacement capacity of the primary lateral-load resisting system. However, current empirical relationships that predict the non-linear response and failure mechanisms of RC columns have been developed mainly for lower aspect ratios (< 7), typical of ordinary multi-storey buildings or short-to-medium bridge piers. What makes slender columns different is their predominant flexural response, larger drifts at nominal strength and corresponding lower ductility demands, smaller ratios between the strain penetration and plastic hinge lengths to the element shear span and risk of P-Delta instability. Therefore, the direct application of analytical models available in the literature to slender columns poses a risk of overestimation of their deformation and dissipative capacity. In turns this could lead to the underestimation of their displacement demand, overall damage and collapse probability of the primary seismic-resisting and load-bearing system. In the present research extensive analysis on the non-linear response of slender columns was performed based on observed post-earthquake damage to buildings in Italy and Turkey, experimental data and numerical predictions of the failure patterns through non-linear fiber element models. The influence of the foundation flexibility and the presence of industrial floor was also investigated. The outcome is a simplified analytical methodology for the prediction of the non-linear force–deformation response and possible failure mechanisms of slender precast columns due to rebar buckling or P-Delta effects, as a fundamental step towards the seismic assessment of the global structural performance and cost-efficient retrofit solutions for precast concrete industrial buildings. [ABSTRACT FROM AUTHOR]

For several years, kites have been representing an innovative technology in the maritime sector to reduce the fuel consumption through an auxiliary propulsion or producing energy onboard. Regarding the continuous increase in kite sizes, one of the main objectives is to determine whether a leading-edge inflatable kite and its components will be able to withstand the pressure field induced by the aerodynamic load. Therefore, an accurate identification of stress fields in them is required by designers. For this aim, a fluid-structure interaction method was developed by coupling a 3D nonlinear lifting-line model with the Abaqus™ 2017 finite-element software tools. Within this framework, a structural analysis was performed for a kite made of a woven fabric by employing the thin-layer finite-element technique for its weak bending properties. This modeling method is new and is not available in the Abaqus™. [ABSTRACT FROM AUTHOR]

An approach based on the computational search for the extrapolated upper boundary of the core and accounting for the axial asymmetry of the assembly that models a high-temperature gas-cooled reactor with an annular core is considered, and its applicability for the development of 3D calculation models of the ASTRA critical facility is justified. Owing to the presence of the lower reflector and absence of the upper one, 2D models based on experimentally determined buckling cannot be used; therefore, an alternative approach based on the use of the extrapolated assembly height is suggested. The use of this method is shown by the example of the computational analysis of the experiments for measuring the efficiency of the control and protection system unit is presented. [ABSTRACT FROM AUTHOR]

Peridynamics is a non-local continuum theory which accounts for long-range internal force/moment interactions. Peridynamic equations of motion are integro-differential equations, and only few analytical solutions to these equations are available. The aim of this paper is to formulate governing equations for buckling of beams and to derive analytical solutions for critical buckling loads based on the nonlinear peridynamic beam theory. For three types of boundary conditions, explicit expressions for the buckling loads are presented. The results are compared with the classical results for buckling loads. A very good agreement between the non-local and the classical theories is observed for the case of the small horizon sizes which shows the capability of the current approach. The results show that with an increase of the horizon size the critical buckling load slightly decreases for the fixed overall stiffness of the beam. [ABSTRACT FROM AUTHOR]

The nonlinear in-plane instability of functionally graded carbon nanotube reinforced composite (FG-CNTRC) shallow circular arches with rotational constraints subject to a uniform radial load in a thermal environment is investigated. Assuming arches with thickness-graded material properties, four different distribution patterns of carbon nanotubes (CNTs) are considered. The classical arch theory and Donnell's shallow shell theory assumptions are used to evaluate the arch displacement field, and the analytical solutions of buckling equilibrium equations and buckling loads are obtained by using the principle of virtual work. The critical geometric parameters are introduced to determine the criteria for buckling mode switching. Parametric studies are carried out to demonstrate the effects of temperature variations, material parameters, geometric parameters, and elastic constraints on the stability of the arch. It is found that increasing the volume fraction of CNTs and distributing CNTs away from the neutral axis significantly enhance the bending stiffness of the arch. In addition, the pretension and initial displacement caused by the temperature field have significant effects on the buckling behavior. [ABSTRACT FROM AUTHOR]

The nonlocal strain gradient and classical shell theories are used to derive the governing equations of functionally graded cylindrical nanopanels (open cylindrical shells). The properties of the nanopanel are graded as a power-law distribution through the thickness direction. The linearization stability equations are obtained using an adjacent equilibrium criterion. Governing equations are solved by Galerkin method to investigate the effects of the material length scale parameter, the nonlocal parameter, the geometric parameters, and the material properties on the buckling behavior of functionally graded cylindrical nanopanels. Numerical results are compared and discussed with available data. The solution of the closed cylindrical shell is recovered when the span angle is taken as 360 degrees. [ABSTRACT FROM AUTHOR]

Based on three-dimensional theory of elasticity, static bending, free vibration and buckling behaviors of functionally graded carbon nanotube-reinforced composite plates are investigated with the isogeometric analysis (IGA). The carbon nanotubes are supposed to be distributed uniformly and graded functionally along the plate thickness. The refined rule of mixtures is applied to predict the effective material properties. Based on the IGA, the displacement field of the plate is expressed by three-dimensional NURBS basis functions. The Hamilton's principle is used to obtain the formulations for the static bending, free vibration and buckling analysis. The convergence study is performed and the accuracy of the present approach is validated by comparing the numerical results with the published literature. In addition, the effects of CNTs volume fractions, CNTs distributions, geometrical parameters and boundary conditions on the static bending, free vibration and buckling analysis of the functionally graded carbon nanotube-reinforced composite plates are investigated. [ABSTRACT FROM AUTHOR]

The 3D nonaxisymmetric local stability loss problem is studied for a hollow cylinder, made of a viscoelastic composite material, under the axial compression. The criterion of an infinitesimal initial imperfection is employed, and the evolution of this imperfection is investigated by 3D geometrically nonlinear exact equations of viscoelasticity theory. The corresponding nonlinear problem is solved by the boundary perturbation method. The material of the cylinder is modeled as a viscoelastic transversely isotropic medium. Numerical results for the critical time and critical compressive forces are presented, discussed, and compared with those obtained by approximate shell theories. [ABSTRACT FROM AUTHOR]

The lattice structures use has increased in several sectors due to the potential for mass reduction without significant rigidity loss. In this paper, an isogrid tube multi-objective optimization considering six objectives is presented. The finite element method was applied to develop a numerical model for this complex structure, and a new optimization algorithm called the Multi-objective Lichtenberg Algorithm was used to find all the best possible designs. The optimizations were made considering two methodologies: (i) using a surrogate model derived from the design of experiments considering the response surface model and (ii) finite element updating, a direct link between the meta-heuristic and the numerical model. The latter is unprecedented in the literature for isogrid tubes and proved to be the best methodology, besides not even needing explicit equations. It discovered isogrid tube designs using TOPSIS that reduced at least 45.69% of the mass, 18.4% of the instability coefficient, 61.76% of the TW, and increased the natural frequency by at least 52.57%. The results show that optimizations via finite element updating associated with meta-heuristics not only allow the true interpretation of complex problems nature through real Pareto fronts, but can also deliver innovative results. [ABSTRACT FROM AUTHOR]

In this research, experimental and theoretical results for bending and buckling of a five-layer sandwich plate with composite face sheets reinforced by carbon nanotubes (CNTs), carbon nanorods, graphene platelets (GPLs), or nitinol shape memory alloy (SMA) wire and foam core are studied. The equations of equilibrium for this sandwich plate based on RFSDT and the principle of minimum total potential energy are derived, and then, the transverse displacement and buckling load are obtained. Using the rule of mixture and the Halpin–Tsai equation, the mechanical properties of the reinforced composite face sheets are calculated and also, and the constitutive equations of the SMA are presented according to the Brinson model. As well as, the influence of various parameters including thickness ratio, aspect ratio, the volume fraction of CNTs, GPLs, and nitinol SMA wire, fiber placement angle, and temperature changes are investigated on transverse deformation and dimensionless critical buckling load. Finally, tensile and buckling experimental tests were performed according to the standard tests ASTM D 3039 and ASTM C 364, respectively. [ABSTRACT FROM AUTHOR]

In this paper, the simple refined plate theory (S-RPT) is extended for the analysis of the bending and buckling behaviours of functionally graded graphene platelets reinforced composite (FG-GPLRC) plates supported by local elastic foundations under different boundaries. For the first time, an analytical method for determining the location of the local elastic foundation distribution by simple integration is extended to the analysis of the bending and buckling behaviour of plates. The method avoids complex calculations compared to previous methods for determining the position of the elastic foundation. Compared with other simplified plate theories, the displacement pattern of S-RPT is able to reflect the interrelationship between the gradient material properties and the displacement distribution along plate’s thickness. The material properties of FG-GPLRC plates are affected by temperature. Using the static equilibrium method, the plate equilibrium equations are derived by directly integrating the three-dimensional elastic equations along the plate cross section. Galerkin’s method is used to solve the governing equations. The accuracy of S-RPT under different boundary conditions and the accuracy of the analytical method for determining the location of the elastic foundation are verified by comparing the numerical results with the existing literature. Finally, the effects of different distribution patterns, weight fractions of GPLs, thickness ratios, aspect ratios, boundary conditions, temperature, elastic foundation distribution patterns, and elastic foundation parameters were investigated in detail. [ABSTRACT FROM AUTHOR]

A buckling model of Timoshenko micro-beam with local thickness defects is established based on a modified gradient elasticity. By introducing the local thickness defects function of the micro-beam, the variable coefficient differential equations of the buckling problem are obtained with the variational principle. Combining the eigensolution series of the complete micro-beam with the Galerkin method, we obtain the critical load and buckling modes of the micro-beam with defects. The results show that the depth and location of the defect are the main factors affecting the critical load, and the combined effect of boundary conditions and defects can significantly change the buckling mode of the micro-beam. The effect of defect location on buckling is related to the axial gradient of the rotation angle, and defects should be avoided at the maximum axial gradient of the rotation angle. The model and method are also applicable to the static deformation and vibration of the micro-beam. [ABSTRACT FROM AUTHOR]

Variable-angle filament-wound (VAFW) cylinders are herein optimized for minimum mass under manufacturing constraints, and for various design loads. A design parameterization based on a second-order polynomial variation of the tow winding angle along the axial direction of the cylinders is utilized to explore the nonlinear steering-thickness dependency in VAFW structures, whereby the thickness becomes a function of the filament steering angle. Particle swarm optimization coupled with three Kriging-based metamodels is used to find the optimum designs. A single-curvature Bogner–Fox–Schmit–Castro finite element is formulated to accurately and efficiently represent the variable stiffness properties of the shells, and verifications are performed using a general purpose plate element. Alongside the main optimization studies, a vast analysis of the design space is performed using the metamodels, showing a gap in the design space for the buckling strength that is confirmed by genetic algorithm optimizations. Extreme lightweight while buckling-resistant designs are reached, along with non-conventional optimum layouts thanks to the high degree of thickness build-up tailoring. [ABSTRACT FROM AUTHOR]

This paper presents a study on an ancient river-damming landslide in the SE Tibet Plateau, China, with a focus on time-dependent gravitational creep leading to slope failure associated with progressive fragmentation during motion. Field investigation shows that the landslide, with an estimated volume of 4.9 × 107 m3, is a translational toe buckling slide. Outcrops of landslide deposits, buckling, toe shear, residual landslide dam, and lacustrine sediments are distributed at the slope base. The landslide deposits formed a landslide dam over 60 m high and at one time blocked the Jinsha River. Optically stimulated luminescence dating for the lacustrine sediments indicates that the landslide occurred at least 2,600 years ago. To investigate the progressive evolution and failure behavior of the landslide, numerical simulations using the distinct element method are conducted. The results show that the evolution of the landslide could be divided into three stages: a time-dependent gravitational creep process, rapid failure, and granular flow deposition. It probably began as a long-term gravitationally induced buckling of amphibolite rock slabs along a weak interlayer composed of mica schist which was followed by progressive fragmentation during flow-like motion, evolving into a flow-like movement, which deposited sediments in the river valley. According to numerical modeling results, the rapid failure stage lasted 35 s from the onset of sudden failure to final deposition, with an estimated maximum movement rate of 26.8 m/s. The simulated topography is close to the post-landslide topography. Based on field investigation and numerical simulation, it can be found that the mica schist interlayer and bedding planes are responsible for the slope instability, while strong toe erosion caused by the Jinsha River caused the layered rock mass to buckle intensively. Rainfall or an earthquake cannot be ruled out as a potential trigger of the landslide, considering the climate condition and the seismic activity on centennial to millennial timescales in the study area. [ABSTRACT FROM AUTHOR]

One of the major drawbacks of material extrusion additive manufacturing (AM) is hot-end clogging. This study aims to answer the question, "How clogging happens and what thermal conditions lead to clogging during filament-based material extrusion?" Answering this question requires a clear understanding of temperature distribution inside the liquefier. However, this could not be achieved only through experimental measurements. Therefore, numerical simulations were also carried out by developing a 3D finite volume model of the hot-end. The results obtained from numerical simulations show good agreement with experimental measurements. They also give us a detailed picture of the temperature gradient near the nozzle. A series of experiments were performed to determine at what thermal conditions clogging occurs, and some criteria for avoiding clogging were presented. The temperature distribution of those thermal conditions that leads to clogging is then investigated numerically to analyze the clogging mechanism. As the results show, overheating the heat barrier increases the length of the filament, whose temperature is above the glass transition temperature. As this length exceeds a critical value, the filament buckles under the extruder motor force, and consequently clogging occurs. [ABSTRACT FROM AUTHOR]

We developed and obtained close-form solutions for the buckling growth rate of microtubule (MT) bundles using the Timoshenko beam theory. We took into consideration the surface effects and the Poisson's ratio of the microtubules surrounded by neighbouring filaments in the viscous cytosol. We developed the motion equation by using the modified couple stress theory (MCST) which will take into account the small-scale effects of the microtubules. We then proceeded by studying the effects of various parameters on the buckling growth rate of microtubule bundles. Our results show that the internal material length scale parameter has a decreasing effect on the buckling growth rate of the microtubule bundle. And as microtubule added in the bundle increases, the buckling growth rate reduces further due to the effects of the surrounding microtubule-associated proteins (MAPs). On the contrary, the Poisson's ratio has an increasing effect on the value of the buckling growth rate of the microtubule bundle. We also investigated the effects of other parameters such as surface energy on the buckling growth rates of microtubule bundles and showed the validity of our model by comparing our results with those obtained by previous researchers. [ABSTRACT FROM AUTHOR]

Background: Accurate predictions of thin sheet material springback during forming processes are of great interest in the forming industry. However, thin sheets are susceptible to buckling under shear loading. Objective: The present research aims at improving the so-called Arcan setup for testing thin (1-5 mm) sheet samples with large gauge areas (i.e., width about 21 mm) by introducing anti-buckling devices to mitigate sample buckling. Method: Three monotonic and one cyclic shear tests were carried out on 1 mm thick C60 high carbon steel. Results: The use of the proposed anti-buckling device resulted in the suppression of sample buckling. Numerical analyses of the experiment where buckling was eliminated revealed predominant shear stress states in the gauge area (i.e., stress triaxiality = 0), which highlights minor influences of the anti-buckling device on the sample stress state. Conclusion: To suppress buckling, the use of anti-buckling devices was essential. Moreover, the friction coefficient between the sample and the proposed devices was calibrated ( μ = 0.33 ) in addition to kinematic hardening parameters. [ABSTRACT FROM AUTHOR]

The behavior of pile groups in an earthquake prone area is governed by soil liquefaction and lateral spreading in addition to soil and pile properties, induced pore water pressure, vertical loads and input ground motions. A 2 × 2 pile group is modeled by using the finite difference-based computer program FLAC3D to obtain the deflection and bending moment behavior along the pile depth, under seismic loading conditions. Dynamic analysis is carried out by subjecting the 2 × 2 pile group to four different types of input motions with simultaneous application of vertical load on the pile cap in the form of surface pressure such that it is uniformly transferred to all the four piles. It is observed that the pile group deflection and bending moments in front and rear piles are increased by 15%, 37% and 30%, respectively when vertical loads are considered in addition to lateral kinematic loadings, and the 2001 Bhuj motion is considered as the input ground motion for a spacing (s) to diameter (d) ratio of 2. The bending moment for both front and rear piles and pile group deflection is maximum when ratio of depth of liquefiable soil layer (Lliq) to total length (l) of the pile is 0.625 and it decreases afterwards for both kinematic and combined loadings. Further, when the s/d ratio changes from 2 to 4, the bending moment in both front and rear piles and pile head deflection reduces by 8%, 7% and 5% for combined loadings and subjected to 2001 Bhuj motion for Lliq/l ratio of 0.625. Hence it is necessary to have a proper assessment of bending–buckling interaction of pile group in liquefiable soil since during an earthquake pile group is simultaneously acted upon by both vertical and lateral loads. [ABSTRACT FROM AUTHOR]

Computational modeling of experiments on measurement of axial distributions of fission reaction rates in configurations of the ASTRA critical facility simulating a HTGR with annular core is performed. Absorbing elements were installed in the internal reflector of critical assemblies to flatten the neutron flux radial distribution. Measurements of the fission reaction rates were performed both in a configuration with a flattened neutron field and in a configuration with control rods (CR) inserted in an external graphite reflector. [ABSTRACT FROM AUTHOR]

Recently, the Double Shear Bolted Brackets (DSBB) moment connection with four-bolt configuration has been introduced as a new fully restrained moment connection for use in shallow beam-column joints. With regards to deep beam connections, it is a requirement to have stiffer and stronger connections in the DSBB connection group. Knowing that similar code-qualified bolted bracket connections, Kaiser Bolted Bracket (KBB) connections, have marginal rotational stiffness, they cannot be considered as a fully restraint moment connection in deep beam-to-column joints. Therefore, in this discourse, six-bolt and eight-bolt configurations of DSBB are developed and their design methodology is outlined. Less thickness of bracket components, less diameter of bolts used, and greater stiffness compared to KBB code-qualified (AISC 358-16 standard) connections by the (KBB connection) are the main advantages of these new connections, making them a more applicable option of fully restrained connections for deep beam joints than their counterpart KBB connection. First, the DSBB design method is developed considering all possible limit states of buckling, yield, and rupture failures for the plate components of each bracket. Then, by using a validated high fidelity finite element study, the cyclic performance of DSBB connections is obtained and successfully accepted based on the AISC 341-16 standard requirements for fully restrained connections in special moment connections. The results indicated the low risk of failure and proper relaxed stress distribution around the connection compared to the corresponding KBB connection. In addition, the material consumption of DSBB six-bolt and eight-bolts were 19.7% and 6.9% in bolts and were 19.9% and 42.9% in brackets less than that of the corresponding KBB connections. Finally, it is concluded that DSBB six-bolt and eight-bolt configurations are efficient choices of fully restrained moment connections for application in deep beam-column joints. [ABSTRACT FROM AUTHOR]

The dynamic characteristics of imperfect pipes conveying fluid in the pre-buckling and post-buckling states are investigated. In this paper, the novel motion equation of fluid-conveying imperfect pipe supported at both ends is derived by considering the geometric imperfection and the geometric nonlinearity induced by mid-plane stretching. The imperfect configurations are chosen as the first bucked modes of pined–pined and clamped–clamped pipes. The exactly analytical solutions for static response are obtained due to the fluid flow. In the linear vibration analysis, the equation is discretized by the Galerkin method and solved as a linear eigenvalues problem. Excellent agreement is observed between the present solution and the available literature. Compared with the supercritical pitchfork bifurcation of the perfect pipe conveying fluid, the results show that the cusp bifurcation occurs in the imperfect pipe when increasing the flow velocity. In the post-buckling state, there are three equilibrium configurations composed of two asymmetry stable branches and an unstable branch. The critical velocity firstly increases and then decreases when the imperfect amplitude increases. The numerical results indicate that initial imperfect amplitude and flow velocity have a complex influence on the natural frequency of the imperfect pipe. The first natural frequency increases when the initial imperfect amplitude increases. The three branches of the imperfect pipe in the post-buckling state provide more interesting and essential dynamic behaviors. [ABSTRACT FROM AUTHOR]

The present study addresses a simplified topology optimization method to improve load bearing capacity. Topology optimization taking account of structurally nonlinear and complex behavior is an important topic from the viewpoint of mechanics. However, most methodologies require complex analytical derivation of sensitivity analysis and high computational cost to obtain the optimal solution. In light of this, we propose a practical design method employing the principal direction of Cauchy stress and the directional statistics, to improve load bearing capacity indirectly with much lower computational cost than those based on complex nonlinear structural analysis. Finally, we discuss setting of optimization problems, and demonstrate the accuracy and performance of the proposed method with a series of numerical examples. [ABSTRACT FROM AUTHOR]

This paper investigates the weight minimization of stiffened panels simultaneously optimizing sizing, layout, and topology under stress and buckling constraints. An effective topology optimization parameterization is presented using multiple level-set functions. Plate elements are employed to model the stiffened panels. The stiffeners are parametrized by implicit level-set functions. The internal topologies of the stiffeners are optimized as well as their layout. A free-form mesh deformation approach is improved to adjust the finite element mesh. Sizing optimization is also included. The thicknesses of the skin and stiffeners are optimized. Bending, shear, and membrane stresses are evaluated at the bottom, middle, and top surfaces of the elements. A p-norm function is used to aggregate these stresses in a single constraint. To solve the optimization problem, a semi-analytical sensitivity analysis is performed, and the optimization algorithm is outlined. Numerical investigations demonstrate and validate the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the vibration and buckling behavior of a functionally graded piezoelectric porous cylindrical microshell under thermo-electro-mechanical loads are explored on the basis of modified couple stress theory and higher-order shear deformation theory. First, the model of a functionally graded piezoelectric porous cylindrical microshell composed of piezoelectric materials with gradient change in the thickness direction was described. Second, the governing equations of the microshell were derived by Hamilton's principle and Maxwell equation. Third, the modal frequency and buckling equations of the microshell with simply supported ends were obtained on the basis of harmonic trigonometric functions. Finally, the effects of parameters on the modal frequency and buckling behavior were carried out by case studies. The results show that the modal frequency of the microshell can be adjusted by changing the porosity volume fraction, power index, applied voltage, axial load and geometric dimensions. It is also found that the vibration of the microshell is suppressed by positive voltage and axial compression but is strengthened by negative voltage and axial tension, and the material length scale parameter increases stiffness. In addition, the effects of applied voltage and axial load on the buckling behavior are larger than those of temperature. Results can be used to guide the design and application of piezoelectric devices. [ABSTRACT FROM AUTHOR]

A mathematical model for nonlocal vibration and buckling of embedded two-dimensional (2D) decagonal quasicrystal (QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional (3D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories. Numerical examples are provided to display the effects of the quasiperiodic direction, length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence, and medium elasticity on the vibration frequency and critical buckling load of the 2D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate. This feature is useful since the frequency and critical buckling load of the 2D decagonal QCs as coating materials of plate structures can now be tuned as one desire. [ABSTRACT FROM AUTHOR]