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• A novel semi-analytical method is developed for stiffened plates. • The method's base functions are the closed-form mode functions of simple plates. • The present method is suitable for all homogenous boundary conditions. • Exact solutions are obtained for simply-supported stiffened plates. Stiffened plates are widely used in various engineering fields as main load-carrying components. Semi-analytical methods are effective for studying the eigenbuckling problems of stiffened rectangular plates, but there are no semi-analytical solutions available for stiffened plates with arbitrary homogeneous boundary conditions. This work aims to develop a semi-analytical method for solving the eigenbuckling problems of orthotropic stiffened thin plates. In this method, base functions for constructing the mode functions of stiffened plate are the mode functions of a simple plate (a plate without stiffener), and the base functions are obtained with the extended separation-of-variable method, which is a closed-form solution method for the eigenvalue problems of plates. The critical buckling load is achieved by substituting the mode functions into the Rayleigh's principle. The present method can deal with arbitrary homogeneous boundary conditions without anticipating the forms of the base functions for different boundary conditions. The accuracy can be improved by using more superposition terms. Besides, an exact closed-form solution of simply supported stiffened plates is achieved, serving as benchmark solutions. Numerical experiments validate the accuracy of the present solutions, and the study on the minimum stiffener stiffness is conducted for different boundary conditions. [ABSTRACT FROM AUTHOR]

• The stability of sandwich nanobeams are interconnected via Kerr-type foundation is investigated. • The three couple equations are extracted using the Eringen's nonlocal elasticity theory. • The buckling loads are determined using the generalized differential quadrature method. • Results are discussed and the importance of some geometric and material parameters is learned. In this study, the endurable buckling load of the elastically connected parallel sandwich nano-beams with varying cross-sections is assessed. In this regard, a layered beam system consisting of two parallel axially loaded tapered sandwich nanobeams that are interconnected via a Kerr-type three-parameter elastic foundation is considered. The geometric properties are assumed to be changed exponentially along the length of the beam element. The governing equilibrium equations of the system are described by a set of three coupled homogeneous differential equations, which originates in the context of Eringen's non-local elasticity theory and Euler beam model. Then, the numerical differential quadrature technique is used to estimate the endurable axial critical loads. Eventually, a comprehensive parameterization research is performed to investigate the sensitivity of linear buckling resistance to tapering ratio, nonlocal parameter, stiffness of elastic connections, volume fraction exponent, and thickness ratio. The research work of the present study is novel, and the attained numerical outcomes can be used as benchmarks for future researches in this field. [ABSTRACT FROM AUTHOR]

• A novel method to extract P cr from load vs. in-plane displacement data. • Highly sensitive to slope changes while reducing adverse graph fluctuations. • Reliable results confirmed by comparison with Southwell plot and strain bifurcation. • Applicable to various column/plate structures including laminates and sandwich panels. • The method can serve as an independent and complementary approach to determine P cr. Based on the literature, the load vs. in-plane displacement diagram (P-u curve) is not sufficiently indicative to provide a reliable determination of the critical buckling load, P cr. This attitude is rooted in three issues. First, the P-u curve often exhibits very gradual slope changes, second, it concerns unavoidable graph fluctuations caused by imperfections in specimens or boundary conditions, and third, the P-u curve behavior during the buckling phenomenon is not fully understood. In the present work, a narrative review is conducted to gain a better understanding of the location of P cr on the P-u curve. Accordingly, a novel method is introduced to correctly extract P cr from the load vs. in-plane displacement diagram as the most accessible buckling test output, compared to out-of-plane displacement and strain monitoring data, which require additional equipment. The proposed method is highly sensitive to changes in the slope of the graph while significantly reducing the adverse effects of undesired fluctuations. This method is applied to several experimental buckling data for composite laminates as well as sandwich panels, and its reliability and accuracy are confirmed by comparison with other well-known methods. [Display omitted] [ABSTRACT FROM AUTHOR]

• A Bloch wave based numerical vibration correlation technique (BW-NVCT) is proposed. • BW-NVCT predicts buckling loads without high experimental or computational costs. • A novel implementation of the Bloch wave method is used for twofold acceleration. • BW-NVCT is shown in high accuracy and efficiency for engineering composite shells. • Results indicate that BW-NVCT can capture both global and local buckling modes. The buckling load revealing structural capacity bears significant value for the design of engineering composite shells, especially in the aerospace industry. Non-destructive methods are prevailing for critical buckling load prediction. However, the experimental costs and computational time for the analysis are unaffordable, especially for large-scale and complex shells. Despite the numerical vibration correlation technique (NVCT) and its modifications proposed for faster critical buckling load prediction, the efficiency requires further improvement. For composite shells with rotational periodicity, analyzing one substructure based on the Bloch wave method can be an alternate for the analysis of the entire shell. Since the NVCT comprises the linear buckling analysis and repeated frequency analyses, twofold acceleration can be performed. Thus, the Bloch wave based numerical vibration correlation technique (BW-NVCT) is proposed. Firstly, the formulations for the Bloch wave method and the NVCT are derived. As the curve of Bloch wave numbers and buckling loads is monotonous or principally comprise a single peak, the computations in the Bloch wave method to determine the minimum buckling load are further reduced. Then, the implementation of BW-NVCT is presented wherein the Bloch wave calculations are simplified compared with the Bloch wave buckling analysis method. Secondly, three types of composite shells including the Z33 composite cylindrical shell, the pressure vessel and the nozzle are analyzed by the proposed method. By applying Bloch boundary conditions to the substructure, the linear buckling loads, natural frequencies are in high accuracy with respect to results by finite element analyses directly. In addition, predicted critical buckling loads by the BW-NVCT are in excellent precision and most importantly, remarkable efficiency is achieved compared with both the NVCT and the dynamic explicit analysis. Results show that the proposed method can capture both global and local buckling modes, even when bend-twist coupling exists. It is concluded that the BW-NVCT is widely applicable for composite shells and is substantiated as an effective method for fast buckling load prediction. [ABSTRACT FROM AUTHOR]

Twenty-four specimens are tested to study the static performance of axially compressed square concrete filled CFRP-steel tubular (S-CF-CFRP-ST) columns. The tested results indicate that, for columns with relatively small slenderness, failure is dominated by the strength lose of the cross-section. However, for columns with relatively large slenderness, failure is controlled by instability. The load versus deflection curves at the mid-height of the composite columns can be divided into three stages, i.e., elastic, elasto-plastic and softening stages. The tested results also show that the longitudinal strain distribution along the depth on the cross-section is approximately linear, and the steel tube and its outer CFRP material can cooperate well both longitudinally and transversely. The longitudinal strain and the transverse strain at a point have opposite actions, and the steel tube under longitudinal tension has no transverse confinement effect on its concrete. Subsequently, axial load verses deflection curves at the mid-height and the deformed modes of the columns are simulated by using finite element (FE) method. The calculated results agree well with the experimental data to indicate that the accuracy of the FE model used is guaranteed. Then, stresses in the concrete, the steel tube and the CFRPs are then investigated by using FE method. The numerical results show that the transverse CFRP in tension provides effective confinement on the specimens and the longitudinal CFRP in tension provides effective enhancement on the flexural stiffness. The interaction force between the steel tube and the concrete reaches its maximum value on the mid-height cross-section, and it decreases when the distance to the end plates becomes smaller. On the cross-section, the interaction force has its maximum value at the corner and it decreases when the position moves to the mid-point of the tube side. The adhesive strength between the concrete and the steel tube has little effect on the critical buckling load and on the elastic stiffness of the columns. Equation for calculating the critical buckling load of the composite columns is proposed, and the estimated results agree well with the experimental data. [ABSTRACT FROM AUTHOR]

This paper focuses on the dynamic buckling of thin cylindrical shells with arbitrary axisymmetric thickness variation under time dependent axial pressure. Based on the derivation of stability and compatibility equations of variable thickness cylindrical shells under dynamic external pressure by Aksogan and Sofiyev, the corresponding stability and compatibility equations of thin cylindrical shells with arbitrary axisymmetric thickness variation under dynamic axial pressure are obtained and expressed in nondimensional form. Combining the small parameter perturbation method, Fourier series expansion and the Sachenkov–Baktieva method, analytical formulas of the critical buckling load of thin cylindrical shells with arbitrary axisymmetric thickness variation under axial pressure that varies as a power function of time are obtained. Two cases of thickness variation are introduced to research the critical dynamic buckling load with the present formulas. Effects of thickness variation parameters and loading speed of dynamic axial pressure on the critical buckling load are discussed. The method is also applied to determine the critical dynamic buckling load of thin cylindrical shells with a classical cosine form thickness variation. Results revel that the thickness variation and pressure parameters play a major role in dictating the buckling capacity of thin cylindrical shells under dynamic axial pressure. [ABSTRACT FROM AUTHOR]

This paper presents an analytical solution for calculating the critical buckling load of simply supported cellular columns when they buckle about the major axis. The solution takes into account the influence of web shear deformation on the buckling of cellular columns and is derived using the stationary principle of potential energy. The formula derived for calculating the critical buckling load is validated using finite element analysis results. It is shown from the present analytical solution that the web shear deformation can significantly reduce the buckling resistance of cellular columns. The influence of the shear deformation on the critical buckling load increases with the cross-section area of the tee section and the radius of circular holes but decreases with the length and the web thickness of the cellular column. [ABSTRACT FROM AUTHOR]

Sway modular steel structures with semi-rigid connections (SMSS-SRCs) have special configurations of connections and columns. Hence, current design requirements regarding effective length factors are unsuitable. Therefore, the displacement method was used to derive expressions for single-module lateral stiffness in the first, middle, and top stories, thereby obtaining the overall lateral stiffness of SMSS-SRCs. The negative lateral stiffness of the modular column was obtained by modifying the rotational constraints at both of its ends. Subsequently, the overall negative lateral stiffness of SMSS-SRCs was obtained as well. The story support factor was used to quantify the degree of mutual support between stories. Finally, formulas for calculating for the critical buckling load and effective length factors of columns in SMSS-SRCs were obtained. Finite element models were established to verify the proposed formulas. The results showed that the proposed method has good accuracy. Hence, this study could provide a reference for calculating the critical buckling load and effective length factor of columns in SMSS-SRCs. • Stability of sway modular steel structures with semi-rigid connections analyzed. • Formulas for the critical buckling load and effective length factors of columns in SMSS-SRCs were obtained. • Expressions derived for single-module lateral stiffness in different stories. • Finite element models were established to verify the proposed formulas. • Theoretical and numerical results showed good accuracy and safer predictions. [ABSTRACT FROM AUTHOR]

This paper carries out the nonlinear stability of nanocomposite multilayer organic solar cell (NMOSC) subjected to axial compressive loads. The model of organic solar cell is assumed to consist five layers: Al, P3HT:PCBM, PEDOT:PSS, IOT and Glass. Based on the classical plate theory, the basic equations are established taking into account the effect of elastic foundations and initial imperfection. The approximation solutions are selected based on the boundary conditions of the four edges of NMOSC. The equation which indicates the relationship between axial compressive loads and deflection amplitude of NMOSC is obtained by using the Galerkin method. Bees Algorithm is applied to maximize the value of critical buckling load with nine variables including the thickness of five layers, the length and the width of NMOSC and two stiffness coefficients of elastic foundations. The numerical results show the effect of geometrical and material parameters, initial imperfection and elastic foundations on the nonlinear static stability and the critical buckling load of NMOSC. Optimal values of nine geometrical parameters of NMOSC are also determined. • The nonlinear stability of nanocomposite multilayer organic solar cell is investigated. • The classical plate theory is used to establish basic equations. • The effect of elastic foundations and initial imperfection are taken into account. • Effects of material and geometrical properties, elastic foundations and initial imperfection are discussed. • Bees Algorithm is used to determine the maximum value of critical buckling load depending on nine variables. [ABSTRACT FROM AUTHOR]