Thermal buckling load optimization of laminated composite plates

In this study, the applicability of the Modified Feasible Direction (MFD) method on the thermal buckling optimization of laminated plates subjected to uniformly distributed temperature load is investigated. The objective function is to maximize the critical temperature capacity of laminated plates and the fiber orientation is considered as design variable. The first-order shear deformation theory is used in the mathematical formulation. For this purpose, a program based on FORTRAN is used for the optimization of laminated plates. Finally, the effect of aspect ratio, antisymmetric lay-up, boundary condition, material anisotropy, ratio of coefficients of thermal expansion, and hybrid laminates on the results is investigated and the results are compared.     

Thermal postbuckling of laminated composite skew plates with temperature-dependent properties

Thermal postbuckling and consequently, the role of temperature dependence of material properties on the thermal postbuckling behavior of laminated composite skew plates have not been addressed in literature. Hence, this problem is investigated here. The plate governing equations are based on the first-order shear deformation theory (FSDT) and the geometrical nonlinearity is modeled using Green’s strain tensor in conjunction with the von Karman assumptions. Since the problem is geometrically and physically nonlinear, the differential quadrature method (DQM) as an accurate, simple and computationally efficient numerical tool is adopted to discretize the governing equations and the related boundary conditions. Then, a direct iterative method is employed to obtain the critical temperature (bifurcation point) and consequently the nonlinear equilibrium path (the postbuckling behavior) of symmetrically laminated skew plates. After validating the formulation and the method of solution, the effects of temperature dependence of the material properties on the postbuckling characteristic of laminated skew plates with different skew angle, boundary conditions, length-to-thickness ratio, number of layers and ply layout are investigated.     

Discrete singular convolution method for buckling analysis of rectangular Mindlin plates

The discrete singular convolution (DSC) method is proposed for solving the elastic buckling problem of thick rectangular plates under a uniaxial compressive loading. To allow for the effect of transverse shear deformation in thick plates, the Mindlin plate theory has been adopted. The numerical results are checked against available analytical and other numerical solutions. It is found that the convergence of the DSC approach is very good and the results agree well with those obtained by other researchers.     

Thermal buckling analysis of rectangular microplates using higher continuity p-version finite element method

In this article, thermal buckling characteristics of rectangular flexural microplates (FMP) subjected to uniform temperature are investigated using higher continuity p-version finite element framework. Invariant form of the governing equation for a microplate with non-local effects based on “modified couple stress theory” is extended for thermal buckling analysis of FMP by considering the strain gradient effects. In this case, the constitutive equation for strain gradient model is based on one constant. Galerkin weak form of the governing equation is derived and subsequently solved for a variety of boundary conditions using higher continuity p-version finite elements to extract critical thermal buckling loads. The computational procedure is verified by comparing its predictions to those of the classical theory and analytic microplate studies that are based on the same strain gradient model. Investigations indicate that length scale parameter affects the computed flexural stiffness of a plate, and the effect is directly proportional to the value of gradient coefficient considered for that plate. Hence, there is a strong influence of length scale parameter on value of the thermal buckling load. Depending on boundary conditions and value of length scale parameter used in numerical experiments, the classical plate model severely underestimates (up to 90%) the thermal buckling load for microplates. Therefore, it is concluded and strongly suggested that the classical plate theory should not be used to predict structural response of microplates.     

Local buckling of steel plates in rectangular CFT columns with binding bars

This paper presents a theoretical study on the elastic local buckling of steel plates in rectangular concrete-filled steel tubular (CFT) columns with binding bars under axial compression. It is assumed that the unloaded edges of the steel plate are elastically restrained against rotation, whereas the loaded edges are clamped. Based on the energy method, the formulas for elastic local buckling strength of the steel plate in rectangular CFT columns under axial compression are derived, which are calibrated with the experimental results. Then the formulas are employed to study the elastic local buckling of steel plates in rectangular CFT columns with binding bars under axial compression. It is shown that the binding bars can increase the local buckling coefficient, which results in improvement of the capacity of the steel plate to resist local buckling. Finally, appropriate spacing of binding bars, appropriate limitation for aspect ratio and corresponding appropriate limitation for width-thickness ratio are suggested for rectangular CFT columns with binding bars under axial compression.     

钢筋混凝土矩形薄板在弹性地基上的热屈曲

基于板的小挠度理论,考虑混凝土材料的非线性,推导了弹性地基上钢筋混凝土矩形薄板在热载作用下的平衡方程和稳定方程,给出了四边简支钢筋混凝土矩形薄板在均匀温度变化时临界屈曲温度变化的封闭解,讨论了板的材料常数、长宽比、相对厚度和基床系数等对临界屈曲温度变化的影响,从而为工程结构中弹性地基上钢筋混凝土矩形薄板的临界屈曲温度的计算提供了理论计算依据。     

基于突变理论的扁拱跳跃屈曲分析

分析了扁拱在静载荷或动载荷作用下发生跳跃屈曲的原因。采用尖点突变理论建立悬链线形拱的跳跃屈曲模型，推导临界荷载公式，并采用Matlab工具计算及Ansys验算模型理论正确性，最后对上述两种方法所得值进行比较。     

Elastic/plastic buckling of a composite flat plate subjected to uniform edge compression

A theoretical approach, based on the plastic theory, has been developed for studying the elastic/plastic buckling behavior of a simply supported rectangular anisotropic plate subjected to edge compression. The said approach was employed to determine the critical buckling stresses of three different types of fiber reinforced composite plates, namely, carbon epoxy, glass epoxy and boron aluminum plates. Since the proposed approach is for a preliminary prediction of critical buckling loads of composite plates, the results obtained are deemed acceptable compared with those obtained by other authors experimentally.     

Lateral buckling analysis of thin-walled laminated composite beams with monosymmetric sections

Lateral buckling of thin-walled composite beams with monosymmetric sections is studied. A general geometrically nonlinear model for thin-walled laminated composites with arbitrary open cross-section and general laminate stacking sequences is given by using systematic variational formulation based on the classical lamination theory. All the stress resultants concerning bar and shell forces are defined, and nonlinear strain tensor is derived. General nonlinear governing equations are given, and the lateral buckling equations are derived by linearizing the nonlinear governing equations. Based on the analytical model, a displacement-based one-dimensional finite element model is developed to formulate the problem. Numerical examples are obtained for thin-walled composite beams with monosymmetric cross-sections and angle-ply laminates. The effects of fiber orientation, location of applied load, modulus ratio, and height-to-span ratio on the lateral buckling load are investigated. The torsion parameter and a newly-defined composite monosymmetry parameter are also investigated for various cases.     

Finite element analysis of local buckling behavior of steel plates in concrete-filled double steel plate composite shear walls

采用ABAQUS有限元软件对双钢板-混凝土组合剪力墙中外包钢板的局部屈曲行为进行了有限元模拟,分析外包钢板在轴压作用下的局部屈曲和屈曲后的受力性能。共开展了15个模型的有限元分析,模型的变化参数包括钢板的宽厚比和对拉钢筋的列数。分析结果表明：对于列间距和行间距相同的对拉钢筋布置方案,钢板局部屈曲始终发生在相邻两对拉钢筋之间;钢板发生屈曲后,与屈曲位置相邻的对拉钢筋承受较大的拉力,且对拉钢筋拉力随着对拉钢筋间距的减小而增大;增加对拉钢筋列数和减小钢板宽厚比可有效改善外包钢板的局部稳定性能,提高钢板的承载能力和变形能力;相比点约束,线约束对钢板局部屈曲的约束更为有效;无对拉钢筋模型、单列对拉钢筋模型和双列对拉钢筋模型达到屈服强度（345MPa）所需的最小宽厚比分别为25、30和37.5。     

Thermal buckling of FGM shells resting on a two-parameter elastic foundation

This paper focuses on the thermal buckling analysis of FGM shells resting on the two-parameter elastic foundation. Material properties of the constituents are graded in the thickness direction according to the power-law distribution. The surrounding elastic medium is modeled as an elastic foundation of the Pasternak-type. After giving the fundamental relations, the stability and compatibility equations of an FGM truncated conical shell subjected to thermal load and resting on a two-parameter elastic foundation have been derived. Critical temperature differences of FGM truncated conical shells with or without elastic foundations subjected to non-linearly distributed temperature across the thickness of the shells are obtained by solving eigenvalue problems. The appropriate formulas for FGM cylindrical shells with or without elastic foundations are found as a special case. In order to assure the accuracy of the present study, convergence properties of the critical temperature are examined in detail.     

Variationally-based theories for buckling of partial composite beam-columns including shear and axial effects

This paper is focused on elastic stability problems of partial composite columns: the conditions for the axial load not to introduce any pre-bending effects in composite columns; the equivalence, similarities and differences between different sandwich and partial composite beam theories with and without the effect of shear, with and without the effect of axial extensibility, and also the effect of eccentric axial load application. The basic modelling of the composite beam-column uses the Euler-Bernoulli beam theory and a linear constitutive law for the slip. In the analysis of this reference model, a variational formulation is used in order to derive relevant boundary conditions. The specific loading associated with no pre-bending effects before buckling is geometrically characterized, leading to analytical buckling loads of the partial composite column. The equivalence between the Hoff theory for sandwich beam-columns, the composite action theory for beam-columns with interlayer slip and the corresponding Bickford-Reddy theory, is shown from the stability point of view. Special loading configurations including eccentric axial load applications and axial loading only on one of the sub-elements of the composite beam-column are investigated and the similarity of the behaviour to that of imperfect ordinary beam-columns is demonstrated. The effect of axial extensibility on kinematical relationships (according to the Reissner theory), is analytically quantified and compared to the classical solution of the problem. Finally, the effect of incorporating shear in the analysis of composite members using the Timoshenko theory is evaluated. By using a variational formulation, the buckling behaviour of partial composite columns is analysed with respect to both the Engesser and the Haringx theory. A simplified uniform shear theory (assuming equal shear deformations in each sub-element) for the partial composite beam-column is first presented, and then a refined differential shear theory (assuming individual shear deformations in each sub-element) is evaluated. The paper concludes with a discussion on this shear effect, the differences between the shear theories presented and when the shear effect can be neglected.     

复合材料层合板的层间应力有限元分析

本文研究复合材料层合板的层间应力,以经典板理论为基础,考虑横向剪切变形和层间相互挤压,构造每一铺层与层间胶层的位移场,采用有限元方法,应用广义势能原理确定位移场中的待定系数,从而确定层合板的位移场和应力场。采用ANSYS计算,计算结果显示,这种解法克服了经典层合板理论的缺点,提高了层间应力的计算精度。     

Experimental verification of an inelastic plate theory based on plastic flow theory

The paper aims to verify a recently proposed inelastic plate theory by Becque (2010) [1]. In a first part, the theory is revisited and some necessary corrections to the derivation are presented.     

Nonlinear analysis of concrete-filled thin-walled steel box columns with local buckling effects

Local buckling of steel plates reduces the ultimate loads of concrete-filled thin-walled steel box columns under axial compression. The effects of local buckling have not been considered in advanced analysis methods that lead to the overestimates of the ultimate loads of composite columns and frames. This paper presents a nonlinear fiber element analysis method for predicting the ultimate strengths and behavior of short concrete-filled thin-walled steel box columns with local buckling effects. The fiber element method considers nonlinear constitutive models for confined concrete and structural steel. Effective width formulas for steel plates with geometric imperfections and residual stresses are incorporated in the fiber element analysis program to account for local buckling effects. The progressive local and post-local buckling is simulated by gradually redistributing the normal stresses within the steel plates. Two performance indices are proposed for evaluating the section and ductility performance of concrete-filled steel box columns. The computational technique developed is used to investigate the effects of the width-to-thickness ratios and concrete compressive strengths on the ultimate strength and ductility of concrete-filled steel box columns. It is demonstrated that the nonlinear fiber element method developed predicts well the ultimate loads and behavior of concrete-filled thin-walled steel box columns and can be implemented in advanced analysis programs for the nonlinear analysis of composite frames.     

分块盖板屈曲约束钢板剪力墙受力性能与设计方法研究

为考察分块盖板屈曲约束钢板剪力墙的抗震性能,采用非线性有限元分析软件ABAQUS对其受力机理进行深入研究。将板墙的高宽比、盖板厚度比等参数作为变量,对屈曲约束钢板墙在水平往复荷载作用下的抗震性能进行分析,考察内嵌钢板面外变形与应力、盖板变形与钢筋应力。分析结果表明:采用非线性有限元数值模拟得到屈曲约束钢板剪力墙的滞回性能、内嵌钢板变形特性均与试验结果较为接近。分块盖板屈曲约束钢板剪力墙在层间位移角接近1/300时进入屈服;加载至层间位移角1/50时,滞回曲线接近于理想弹塑性。当盖板厚度比t_c/t_w不小于7时,可以形成对内嵌钢板面外变形的有效约束,钢板屈曲半波长度与钢板厚度之比λ/t_w基本保持不变。在此基础上,建立内嵌钢板与分块盖板简化计算模型,根据内嵌钢板主压应力推导出挤压应力计算公式,从而可以方便地确定对拉螺栓的内力与分块盖板的弯矩。简化计算方法与有限元数值模拟得到混凝土盖板弯矩的分布规律非常接近,简化计算方法偏于安全。     

A shear deformable theory for the analysis of steel beams reinforced with GFRP plates

A shear deformable thin-walled beam theory is developed for the analysis of steel beams reinforced with a GFRP plate to one of the flanges. Starting with the principle of stationary potential energy, the governing equilibrium equations and boundary conditions are formulated for the problem. The theory results in two sets of fully coupled systems of equilibrium equations. The first system describes the longitudinal-flexural response of the system and involves four generalized displacement fields and the second system governs the lateral-torsional response and involves six generalized displacement fields. The resulting coupled systems are then solved numerically for practical problems. Detailed comparisons with three dimensional and shell solutions under ABAQUS show that the present theory provides reliable predictions for displacements and stresses. A comparison with results from a non-shear deformable theory illustrates the necessity of incorporating shear deformation effects in cases involving predominantly twisting responses.     

A finite element model based on coupled refined high-order global-local theory for static analysis of electromechanical embedded shear-mode piezoelectric sandwich composite beams with various widths

In this study, a new theory for the accurate simulation of the shear-mode behaviour of thin or thick piezoelectric sandwich composite beams is developed. The effects of transverse normal stress and transverse flexibility of layers are considered in the development of the proposed formulation. In order to increase the computational accuracy, all kinematic and stress continuity conditions are satisfied at layer interfaces. Moreover, for the first time, both the electrically induced strain components and the transverse flexibility are taken into account in the proposed formulation. Despite the fact that the number of unknown mechanical parameters in this theory is only one degree higher than the first order shear deformation theory, the accuracy is surprisingly more pronounced for the thicker beams.     

A study of the thermal buckling behavior of a circular aluminum plate using the digital image correlation technique and finite element analysis

In this study, the thermal buckling behavior of a circular aluminum plate that results from thermal loading was investigated using a digital image correlation (DIC) technique. The aluminum plate was placed in a titanium ring and the structure was heated from room temperature 25 °C to 160 °C. Due to the differences in the coefficients of thermal expansion (CTEs) between aluminum and titanium, the aluminum plate buckles at a certain temperature. The buckling temperature was determined from the full-field deformation shape and temperature-displacement curve that were obtained using the DIC-based ARAMIS^® software. In order to obtain an appropriate full-field deformation, a polarized light filter was used to reduce the out-of-plane displacement error, which is an unavoidable error in the experiment. Using this method, the standard deviation of the z directional displacement was reduced from ±3.14 μm to ±2.70 μm. In addition, the results demonstrated that the measured buckling temperature was close to the theoretical buckling temperature of the circular plate in a simply supported boundary condition. In order to verify the proposed measurement method, a finite element analysis of the structure was performed using the ABAQUS software. The results of the DIC-based measurement and finite element analysis were in good agreement regarding the deformation curve tendency. The buckling temperature from the finite element method (FEM) was slightly larger than that from the experimental results due to the initial imperfections of the aluminum specimen. These results provide a good method for studying thermal buckling for the design and analysis of engineering structures in diverse fields such as aerospace engineering, oil refineries, and nuclear engineering.