Higher-Order Finite Strip Method for Postbuckling Analysis of Imperfect Composite Plates

Postbuckling analysis is essential to predict the capacity of composite plates carrying considerable additional load before the ultimate load is reached, and manufacturing-induced geometric imperfections often reduce the load-carrying capacity of composite structures. A higher-order finite strip method based on the higher-order shear deformation plate theory is developed for postbuckling analysis of laminated composite plates with initial geometric imperfection subjected to progressive end shortening. The arbitrary nature of initial geometric imperfection induced during manufacturing is accounted for in the analysis. Nonlinear equilibrium equations are solved by a Newton-Raphson procedure. Examples of postbuckling analyses of unsymmetric cross-ply, angle-ply, and arbitrary laminates are presented, and the accuracy and performance of the method are examined. The numerical higher-order finite strip method presented can be used as an accurate and efficient tool for postbuckling analysis of imperfect composite plates.     

Postbuckling of Shear Deformable Laminated Cylindrical Shells

A postbuckling analysis is presented for a shear deformable laminated cylindrical shell of finite length subjected to compressive axial loads. The governing equations are based on Reddy’s higher-order shear deformation shell theory with a von Kármán–Donnell type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of shear deformable laminated cylindrical shells under axial compression. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, unstiffened or stiffened, moderately thick, cross-ply laminated cylindrical shells. The effects of transverse shear deformation, shell geometric parameters, total number of plies, fiber orientation, and initial geometric imperfections are studied.     

Asymptotic-Numerical Method to Analyze the Postbuckling Behavior, Imperfection-Sensitivity, and Mode Interaction in Frames

The paper presents the formulation and illustrates the application of an asymptotic-numerical (semianalytical) method to analyze the geometrically nonlinear behavior of plane frames. The method adopts an “internally constrained” beam model and involves two distinct procedures: (1) an asymptotic analysis, which employs a perturbation technique to establish a sequence of systems of equilibrium differential equations and boundary conditions, and (2) the successive numerical solution of such systems, by means of the finite element method. This method can be applied to investigate the behavior of frames with arbitrarily complex configurations (member number and orientation) and leads to the determination of analytical expressions which provide: (1) the initial postbuckling behavior of perfect frames and (2) the nonlinear equilibrium paths of frames containing small initial imperfections or acted by primary bending moments, including the influence of eventual buckling mode interaction phenomena. In order to validate and illustrate the application and potential of the proposed method, several numerical results are presented, concerning (1) four validation examples (Euler column and three simple frames—two or three members), for which there exist some (perfect frame) analytical and numerical asymptotic results reported in the literature; (2) a single-bay pitched-roof frame with partially restrained column bases; and (3) a three-bay frame with two leaning columns. These results comprise (1) the initial postbuckling behavior of perfect frames (individual and coupled buckling modes) and (2) geometrically nonlinear equilibrium paths describing the behavior of frames containing initial geometrical imperfections or primary bending moments. In the latter case, most of the semianalytical results are compared with fully numerical values, yielded by finite element analyses performed in the commercial code ABAQUS.     

Postbuckling of Pressure-Loaded Functionally Graded Cylindrical Panels in Thermal Environments

A postbuckling analysis is presented for a functionally graded cylindrical panel of finite length subjected to lateral pressure in thermal environments. Material properties are assumed to be temperature dependent, and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations of a functionally graded cylindrical panel are based on Reddy’s higher-order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity and include thermal effects. The two straight edges of the panel are assumed to be simply supported and two curved edges are either simply supported or clamped. The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflection in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of functionally graded cylindrical panels. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of simply supported, pressure-loaded, perfect and imperfect, functionally graded cylindrical panels with two constituent materials under different sets of thermal environments. The influences played by temperature rise, volume fraction distributions, transverse shear deformation, panel geometric parameters, as well as initial geometric imperfections, are studied.     

Hybrid Beam-Column Element with End Frictional Joints

Most research on semirigid jointed frames include only the rotational flexibility of the joint without consideration of the flexibility in the direction of the shear force. This paper investigates the nonlinear frictional behavior of a bolted slotted joint which includes flexibility in the tangential direction. The contact behavior at the end of the slot is also studied. The joint is prestressed with axial tension in the bolt shank. A virtual connection spring element is included at the intersection point between the beam and the column members. The formulation of the hybrid beam-column element including the end springs is presented, and the elemental matrices are also given for easy and direct implementation into finite-element analysis for static and/or dynamic loading.     

考虑初始缺陷的加劲板的非线性稳定性

实际板壳结构中的初始缺陷会影响结构的安全性和稳定性.以某实际钢结构工程为研究背景,重点考虑初始缺陷的影响,研究了不同的缺陷大小、加劲形式、加载方式及边界条件下,加劲板的非线性稳定性情况.结果表明:对于四边简支板,板的厚度越小,缺陷的影响越明显;初始缺陷相同,扁钢的非线性应力值最大;单边加载状况下,初始缺陷对板的非线性稳定性影响较大;初始缺陷对四边简支和四边固结加劲板的影响较平稳.     

Imperfections in Cylindrical Shells Resulting from Fabrication Misfits

This paper presents part of a rigorous numerical study of the geometry changes in cylindrical shells due to localized fabrication misfit and the associated consistent residual stress field. The search for practically useful and credible modes of imperfections has led to this study of the geometric imperfections arising from misfits of construction. These are treated here by using a geometrically nonlinear analysis to study the effect of a mismatch in geometry at a point or a seam in a cylinder, or alternatively to explore the role of weld shrinkage in the formation of geometric imperfections. The imperfect geometries arising from these misfits are demonstrated, and some simplifications are given so that their shape may later be used in methods for characterizing imperfection patterns that can be applied to measurements of structures in service. It is found that the geometrical changes are essentially linear for most of the shrinkages considered.     

Transverse Natural Vibration of a Beam with an Internal Joint Carrying In-Plane Flexibilities

Existing research on semirigid jointed frame includes only the rotational flexibility of the joint without consideration of the flexibility in the direction of the transverse shear force. This omission would lead to inaccuracies in the dynamic response of structures, especially in the nonlinear analysis. This paper investigates the dynamic behavior of a bolted joint which has flexibility in both the tangential and rotational directions. The joint is prestressed with axial tension in the bolt shank. It is represented as a virtual connection spring element at the intersection between the beam and the supporting member. The formulation of the hybrid beam–column element including the end springs is presented, and the dynamic behavior of a cantilever beam with this nonlinear semirigid joint is studied. The natural frequencies and mode shapes remain relatively unchanged only for a limited range of the joint stiffnesses, and the eigenpair is influenced by the instantaneous stiffness of the joint defined at a point on the hysteretic loop, particularly when the initial moment stiffness is small.     

Compression Tests on Cylinders with Circumferential Weld Depressions

The behavior of thin cylindrical shells under axial compression is very sensitive to imperfections in the initial geometry. Local axisymmetric imperfections are among the most detrimental and have been shown to be a regular feature of circumferentially welded joints in civil engineering shell structures such as steel silos and tanks. Many of the experiments on which current design rules are based were performed on elastic Mylar, copper, or aluminum specimens, which have some very different characteristics to those of steel shells. Furthermore, very few laboratory tests have ever examined the consequences of fabrication processes on shell buckling strength, although these strongly influence the amplitudes and forms of geometric imperfections. This paper presents the findings of a careful experimental program on large steel cylinders fabricated with a fully welded circumferential joint. Thorough measurements were made of the initial imperfections and their transformation into a buckling mode. The results are compared with elastic-plastic finite-element predictions and the most recent design standard.     

Postbuckling of Axially Loaded Functionally Graded Cylindrical Panels with Piezoelectric Actuators in Thermal Environments

A compressive postbuckling analysis is presented for a functionally graded cylindrical panel with piezoelectric actuators subjected to the combined action of mechanical, electrical, and thermal loads. The temperature field considered is assumed to be of uniform distribution over the panel surface and through the panel thickness and the electric field considers only the transverse component EZ. The material properties of the presently considered functionally graded materials (FGMs) are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, whereas the material properties of the piezoelectric layers are assumed to be independent of the temperature and the electric field. The governing equations are based on a higher-order shear deformation theory with a von Kármán-Donnell-type of kinematic nonlinearity. A boundary layer theory for shell buckling is extended to the case of hybrid FGM cylindrical panels of finite length. The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the compressive postbuckling behavior of perfect and imperfect FGM cylindrical panels with fully covered piezoelectric actuators, under different sets of thermal and electrical loading conditions. The effects due to temperature rise, volume fraction distribution, applied voltages, panel geometric parameters, in-plane boundary conditions, as well as initial geometric imperfections are studied.     

Force Identification Based on Sensitivity in Time Domain

A new method is proposed for identifying the time history of the input excitation using the dynamic response of the structure. The sensitivities of dynamic response with respect to the parameters of the input force are calculated in the time domain. These sensitivities are used to update the parameters of the identified force(s) iteratively in the inverse analysis. Both sinusoidal excitation and impulsive force are used in the simulation study. Three numerical examples show that the proposed method is effective and highly accurate in identifying the force(s). Both the effects of measurement noise and modeling error of the structure are found negligible on the accuracy of the identified force in the studies. The proposed method is further verified with laboratory measurements from a steel bar under sinusoidal excitation with very good results.     

C-Mn钢窄带热轧时的再结晶软化规律

针对唐山钢铁有限责任公司带钢厂的生产实际,借助理论与实验结果,研究了C-Mn钢热轧过程中各道次奥氏体的再结晶规律,计算结果与实测结果吻合较好,说明给出的组合模型用于窄带热轧的生产是可行的,它为在生产中控制与预报带钢的组织性能提供了奥氏体再结晶的定量化基础,并为再结晶软化不充分时的力能计算提供了修正依据.     

Structure of IF steel in continuous annealing

The recovery and recrystallization kinetics of IF titanium steel is studied by investigating the microstructure, measuring the coercive force, and analyzing the residual stress. The results are familiar, except for the initial and final temperatures of these processes, which are specific to the steel employed. We assume that, on heating cold-rolled IF steel in the range 550?C650°C, the dislocation density is unchanged on account of retardation by small TiC particles. Formulas are derived for the coercive force as a function of the grain size and may be used for monitoring purposes.     

Further Tests of Beam-to-Column Connections for Pultruded Frames: Flange-Cleated

Four full-sized physical tests have been conducted to determine the behavior of semirigid beam-to-column connections for frames of pultruded profiles. The tests were on 203 mm (8 in.) sized joints with connection details specifically chosen to provide moment resistant connections, thereby making it an option to include their semirigid action in frame design. Full details on the preparation of specimens and the physical test results are presented. Experimental moment-rotation curves have been obtained under short-term loading and modes of failure established. The suitability of the four connections to provide acceptable semirigid properties is assessed and future work recommended.     

Lateral Load Distribution in Curved Steel I-Girder Bridges

The purpose of this paper is to develop new formulas for live load distribution in horizontally curved steel I-girder bridges. The formulas are developed by utilizing computer model results for a number of different horizontally curved steel I-girder bridges. The bridges used in this study are modeled as generalized grillage beam systems composed of horizontally curved beam elements for steel girders and substructure elements for lateral wind bracing and cross frames which consist of truss elements. Warping torsion is taken into consideration in the analysis. The effect of numerous parameters, including radius of curvature, girder spacing, overhang, etc., on the load distribution are studied. Key parameters affecting live load distribution are identified and simplified formulas are developed to predict positive moment, negative moment, and shear distribution for one-lane and multiple-lane loading. Comparisons of the formulas with finite element method and grillage analysis show that the proposed formulas have more accurate results than the various available American Association of State Highway and Transportation Officials specifications. The formulas developed in this study will assist bridge engineers and researchers in predicting the actual live load distribution in horizontally curved steel I-girder bridges.     

提高轧制力设定精度的一种离线优化方法

轧制力参数设定是轧机设定模型的核心参数之一,对决定成品卷的厚度精度及板型质量至关重要。京唐酸轧二级模型计算轧制力时采用Bland-Ford-Hill公式,经分析确定影响轧制力计算精度的参数主要为变形抗力和摩擦力因数。因此提出了一种利用特定钢种的初始历史实际轧制数据离线调整其变形抗力和摩擦力因数的方法,从而提高本钢种在线轧制力模型的设定精度。实际应用表明,使用通过此方法优化后的变形抗力和摩擦力参数计算轧制力,轧制力设定模型的精度得到了明显提高,能够满足在线控制需求。     

Return Mapping Procedure for Frictional Force Calculation: Some Insights

The return mapping procedure is studied to gain insights for its numerical implementation to calculate the frictional force during contact analysis. A simple quasistatic truss–wall frictional contact analysis problem is used in the study. The problem has closed-form solutions which provide exact target solutions for a numerical algorithm. The penalty method and a true augmented Lagrangian method that automatically determines an accurate value of the penalty parameter are employed in the numerical study. It is determined that the return mapping procedure is not applicable unless the contacting node is constrained to stay at the initial contact point, and the total normal reaction force, the tangential reaction force and the friction limit have been determined. If these requirements are not met, inaccurate or even incorrect solutions are obtained. This characteristic of the procedure is studied by solving slip and stick cases with several different load increments. It is concluded that the return mapping procedure for friction force calculation should be implemented carefully to obtain accurate solutions for contact analysis problems.     

Numerical Investigation of Desulfurization Kinetics in Gas-Stirred Ladles by a Quick Modeling Analysis Approach

A quick modeling analysis approach for predicting the slag-steel reaction and desulfurization kinetics in argon gas-stirred ladles has been developed in this study. The model consists of two uncoupled components: (i) a computational fluid dynamics (CFD) model for predicting the fluid flow and the characteristics of slag-steel interface, and (ii) a multicomponent reaction kinetics model for calculating the desulfurization evolution. The steel-slag interfacial area and mass transfer coefficients predicted by the CFD simulation are used as the processing data for the reaction model. Since the desulfurization predictions are uncoupled from the CFD simulation, the computational time of this uncoupled predictive approach is decreased by at least 100 times for each case study when compared with the CFD-reaction kinetics fully coupled model. The uncoupled modeling approach was validated by comparing the evolution of steel and slag compositions with the experimentally measured data during ladle metallurgical furnace (LMF) processing at Nucor Steel Tuscaloosa, Inc. Then, the validated approach was applied to investigate the effects of the initial steel and slag compositions, as well as different types of additions during the refining process on the desulfurization efficiency. The results revealed that the sulfur distribution ratio and the desulfurization reaction can be promoted by making Al and CaO additions during the refining process. It was also shown that by increasing the initial Al content in liquid steel, both Al oxidation and desulfurization rates rapidly increase. In addition, it was found that the variation of the initial Si content in steel has no significant influence on the desulfurization rate. Lastly, if the initial CaO content in slag is increased or the initial Al₂O₃ content is decreased in the fluid-slag compositional range, the desulfurization rate can be improved significantly during the LMF process.     

Stability of Stiffened Plates with Initial Imperfections

An experimental study of the effect of plate slenderness ratio and column slenderness ratio on the collapse load of simply supported stiffened plates with initial imperfections, loaded in compression, is presented. A generalized computer program for the semiempirical solutions based on the strut approach and the orthotropic plate approach is developed. A finite element analysis program based on the orthotropic plate approach is developed and a new collapse criterion is introduced. The analytical calculations are compared with the experimental results and uncertainty parameters are calculated. The effect of initial geometric imperfections, plate slenderness ratios, and column slenderness ratios on the collapse load of stiffened plates is studied. A set of conclusions is drawn based on the experimental and analytical studies carried out.     

Large Deflection Stability of Slender Beam-Columns with Semirigid Connections: Elastica Approach

The large-deflection elastic analysis of slender beam-columns of symmetrical cross sections with semirigid connections under end loads (forces and moments) including the effects of out-of-plumbness is developed in a classical manner. The classical theory of the “Elastica” and the corresponding elliptical functions are utilized in the proposed method which can be used in the large-deflection stability analysis of slender beam-columns with rigid, semirigid, and simple connections under any combination of end loads (conservative and nonconservative). The proposed method consisting of a closed-form solution of the Elastica can also be utilized in the large deflection analysis of beam-columns whose connections suffer from flexural degradation or, on the contrary, flexural stiffening. The main limitation of the Elastica is that only flexural strains are considered (the effects of axial and shear strains are neglected). Therefore results from the proposed method are theoretically exact from small to very large curvatures and transverse and longitudinal displacements for plane beam-columns under bending actions. The large-deflection analysis of a beam-column with flexible connections at both ends becomes a complex problem requiring the simultaneous solution of at least two highly nonlinear equations with elliptical integrals. The solution of this problem becomes even more complex when the end connections are nonlinear or the direction of the applied end load changes (like “follower” loads). The validity and effectiveness of the proposed method and equations are verified against available solutions of very large deflection elastic analysis of beam-columns. Four comprehensive examples are included for verification and easy reference.