Effects Of Initial Imperfections Research Articles

Stability Analysis of Symmetric Laminated Composite Plates with Geometric Imperfections Under Longitudinal Temperature Gradient

AbstractThermal buckling behaviour of rectangular laminated composite plates with initial geometrical imperfections is investigated in this article. The equilibrium, stability, and compatibility equations of an imperfect composite plate are derived using the first order shear deformation plate theory. The plate is assumed to be under longitudinal temperature rise. Resulting equations are used to obtain the thermal buckling load of the composite plate in closed-form solutions. The effect of initial imperfections on buckling loads are discussed.

Shear Failure of Pultruded Fiber-Reinforced Polymer Composites under Axial Compression

When structural elements are subjected to compressive loads, the shear forces and stresses induced by second-order effects may lead to shear failure prior to compressive failure. This is particularly likely to occur in the case of pultruded glass fiber-reinforced polymer profiles, which normally exhibit low shear strength in relation to compressive strength. This paper analyzes the effects of initial imperfection, slenderness, shear-to-compressive strength ratio, shear coefficient, and type of shear failure criterion on ultimate load and failure mode (shear or compressive failure). A formulation for predicting ultimate load based on shear failure and second-order deformation is proposed. The results obtained compare well with similar results obtained using other methods and experimental data available in literature. The proposed method is based strictly on mechanics and thus requires no fitting to experimental data.

Buckling Modes of Thin Circular Cylindrical Shells Under Fundamental Loads

O VER the past 100 years, much research has been directed at circular cylindrical shell buckling. One area of particular interest is in clarifying the reasons for the discrepancy between theoretical and experimental buckling stress of thin isotropic circular cylindrical shells, especially under axial compression. Postbuckling behavior, initial imperfections, or boundary conditions have been used to explain the discrepancy, although the main causes are now considered to be the effects of initial imperfections and their relationship to postbuckling characteristics [1,2]. The effects of boundary conditions, on the other hand, were discussed by Hoff [3], who showed that axial buckling stress calculated for the special boundary conditions is one-half of the classical value. The employed boundary conditions, however, are considered to be unrealistic [4]. Yoshimura [5] attributed postbuckling characteristics under axial compression to the developability of the initial cylindrical surface; that is, the Gauss curvature equals zero. The postbuckling mode presented by Yoshimura is a developable polyhedral surface (Fig. 1a) that is different from the chessboard-type (rectangle-type) mode andwas named the “Yoshimura pattern” byHoff et al. [6]. Key references related to the present problem are found in texts by Yamaki [7] and Singer et al. [8]. In recent years, numerous studies have focused on buckling of composite or laminated cylindrical shells. For example, Riddick and Hyer [9] employed finite element analysis for segmented circular composite cylindrical models under axial compression, ultimately showing calculated postbuckling modes. Here, it is shown that the developability of cylindrical surfaces also leads to buckling mode patterns under torsional load (Fig. 2a) and external lateral pressure (Fig. 2b). Such developability leads to buckling and postbuckling characteristics that are quite different from flat-plate problems. In other words, the developability provides the mechanics of the cylindrical shell buckling process. It is concluded that 1) Buckling and postbuckling modes under axial compression should be the same. 2) The number of waves may change during the postbuckling process. Moreover, the axial buckling modes should be similar to the modes described by Yoshimura [5], being different from the socalled chessboard pattern that has been traditionally been used in previous studies.

Nonlinear in-plane behavior of circular steel arches with hollow circular cross-section

In this work the nonlinear in-plane behavior of circular arches with hollow circular cross-section is investigated. The influence of a number of design parameters, such as the boundary conditions, the rise-to-span ratio, and the included angle on the strength is presented. Moreover, the effect of other behavior factors, such as the geometrical and material nonlinearities and the initial imperfections, is investigated. A criterion for the prediction of the type of nonlinear behavior of arches is given, and a formula for the determination of the nonlinear buckling load is proposed. It is found that the effect of initial imperfections on the strength depends largely on the arch slenderness and the imperfection magnitude in the case of shallow arches. When arches are deep this dependence becomes less significant. The effect of geometrical nonlinearity depends significantly on the shallowness and the slenderness of the arches. Stocky arches are less influenced by the rise-to-span ratio than slender ones. The effect of boundary conditions depends significantly on the shallowness of arches and the arch slenderness. The reduction of strength is larger in slender arches than in stocky ones.

Buckling strength of uniaxially compressed orthogonally stiffened plates

The bucking strength calculation includes the determination of global buckling strength, the effective plate width and the torsional buckling strength of open section stiffeners. In each calculation the classic strength formula should be modified considering the effect of initial imperfections and residual welding stresses. The calculation method of Det Norske Veritas design rules and the Eurocode 3 are compared to each other.

Analysis of the failure mode and softening behaviour of sands in true triaxial tests

This paper presents a theoretical analysis and a numerical study of the failure mode in sands based on a hypoplastic description of the material. A bifurcation analysis is performed to study the failure mode in sands under true triaxial stress conditions at the material response level. It is shown that either uniform failure or localized failure can occur, depending on the intermediate principal stress. Uniform bifurcation occurs in tests along stress paths with a lower Lode angle, including the stress path for a conventional triaxial compression test. Localized failure occurs in tests along stress paths with a higher Lode angle, including stress paths for biaxial compression and triaxial extension tests. Specimen responses under laboratory conditions are then studied numerically by 3D FE simulations of biaxial compression, triaxial compression, and triaxial extension tests. The effects of initial imperfection from a homogeneous state are taken into account by introducing a frequency distribution of the initial void ratio. This permits the softening behaviour and shear localization in sand specimens to be analysed for different degrees of initial heterogeneity.

Optimum design of stiffened plates

In this overview of loaded stiffened plates various types, loadings, and stiffener shapes are investigated. Mikami and API methods are used for the optimum design and comparison of the two methods. Both methods consider the effect of initial imperfection and residual welding stresses, but their empirical formulae are different. The elastic secondary deflection due to compression and lateral pressure is calculated using the Paik's solution of the differential equation for orthotropic plates, and the self-weight is also taken into account. The unknowns are the thickness of the base plate as well as the dimensions and number of stiffeners. The cost function to be minimized includes two kinds of material and three kinds of welding costs.

Effect of Initial Imperfections on Thermal Buckling of Functionally Graded Plates

ABSTRACT Thermal buckling analysis of rectangular functionally graded plates with initial geometrical imperfections is presented in this article. The equilibrium, stability, and compatibility equations of an imperfect functionally graded plate are derived using the first-order shear deformation plate theory. It is assumed that the nonhomogeneous mechanical properties of the plate, graded through the thickness, are described by a power function of the thickness variable. The plate is assumed to be under three types of thermal loading, namely: uniform temperature rise, nonlinear temperature rise through the thickness, and axial temperature rise. Resulting equations are employed to obtain the closed-form solutions for the critical buckling temperature change of an imperfect functionally graded plate. The influence of transverse shear on thermal buckling load is discussed.

Initial Imperfection Models for Segments of Line Pipe

Initial imperfections have long been acknowledged as having an effect on the behavior of shell structures, affecting both the global and local behavior. Yet, despite their significance, initial imperfections are rarely included in analytical models for pipelines. This is usually because of the complicated nature of initial imperfections, the difficulty in measuring them, and the small amount of available literature that describes their geometry. Some recent investigations at the University of Alberta in Edmonton have focused on the effect of initial imperfections on the behavior of segments of line pipe. Imperfections measured across the inside surface of pipe test specimens were incorporated into a finite element model that was developed to predict the experimental behavior of the specimens tested under combined loads of internal pressure, axial load and bending moment. Test-to-predicted ratios for the load carrying capacity of the test specimens had a mean value of 1.035 with a coefficient of variation of 0.047. The improvements in the accuracy of the finite element analysis models that include the initial imperfection pattern indicate their importance in modeling the experimental behavior. Once the importance of initial imperfections was established, idealized patterns were developed to simplify numerical modeling. This paper presents the results of different patterns investigated for both plain and girth-welded segments of line pipe and provides recommended simplified assumed initial imperfection patterns.

Sensitivity analysis of the effect of initial imperfections on the (i) ultimate load and (ii) fatigue behaviour of steel plate girders

Abstract The study is divided into two parts: (i) in the first one, the plate girder (Fig 1) is considered to be exposed to quasi‐constant loading (ie to loads which are either constant or repeated in a very small number of cycles), while (ii) in the other one, the girder is assumed to be subjected to repeated loading. Then it is understandable that the objective of the first part should be to look into the influence of initial imperfections on the static ultimate load of the girder related to the formation of a plastic failure mechanism in it, while that of the second part was to study the effect of imperfections on the stress state under considerably lesser loads, viz under such as to correspond to the development of fatigue cracks in the girder and, consequently, to its fatigue limit state. In this case the state of stress was measured by bending stresses developing in the crack‐prone areas (Fig 4) of the web “breathing” under the repeated loads, which ‐as demonstrated by the Prague experiments ‐ occur...

A semi-analytical method for the elastic–plastic large deflection analysis of stiffened panels under combined biaxial compression/tension, biaxial in-plane bending, edge shear, and lateral pressure loads

In the earlier publications [Paik JK, Thayamballi AK, Lee SK, Kang SJ. A semi-analytical method for the elastic-plastic large deflection analysis of welded steel or aluminium plating under combined in-plane and lateral pressure loads. Thin-Walled Struct 2001;39;125–52; Paik JK, Thayamballi AK. Ultimate limit state design of steel-plated structures. Chichester: Wiley; January 2003], the author presented a semi-analytical method for the elastic–plastic large deflection analysis of unstiffened plates under biaxial loads, edge shear, biaxial in-plane bending and out-of-plane (lateral) pressure loads until the ultimate strength is reached. In the present paper, a similar method is applied to stiffened panels subjected to the same type of loading. The effect of initial imperfections in the form of initial deflection and welding residual stresses is accounted for in the calculations. The validity of the developed method is demonstrated by comparing with existing theoretical and numerical results where relevant. The present theory can be useful for ultimate strength analysis of plates and stiffened panels made of steel or aluminium alloys.

Nonlinear buckling of imperfect systems with symmetric imperfections

The nonlinear stability of a 2-DOF imperfect elastic system with symmetric imperfections under a concentrated load is thoroughly discussed using an analytical approach. The perfect system loses its stability via an unstable symmetric bifurcation, which upon inclusion of imperfections is degenerated to a limit point. In this paper, it is shown that when the imperfections are symmetric, the system loses its stability through an unstable symmetric bifurcation point lying on the nonlinear prebuckling path. The corresponding critical (bifurcational) load is much lower than the limit point load related to symmetric buckling. The effect of initial imperfections on the critical bifurcational load (imperfection sensitivity) is also analytically discussed in detail. The paper is supplemented by various numerical results.

一葉双曲面RC造冷却塔の構造特性に及ぼす形状不整の影響の分析 : 実測された形状の再現モデルを用いた損傷・耐力評価

In the inland in Europe and America, construction case of many reinforced concrete cooling towers exists mainly on the power plant which is hard to utilize much cooling water. It is long in the history of such tower construction, and many towers constructed in 40〜70's are used at present. In China and India, the construction of towers in the power plants increases. In such situation, it is reoorted that the collapse accidents by the gust repeatedly arose in United Kingdom and France in a past. Investigation of the cause of those accidents and examination of the countermeasure are developing, and the evaluation of the safety of the existing facilities becomes important problem. On the thin RC shells for these towers, the much research analyzes buckling / vibration problem and effect of initial imperfection on structural properties, and the proposal of design guidelines has been made. To begin with, using the initial imperfection of the distribution idealized axisymmetrically and asymmetrically, a useful knowledge on fundamental phenomenon and analysis method were obtained, and the recommendations for the tolerance limit of the initial imperfection magnitude were proposed. It was analyzed that according to the many leading research results. the fluctuation of meridian direction in-plane stress by initial imperfection was inversely proportional to the shell thickness due to dead weight and wind load within elastic stress analysis, and that it largely affects meridian direction in-plane stress and circumferential direction bending stress for the circumferential curvature error. In addition. partial initial imperfections with small amplitudes play a major role in meridian and circumferential stresses. Concerning the characteristic of initial imperfection itself, the probability-statistical technique for simulating the spatial distribution property is examined, and the statistical analysis procedure to simulate the effect of imperfection on the stress and buckling load is proposed. Recently, the effect of material nonlinearity of RC members on the ultimate strength also became remarkable problem by some researches. In this study, the three-dimensional distribution of the geometric error based on the reported measured data in the shell surface is reproduced numerically in detail for the tower which caused the collapse accident in a past, and the spatial distribution characteristic is analyzed. Next, the effect of the geometric imperfection of reoroduced shape on elastic stress distribution due to dead weight is examined, and the effect on the wind resistance performance is examined by the elasto-plastic analysis. In addition, the evaluation on the performance of the tower by the thermal stress is made, and the numerical examination on the reinforcing method of the tower is tried. By this study, some results shown below were obtained. Reproduced geometric imperfection widely exists for the shell full face, and it becomes a waveform which recurs in circumferential and meridian direction, and the complicated distribution in which the component which recurs periodically overlaps with the local component is shown. The peak of the imperfection component exists from N=0(axisymmetric) to N=5 on the circumferential direction and from 0 to 10(cycle/100m)in the height direction. ・ The possibility of changing to tension from compression exists on hoop stress due to dead load within large area by the effect of the imperfection. ・Due to wind load, the bending cracks develop in the windward of the imperfect shell, and next, it leads to the failure of the tower by the tension which arises by the bending of the meridian direction. This situation is similar to the thing for the perfect shell. From the result shown in the model which reoroduced the imperfection, the turbulence of the remarkable section forces existed further than the case of the perfect shell, and the result of predicting the l

Effects of imperfections of the buckling response of composite shells

The results of an experimental and analytical study of the effects of initial imperfections on the buckling response and failure of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The shells considered in the study have six different shell-wall laminates two different shell-radius-to-thickness ratios. The shell-wall laminates include four different orthotropic laminates and two different quasi-isotropic laminates. The shell-radius-to-thickness ratios includes shell-radius-to-thickness ratios equal to 100 and 200. The numerical results include the effects of traditional and nontraditional initial imperfections and selected shell parameter uncertainties. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The nontraditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. The cylinder parameter uncertainties considered include uncertainties in geometric imperfection measurements, lamina fiber volume fraction, fiber and matrix properties, boundary conditions, and applied end load distribution. Results that include the effects of these traditional and nontraditional imperfections and uncertainties on the nonlinear response characteristics, buckling loads and failure of the shells are presented. The analysis procedure includes a nonlinear static analysis that predicts the stable response characteristics of the shells, and a nonlinear transient analysis that predicts the unstable response characteristics. In addition, a common failure analysis is used to predict material failures in the shells.

Effects of imperfections on the buckling response of compression-loaded composite shells

The results of an experimental and analytical study of the effects of initial imperfections on the buckling and postbuckling response of three unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells with different orthotropic and quasi-isotropic shell-wall laminates are presented. The results identify the effects of traditional and non-traditional initial imperfections on the non-linear response and buckling loads of the shells. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The non-traditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, non-uniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity non-linear shell analysis procedure that accurately accounts for the effects of these traditional and non-traditional imperfections on the non-linear responses and buckling loads of the shells is described. The analysis procedure includes a non-linear static analysis that predicts stable response characteristics of the shells and a non-linear transient analysis that predicts unstable response characteristics.

Effects of initial imperfections on nonlinear behaviors of thin-walled members

The effect of the initial imperfections on the nonlinear behaviors and ultimate strength of the thin-walled members subjected to the axial loads, obtained by the finite element stability analysis, are examined. As the initial imperfections, the bucking mode shapes of the members are adopted. The buckling mode shapes of the thin-walled members are obtained by the transfer matrix method. In the finite element stability analysis, isoparametric degenerated shell element is used, and the geometrical and material nonlinearity are considered based on the Green Lagrange strain definition and the Prandtl-Reuss stress-strain relation following the von Mises yield criterion. The U-, box- and I-section members subjected to the axial loads are adopted for numerical examples, and the effects of the initial imperfections on the nonlinear behaviors and ultimate strength of the members are examined.

Finite strip analysis of laminated plates with general initial imperfection under end shortening

Description of a finite strip method is given for predicting the post-buckling response of rectangular laminated plates when subjected to progressive end shortening. Initial imperfection in very general shape is also included. Polynomial expression is used to simulate the actual imperfection along each nodal line while the deformations are represented by trigonometric series. The analysis, under the assumption that thin plates are used, is based on the classical plate theory. Geometric non-linearity is introduced in the strain-displacement equations in the manner of the von Karman assumptions. The Newton–Raphson method is used to solve the non-linear equilibrium equations. A number of applications involving both isotropic and laminated plates are described to investigate the effects of initial imperfection.

Effect of Initial Imperfections on the Flexural Eigenvibrations of Cylindrical Shells

The effect of small initial deviations from the ideal circular shape of a shell on the frequencies and modes of flexural eigenvibrations is studied with the use of the linear theory of thin shallow shells. It is assumed that the initial deviations are responsible for interaction between flexural and radial vibrations of the shell. The modal equations are derived by the Bubnov—Galerkin method. It is shown that the initial deviations from the ideal circular shape split the flexural vibration spectrum, and the fundamental frequency decreases compared to that of the ideal shell.

Initial imperfections and the initiation of wrinkling in finite element modelling of deep drawing

The effect of initial imperfections on the initiation of wrinkling in finite element models of deep drawing operations is assessed. Models of an annular plate are subjected to radial in-plane loading and the effects of different types, magnitudes and distributions of imperfections are investigated. A model of a circular plate subjected to out-of-plane loading from a punch and die is similarly investigated and the results are compared with experimental data. It is confirmed that initial imperfections are an essential requirement for the initiation of wrinkling for the case of in-plane loading. Initial imperfections are shown to be unimportant in the initiation of wrinkling for the case of out-of-plane loading.

Finite Element simulation of dynamic buckling of cylinders subjected to periodic shear

This paper deals with the buckling of cylindrical shells under a dynamic shear load. The aim of our study is to compare static buckling load and buckling load during a sweep frequency excitation. First, we describe the special experimental device and the two Finite Element codes used in this study. In a second part static tests and corresponding Finite Element calculations are presented in order to have a reference buckling load and to understand the effect of initial imperfections. Then, a vibration analysis is performed in order to investigate the effect of geometric imperfection and a preload. In the last part, we discuss dynamic results. When we reach the first eigen frequency, the buckling load drops and the buckling deformations increase due to a parametric resonance. There is a coupling between vibration and buckling modes.