金属加筋板压缩稳定性分析的随机缺陷法

为使金属加筋板稳定性分析更加真实可靠,在分析中引入随机的初始几何缺陷,采用一致缺陷法通过ANSYS对金属加筋板进行压缩稳定性有限元分析,总结一致缺陷法的优缺点,进而提出一种考虑加筋板初始几何缺陷的随机缺陷法并进行试验.结果表明:一致缺陷法对非线性变形分析有一定的引导作用,使非线性变形朝着特征值屈曲模态的方向发展;随机缺陷法将结构的初始缺陷看作是随机的,缺陷大小和分布无法预测,更能反映加筋板真实的工作性能.编写加筋板自动建模程序和随机缺陷自动分析程序,从而大大提高分析效率,使随机缺陷法用于设计成为可能.     

Stochastic inverse identification of geometric imperfections in shell structures

It is now widely known that the presence of geometric imperfections in shell structures constitutes an important contribution to the discrepancy between theoretical and experimentally realizable ultimate loads governed by buckling. The present paper describes a method by which an actual initial imperfection field may be estimated using the service load response of a shell structure. The approach requires solving a stochastic inverse problem wherein uncertainty regarding initial imperfection predictions is expressed within the context of a Bayesian posterior distribution. The proposed approach could be applied to condition assessment and performance evaluation activities in practice.     

Buckling analysis of imperfect frames using a stochastic finite element method

A stochastic finite element method is developed for the buckling analysis of frames with random initial imperfections, uncertain sectional and material properties. The random geometrical imperfections of the frames are described by member initial crookednesses which are modeled as given initial displacement functions with amplitudes treated as random variables. The effects of the random initial geometric imperfections are formulated as a set of equivalent random nodal coordinates in the finite element discretization of the members. The mean-centered second-order perturbation technique is used to formulate the stochastic finite element method for the buckling analysis of the imperfect frames. Use of the present method is illustrated by several examples of buckling analysis of random frames. Results derived from the Monte Carlo method are also obtained for comparison.     

Dynamic buckling of orthotropic shallow spherical shells

The dynamic axisymmetric behaviour of clamped orthotropic shallow spherical shell subjected to instantaneously applied uniform step-pressure load of infinite duration, is investigated here. The available modal equations, based on an assumed two-term mode shape for the lateral displacement, for the free flexural vibrations of an orthotropic shallow spherical shell is extended now for the forced oscillations. The resulting modal equations, two in number, are numerically integrated using Runge-Kutta method, and hence the load-deflection curves are plotted. The pressure corresponding to a sudden jump in the maximum deflection (at the apex) is considered as the dynamic buckling pressure, and these values are found for various values of geometric parameters and one value of orthotropic parameter. The numerical results are also determined for the isotropic case and they agree very well with the previous available results. It is observed here that the dynamic buckling load increases with the increase in the orthotropic parameter value. The effect of damping on the dynamic buckling load is also studied and this effect is found to increase the dynamic buckling load. It is further observed that this effect is more pronounced with increase in the rise of the shell.     

Application of folded plate analysis to bending,buckling and vibration of multilayer orthotropic sandwich beams and panels

A unified analysis method based on two-dimensional elasticity theory is outlined for evaluation of bending, buckling and vibration of multilayer orthotropic sandwich beams and panels. The effects of initial geometric imperfections are included. It is shown that beams or panels deforming under conditions of plain stress or plane strain may be treated as special instances of folded-plate structures using computer programs which are now widely available. Examples are given, including evaluation of stress contours in a sandwich panel under patch load and analysis of overall and local (face-wrinkling) buckling modes in sandwich panels with stiff and soft cores.     

Nonlinear dynamic buckling of spherical caps with initial imperfections

A finite difference method is developed for the large deformation elastic-plastic dynamic buckling analysis of axisymmetric spherical caps with initial imperfections. The problem formulation is based on governing differential equations of motion, treating the plastic deformation as an effective plastic load. Both perfectly plastic and strain hardening behavior are implemented in the program. Strain hardening is incorporated through use of the Prager-Ziegler kinematic hardening rule, so that the Bauschinger effect is accounted for. The solution for the large deformation elastic-plastic dynamic response of a spherical cap is compared very favorably with other findings. Two spherical cap models are selected to study the title problem. Results obtained indicate that both plastic yielding and initial imperfection play significant roles in reducing the load carrying capacity of these shell structures. Both increase their influence as the thickness to radius ratio and the imperfection magnitude increase, respectively. It is also found that dynamic effect has the influence of lowering load carrying capacity of perfect spherical caps; however, its influence on imperfect spherical caps depends on the magnitude of initial imperfections.     

Parametric instability of a circular cylindrical shell with geometric imperfections

The static and dynamic behavior of a compressed circular cylindrical shell having geometric imperfections is analyzed. The analysis is mainly performed by means of the Donnell’s nonlinear shallow-shell theory. However, the refined Sanders shell theory is also used for comparison. A suitable expansion of the radial displacement, able to describe both buckling and dynamic behaviors is developed; the effect of geometric imperfections is accounted for by means of a modal representation. The response of the shell subjected to a sinusoidal axial excitation at its ends, giving rise to a parametric excitation, is considered. The effect of imperfections on the critical value of the dynamic load, that causes the loss of stability of the system, is analyzed. Interesting nonlinear dynamic phenomena are observed: direct resonance with softening behavior and parametric instability with period doubling response.     

A sequel to the article “buckling analysis with the aska program system”

In the above-mentioned article [1]buckling of an axially compressed open cylindrical shell was used as a qualification test by comparing the ASKA results with experimental results published [2]. ASKA predicted bifurcation buckling at a load level slightly larger than that at which the shell collapsed in the experiment. However, the marked nonlinearities in the prebuckling range, reported in [2], could only be explained by assuming geometrical imperfections with an order of magnitude of the shell thickness. No indication, however, on the order of magnitude of possible imperfections in the experiment is given in [2].In a different publication [3] a complete numerical solution is presented for the considered problem, including specific imperfections in loading and geometry. This solution is evaluated, however, for slightly different dimensions, elasticity data and boundary conditions than those used in [1]and in [2].Thus, to confirm the ASKA results, one of the configurations evaluated in [3](including geometrical imperfections) has been reanalyzed, and fairly good agreement between the ASKA results and those of [3] has been obtained. The comparison gives some insight into the performance and limits of the buckling mode superposition method adopted in ASKA for the treatment of nonlinear prebuckling behaviour.     

Large deformation elastic-plastic buckling analysis of spherical caps with initial imperfections

Large deformation elastic-plastic buckling loads are obtained for axisymmetric spherical caps with initial imperfections. The problem formulation is based on equilibrium equations in which the plastic deformation is taken as an effective plastic load. Both perfectly plastic and strain hardening behavior are considered. Strain hardening is represented by the Prager-Ziegler kinematic hardening theory, so that the Bauschinger effect is accounted for. Solutions of elastic-plastic circular plates and spherical caps are in good agreement with previous results. For the spherical cap it was determined that both initial imperfection and plastic deformation have the same effect of reducing buckling capacity; as the magnitude of the imperfection increases, the influence of plastic deformation becomes less important. It is also found that the geometric parameter λ, which is used as an important factor in elastic response, becomes meaningless for the elastic-plastic buckling analysis of spherical caps.     

Further comparison of the numerical and experimental buckling behaviors of composite panels

Experimental buckling behaviors for fiber-reinforced, circular cylindrical panels under prescribed uniform end-displacement are compared with numerical buckling behaviors computed from an energy-based, finite-difference computer program.Buckling behaviors were obtained for five test panels with simply-supported straight edges and clamped curved edges, and for five test panels with unsupported straight edges.Numerical buckling behaviors were obtained for one panel from each of the two groups using measured initial transverse imperfections.Experimental buckling loads for test panels with simply-supported straight edges ranged from 4600 to 5775 lb. This range of experimental buckling loads was due principally to an inability to impose circumferential displacements precisely, and to differences between distributions of initial transverse imperfections for various test panels. Numerical computations using measured initial transverse imperfections and boundary conditions along the straight edges that allowed circumferential displacements to either occur freely or to be completely restrained tend to confirm these assertions. Favorable agreement was observed, since the experimental buckling loads were included between the two limiting numerical buckling loads (4505 and 6106 lb).Experimental buckling loads for test panels with unsupported straight edges ranged from 2165 to 2715 lb. This range of experimental buckling loads was due principally to differences between distributions of initial transverse imperfections for various test panels, and, possibly, small initial stresses that accompany installation of a test panel in the testing device. Numerical computations indicate that the experimental buckling loads are associated with a limit point that correspond to equilibrium configurations remote from the equilibrium configuration corresponding to buckling of the straight edges. The computed buckling load (2500 lb) compared favorably with the experimental buckling (2715 lb) corresponding to the initial imperfections used to calculate the numerical buckling load.     

Buckling and postbuckling of circular plates containing concentric penny-shaped delaminations

Buckling and postbuckling analyses of circular laminated composite plates with delaminations are presented. An axisymmetric finite element model based on a layer-wise laminated composite plate theory is developed to formulate the problem. Geometric nonlinearity in the sense of von Kármán and imperfections in the form of initial global deflection and initial delamination openings are included. A simple contact algorithm which precludes the physically inadmissible overlapping between delaminated surfaces is proposed and incorporated into the analysis.

Numerical results are obtained addressing the effects of the initial imperfections, the number of delaminations and their sizes on the critical buckling load and buckling mode shapes as well as postbuckling responses.     

Optimization of shell buckling incorporating Karhunen-Loève-based geometrical imperfections

The optimization of shell buckling is performed considering peak normal force and absorbed internal energy in the presence of geometrical imperfections implemented through Karhunen-Loève expansions. Initially, the mass of a shell is minimized in the presence of random initial imperfections by allowing cutouts in the material, subject to constraints on the average peak force and average internal energy. Then, robustness is considered by minimizing the coefficient of variation of the normal peak force while constraining the average peak force and average internal energy. LS-OPT® is used both to generate an experimental design and to perform a Monte Carlo simulation (96 runs) using LS-DYNA® at each of the experimental design points. The effect of imperfections when minimizing the mass is not large, but when considering robustness, however, the optimal design has a substantially increased hole size and increased shell thickness, resulting in a heavier design with maximal robustness within the constraints.     

Optimization of geometrically imperfect stiffened cylindrical shells under axial compression

A procedure is outlined for optimizing stiffened, thin, circular, cylindrical shells under uniform axial compression against general instability, in the presence of initial geometric imperfection. The procedure consists of two parts (a) optimization on the basis of a linear buckling analysis and perfect geometry, and (b) parametric studies on a reasonable region in the design space surrounding the optimum point (as obtained from part (a)) to assess the effect of initial geometric imperfections. This procedure is demonstrated through two design examples, for which it is concluded, that the presence of initial geometric imperfections does not alter the optimum weight and the corresponding design variables appreciably.     

Inelastic stability of laterally unsupported i-beams

A computer method to study the inelastic stability of laterally unsupported steel I-beams and based on a general non-linear theory is presented.Traditionally, the problem of flexural-torsional stability of beams is treated as a lateral buckling problem. Some of the draw-backs of these earlier studies are given below:The classical theory assumes that the deformations are small. In addition the deformation field is linearized. This theory is therefore valid only when the major axis flexural rigidity is much greater than its minor axis rigidity, so that deformations before the onset of lateral buckling are negligible.The lateral buckling theory is valid for straight beams, with loads applied rigorously in the plane of symmetry. Practical beams have initial imperfections and unavoidable load eccentricities. So the true behavior is better described by the stability phenomenon.For beams of intermediate length for which buckling occurs in the inelastic range, the tangent modulus theory is generally used. For ideally straight beams the tangent modulus theory provides an estimate for the collapse load which is slightly conservative. However, for practical beams with initial deformations, this need not be the case.In the majority of existing studies on inelastic lateral buckling, the differential equations for beams under uniform moment are used without modification for beams under moment gradient. In the later case the shear center line is inclined to the centroidal and geometrical axes. The differential equations for beams under uniform moment should therefore be modified by adding additional terms.The majority of the existing studies are limited to the behavior of isolated beams with simple end-conditions and so the beneficial effect of adjacent members on the beam collapse load cannot be studied accurately.A general non-linear theory to describe the spatial behavior of beams and that doesn't have the deficiencies mentioned above, is developed in the present paper.The paper also presents a computer method of solving these non-linear equations using the method of finite differences. Several numerical examples presented and comparison with the existing theoretical and experimental results show the applicability of the theory to a wide range of problems.     

A numerical study of dynamic pulse buckling of ring-stiffened cylinders

Ring-stiffened cylinders are primary components of civilian and military structures which may be subject to impulsive loads that can induce a dynamic buckling response. Over the past 30 years there have been analytical, numerical and experimental investigations of dynamic pulse buckling of unstiffened cylinders, but no known references have been found which consider the effects of a ring-stiffener on the response. This paper presents a comparative finite element numerical study of the effect of a ring-stiffener and its size and spacing on the dynamic buckling response of a cylinder. Dynamic buckling behaviour is established by monitoring the nonlinear growth of initial shape imperfections in the finite element models in response to a uniform initial velocity. The finite element results show that the predominant harmonics and amplitudes of response are affected by the addition of, and the size and spacing of, a ring-stiffener. For a given initial impulse value, the addition of a ring-stiffener causes the predominant harmonics and amplitudes of response to be reduced. A variation in the modal content of the dynamic buckling modeshape from the ring-stiffener to midbay position also occurs. Results also show that pulse buckling theory, with effective radius to thickness ratios for the combined ring-stiffened shell, can give a reasonable estimate of the critical buckling modes.     

Design sensitivity analysis with isoparametric shell elements

This paper deals with design sensitivity calculation by the direct differentiation method for isoparametric curved shell elements. Sensitivity parameters include geometric variables which influence the size and the shape of a structure, as well as the shell thickness. The influence of design variables, therefore, may be separated into two distinct contributions. The parametric mapping within an element, as well as the influence of geometric variables on the orientation of an element in space, is accounted for by the sensitivity calculation of geometric variables, and efficient formulations of sensitivity calculation are derived for the element stiffness, the geometric stiffness and the mass matrices. The methods presented here are applied to the sensitivity calculations of displacement, stress, buckling stress and natural frequency of typical basic examples such as a square plate and a cylindrical shell. The numerical results are compared with the theoretical solutions and finite difference values.     

Structural optimization with member dimensional imperfections

The paper deals with the effect of dimensional imperfections of truss members on the minimum weight design of a structure. It is assumed that for each element its imperfections cannot exceed given a priori maximum values, called tolerances. The incorporation of the considered imperfections into the design is achieved by diminishing the limit values of state functions by the product of assumed imperfections and appropriate sensitivities. Therefore, the given method allows the introduction of tolerances into the design in a relatively simple way. In the submitted paper both members’ cross-section and length imperfections are discussed. The paper is illustrated with several design examples, considering cases with multiple loading conditions and buckling analysis. The achieved optimum solutions for designs with admissible tolerances show significant differences in structural weight and material distribution compared to ideal structures (i.e. having nominal dimensions). The calculations for designs with buckling analysis also reveal changes in material distribution compared to the designs without buckling constraints.     

Dynamic buckling of axisymmetric spherical caps with initial imperfections

Dynamic buckling loads are obtained for axisymmetric spherical caps with initial imperfections. Two types of loading are considered, namely, step loading with infinite duration and right triangular pulse. Solutions of perfect spherical caps under step loading are in excellent agreement with previous findings. Results show that initial imperfections do indeed have the effect of reducing the buckling capacity for both dynamic and static responses, although they are affected in a different manner. From the solutions obtained for triangular pulse situations, it is revealed that pulse duration has a very significant impact on the magnitude of the dynamic buckling load. When comparing these solutions with those of step loading, it is concluded that the step loading with infinite duration is the limiting case of a triangular pulse, and that the step loading provides the most severe loading situation for dynamic analysis.     

On finite element large displacement and elastic-plastic dynamic analysis of shell structures

Finite element procedures for nonlinear dynamic analysis of shell structures are presented and assessed. Geometric and material nonlinear conditions are considered. Some results are presented that demonstrate current applicabilities of finite element procedures to the nonlinear dynamic analysis of two-dimensional shell problems. The nonlinear response of a shallow cap, an impulsively loaded cylindrical shell and a complete spherical shell is predicted. In the analyses the effects of various finite element modeling characteristics are investigated. Finally, solutions of the static and dynamic large displacement elastic-plastic analysis of a complete spherical shell subjected to external pressure are reported. The effect of initial imperfections on the static and dynamic buckling behavior of this shell is presented and discussed.