Buckling of eccentrically stringer-stiffened cylindrical panels under axial compression

This paper investigates the effects of boundary conditions and panel width on the axially compressive buckling behavior of eccentrically stringer-stiffened circular cylindrical panels. Numerical results are presented for eight different sets of boundary conditions along the straight edges of the panels. As the panel width is increased, the results show that the complete cylinder buckling load is reached only for one set of boundary conditions (SS3, classical simple support conditions). However, for 180° and wider panels, the panel buckling loads are within ± 10% of the complete cylinder load for all cases except SS1 panels (free in-plane edge displacements) with outside stringers. Low buckling loads, as low as half the complete cylinder load, are found for some SS 1 panels. It is also observed that the prevention of circumferential edge displacement is the most important in-plane boundary condition from the point of view of increasing the buckling load, and that the prevention of edge rotation (i.e. clamping) in the circumferential direction is more effective in increasing the buckling loads of panels with free circumferential edge displacement υ that it is for panels with υ = 0. From stringer-eccentricity studies, it is shown that buckling loads are generally at least 40–50% higher for the case of outside stringers, and that eccentricity effects are generally similar for clamped and simply supported panels with the same in-plane boundary conditions.     

Buckling and postbuckling of imperfect cylindrical shells under axial compression

A solution methodology is described for the complete analysis of a geometrically imperfect, thin, circular, cylindrical shell loaded by a uniform axial compression. The analysis includes pre-limit point behavior, the establishment of critical conditions (limit point) and post-limit point behavior. The solution scheme is then utilized to study the effects of various geometrical parameters (radius to thickness and length to radius ratios) on the response characteristics of an imperfect, unstiffened, thin, cylindrical shell. These effects are assessed for a virtually axisymmetric-type of geometric imperfection.     

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.     

轴向冲击下波纹腹板梁的失稳控制和能量吸收

针对Sine波纹腹板梁结构,通过设计其初始振幅缺陷,控制不同波形阶数下波纹梁的失稳模态,引导上下翼板按预期渐进、稳定、可重复的压溃变形模式发展.采用Abaqus/Explicit中的显式动力学方法数值模拟初始振幅缺陷与比吸能(Specific Energy Absorption,SEA)的关系.通过对比低阶、中阶和高阶波形的载荷-位移曲线说明波形阶数对吸能特性和失稳控制的影响.结果表明:对于给定的波形阶数,存在初始振幅缺陷的临界值使Sine波纹腹板梁结构达到预期的临界失稳状态,同时SEA最大;初始振幅缺陷越大,失稳控制越容易,但吸能效果随之降低.     

Buckling of cylindrical shells with spiral stiffeners under uniform compression and torsion

This paper investigated the general instability of cylindrical shells in which the stiffeners formed spirals along the length and at an arbitrary angle with the axis. Two loading conditions were considered: uniform axial and lateral compressions and torsion. The stress-strain relations of the stiffeners were developed by rotation of the strain tensor. The buckling determinate was obtained by introducing into the equilibrium equations the admissible displacement functions consistent with the end constraints, thereby enforcing equilibrium by satisfying the characteristic equations.

The buclking equations were programmed for a computer which rearched through a finite set of stress resultants for assigned values of spiral angle and modes and printed out the buckling load. The optimum structure weight of the stiffened shell was determined by iterating the design parameters at the required spiral angle so that the buckling load approached the applied load as a limit until the difference between these loads was within the design allowance.     

Buckling length of non-uniform members under stepped axial loads

In this paper an axially compressed non-uniform column connected with beams at its two ends is studied. The stepped axial loads act eccentrically on the column at intermediate points. The non-linear equilibrium equations of this model are established in the case of non-sway and sway mode, respectively. Using these equations and following an iteration procedure, the equivalent buckling length coefficients and the corresponding critical loads are obtained and the results are presented in an easy to use graphical form.     

Weight optimization of stiffened cylinders under axial compression

A procedure is developed for the design of a stiffened cylinder under a given uniform axial compression with minimum weight. The approach allows the consideration of various shapes of stiffening members. The effective stiffness of the skin in its post-buckled state is taken into account in the basic analysis. The buckling analyses are accomplished as a minimum problem in the buckling mode shape parameters space using the variable metric method. A mixed procedure which combines the exterior penalty function concept and random search is used to minimize the weight of the stiffened cylinders. The design examples demonstrate the validity of the present approach.     

Weight optimization of stiffened cylinders under axial compression

A methodology is developed, by which one may design a stiffened cylinder of specified material, radius, and length, such that it can safely carry a given uniform axial compression with minimum weight. The solution procedure is divided into two stages, Phase I and Phase II. In Phase I, an unconstrained minimization is performed against one of the active constraints (in this paper-general instability) and data are generated in a sufficiently large region of the design space by employing efficient mathematical search techniques, in Phase II, these data are employed to arrive at the minimum weight configuration that satisfies all other constraints. Two design examples are presented which demonstrate the methodology.     

Buckling of cylindrical shells under the action of nonuniform external pressure

Over the last few decades, storage tanks have become bigger and thinner. Because of this, the buckling capacity of these cylindrical shells may well be the determining factor of shell thickness. In this paper, the critical buckling load of isotropic and orthotropic cylinders subjected to different types of wind load distributions is investigated. The prebuckling displacements are obtained by using the membrane theory of shell analysis. The principle of minimum potential energy in conjunction with Ritz's approach is used to obtain the stability matrix. The size of the stability matrix in this analysis is (81 × 81). By solving the stability matrix as an eigenvalue problem, the critical pressures are obtained as eigenvalues and the deflection shapes as eigenvectors. In the present study cylindrical shells of various dimensions, which are fixed at the base and free at the top, are investigated. The buckling load curves for isotropic and orthotropic cylinders of various dimensions are given for practical use.     

Thermo-elastoviscoplastic snapthrough behavior of cylindrical panels

The thermo-elastoviscoplastic snapthrough behavior of simply supported cylindrical panels is investigated. The analysis is based on nonlinear kinematic relations and nonlinear rate-dependent unified constitutive equations which include both Bodner-Partom's and Walker's material models. A finite element approach is employed to predict the inelastic buckling behavior. Numerical examples are given to demonstrate the effects of several parameters which include the temperature, thickness and flatness of the panel. Comparisons of buckling responses betweeen Bodner-Partom's model and Walker's model are given. The creep buckling behavior, as an example of time-dependent inelastic deformation, is also presented.     

Buckling analysis of ring-stiffened oval cylindrical shells

An energy principle is employed to derive the equations governing the stability of a simply-supported, eccentrically ring-stiffened, oval, orthotropic cylindrical shell. The kinematic relations used are those of Love-type shell theory and the effect of reinforcing rings is accounted for by a distributed stiffness approach. The cylinder is subjected to a combination of uniform axial and lateral pressures.

It is determined that the domain of stability of such a stiffened cylinder is bounded by two distinct solutions, herein denoted as corresponding to ‘long’ and ‘short’ axial wavelengths, with the extent of the short wavelength solution being dependent upon the degree of stiffening afforded by the rings.

The analysis of the effects of ring eccentricity shows that ovals are affected in a similar manner to circular cylinders in that outside rings provide the greatest capacity for sustaining axial compression, while inside rings are capable of supporting the greatest lateral pressure.

Finally, it is found that the buckling load of an oval cylinder under uniform lateral pressure slightly exceeds the corresponding value for an equivalent circular cylinder. As a further verification of this phenomenon, a Rayleigh-Ritz procedure is employed to determine the buckling load of an oval ring under uniform radial load. The results of this analysis corroborate those obtained for the cylinder.     

Considerations of cutouts in composite cylindrical panels

Over the past five years the Air Force Institute of Technology has been carrying out an investigation of small and large unreinforced cutout effects on composite cylindrical panels acting under compressive axial loads. Some of the original findings are reviewed and, in addition, new results are presented relating to different loading conditions. In general, not only does a small cutout reduce the panel's collapse load by at least 50%, but the cutout's position and size have further effect.     

Reliability-based optimum design of a welded stringer-stiffened steel cylindrical shell subject to axial compression and bending

The economy of stiffened shells vs the unstiffened version depends on loading, type of stiffening and stiffener profile. The stiffening is economic when the shell thickness can be decreased in such a measure that the cost savings caused by this decreasing is higher than the additional cost of stiffening material and welding. The present work deals with cylindrical shell columns fixed at the bottom and free at the top subject to axial compression and horizontal force acting on the top of the column. The shell is stiffened outside with stringers welded by longitudinal fillet welds. Half rolled I-section (UB) stiffeners are used to reduce welding cost. The cost function to be minimized includes the costs of the materials, forming of shell elements into the cylindrical shape, assembly, welding and painting. The design variables are the shell thickness, number and profile of stiffeners for the stiffened shell, but only the first type of variable in the unstiffened case. Randomness is considered both in loading and material properties. A level II reliability method (first-order reliability method) is employed. Individual reliability constraints related with shell buckling, stringer panel buckling and the limitation of the horizontal displacement of the column top are considered. The overall structural reliability is obtained by using Ditlevsen's method of conditional bounding. The costs of both the stiffened and unstiffened shells designed to ensure a stipulated probability of failure will be compared with the solutions obtained for a code-based method, which employs partial safety factors. Results are given illustrating the influence of the constraint on the horizontal displacement.     

The non-membrane prebuckling effects on stiffened cylindrical panels

The effects of various boundary conditions on the buckling of stiffened cylindrical panels is considered. Pre-buckling effects are included in the analysis with both external and internal stiffness.     

Optimal design of clamped columns for stability under combined axial compression and torsion

In this paper the problem of the optimal design of columns under combined compression and torsion is investigated. A cross-sectional area varying along the axis of the column which leads to the maximal critical loading is sought. The varying cross-section is approximated either by a function with free parameters or is determined using Pontriagin’s maximum principle.     

Optimum buckling design of compression panels using VICONOPT

The structural efficiency of a range of panels under uniaxial compression is investigated using the optimum buckling design program VICONOPT. The design uses very efficient VIPASA analysis to guard against all possible modes of failure, together with a tailored sizing strategy. The panels all have nine blades, zed or hat stiffeners and between three and fifteen design variables, covering traditional design using one size of stiffener and more sophisticated design with five sizes of stiffener. Results show that using two stiffener sizes or two stiffener types in alternate positions across the panel width can produce mass savings of up to 30% compared with traditional design. Convergence on an optimum normally occurs within six sizing cycles, but up to twelve sizing cycles are required for sophisticated designs when the initial configuration is poorly chosen. Computational efficiency and material strength constraints are also considered.     

Buckling of double functionally-graded nanobeam system under axial load based on nonlocal theory: an analytical approach

Buckling treatment of a bonded compressed double-FG nanobeam system (DFGNBS) is studied in this paper based on Eringen’s nonlocal elasticity theory and Euler–Bernoulli beam model. Differential equations and boundary conditions are obtained using Hamilton’s principle, and the nonlocal theory is employed to derive differential equations in small scale. The material properties are assumed to be functionally graded (FG) along the thickness direction. The synchronous, asynchronous and stationary-type buckling are considered in detail. Results reveal that the small-scale effects are higher with increasing values of nonlocal parameter for the case of in-phase (synchronous) buckling modes in compare to the out-of phase (asynchronous) buckling modes. Increasing the stiffness of the coupling elastic medium double-FG nanobeam system decreases the small-scale effects during the out-of-phase (asynchronous) buckling modes. A detailed parametric study is conducted to investigate the influences of nonlocal parameter, higher modes, spring constant and distributed coefficient of DFGNBS. Some illustrative examples are also stated to verify the present formulation and solutions which showed an excellent agreement.

     

Variable-stiffness composite panels: Buckling and first-ply failure improvements over straight-fibre laminates

One of the primary advantages of using fibre-reinforced laminated composites in structural design is the ability to change the stiffness and strength properties of the laminate by designing the laminate stacking sequence in order to improve its performance. This procedure is typically referred to as laminate tailoring. Traditionally, tailoring is done by keeping the fibre orientation angle within each layer constant throughout a structural component. Allowing the fibres to follow curvilinear paths within the plane of the laminates constitutes an advanced tailoring option that can lead to modification of load paths within the laminate to result in more favourable stress distributions and improve the laminate performance.Based on numerical simulations, the present work demonstrates the advantages of variable-stiffness over straight-fibre laminates in terms of compressive buckling and first-ply failure. A physically based set of failure criteria, able to predict the various modes of failure of a composite laminated structure, is implemented in finite element models of straight and variable-stiffness panels under compression. Non-linear analyses are carried out to simulate first-ply failure in the postbuckling regime.