Simple solution for buckling of orthotropic circular cylindrical shells

Buckling of cracked cylindrical thin shells under combined internal pressure and axial compression

Based on a systematic literature review, no design guidelines addressing practical issues related to steel circular hollow section (CHS) members under hydrostatic pressure have been documented thus far, except for the design recommendations proposed by the European standard EN 1993-1-6 concerning the strength and stability of shell structures. Considering that the existing codes are often outdated and subject to improvement, there is a growing demand for modern solutions that can accurately replicate the stability loss response of equipment subject to external pressure. The development of a more direct and simple method, augmented by reliable computational techniques, is advisable to avoid the numerous challenges associated with manual calculations. This approach will streamline the design process and mitigate the complexity of current practical or technical approaches. Thus, this research has formulated a method to predict design strength through the direct application of the critical elastic buckling stress, determined from Generalised Beam Theory (GBT) analyses, induced by hydrostatic pressure in custom-crafted equations, finely tuned for this specific objective. The authors present a formulation of GBT to analyze the elastic buckling behavior of CHS subject to both combined axial compression and external pressure. This work provides an extensive study of the behavior of circular cylindrical shells under external loading conditions. It first introduces the analyses of GBT and the theoretical and empirical formulas applicable to this objective. It then describes the steps involved in the development and validation of a numerical model that simulates the response of circular cylindrical shells under hydrostatic pressure, conducting an extensive parametric study using finite element analyses (FEAs). The results from available tests validate the finite element (FE) model. Upon achieving adequate agreement between the generated numerical and experimental results, new resistance reduction curves for cylindrical shell members are developed based on the results of the parametric study. Additionally, the study compares the existing provisions of EN 1993-1-6 for the design of cylindrical shells under hydrostatic pressure. Finally, a statistical approach is adopted to compare the responses of cylindrical shells calculated according to the EN 1993-1-6 code recommendations with those obtained through the newly proposed method.

Delamination buckling and postbuckling in composite cylindrical shells under combined axial compression and external pressure

A new unified procedure for designing tubular members under combined axial load (compression or tension), bending, and hydrostatic pressure on offshore structures, fixed or compliant, is presented. The equations are applicable to members at all water depths, but are limited to members with outside diameter to wall thickness ratios less than 80. In addition to a pure hydrostatic check against hoop collapse, the procedure recommends only one check each for the axial compression and tension cases. The new design equations have been calibrated to test data from several recently completed test programs, and are thus more reliable than currently available technology. The new equations are also simpler to use. The procedure can replace several subsections in the 18th edition of API RP 2A-ASD and the draft RP 2A-LRFD (yellow copy). The recommended procedure provides unambiguous guidance for determining the member axial, bending, and hoop stresses from a frame analysis in order to check the design adequacy or determine the unity check (member utilization) of the member. The recommended procedure includes a reduced safety factor for hoop compression, but other safety factors in RP 2A-ASD are unchanged. Further examination of the reliability question may be warranted, but it is not envisioned that such an evaluation would alter the proposed procedure so as to become more conservative. A comparative design study using the new equations on a 2500-foot compliant pile tower resulted in about 5% tower steel-weight saving (2300 tons) compared to the approach proposed by Chen, Bubonic, and Sohal. Even larger weight savings can be expected for TLP tendons although a comparative design example is not yet available. The new equations are currently being reviewed as part of an ongoing API PRAC 89-56 study on analysis of the cylindrical shell database and validation of design formulations. INTRODUCTION Both API RP 2A-ASD1 and RP 2A-LRFD2 provide incomplete guidance for the design of tubular members under combined axial compression, bending, and external hydrostatic pressure loads, as shown in Fig. 1. The guidance in both documents is limited to checking local cross-sectional buckling. (Shear forces are not shown in Fig. 1. These forces have negligible impact on the strength of beam-columns.) In addition, there is an inconsistency in both documents relating to the allowable bending capacity term. However, this inconsistency generally results in a conservative design. In addition to hoop stress, external hydrostatic pressure will impose a capped-end axial compression force in a member if the ends are capped, as shown in Fig. 2. On the other hand, external radial pressure only imposes hoop compression in a tubular member and no capped-end compression. Since the hoop and capped-end axial stresses from external pressure are always in compression, they are assumed to have a positive sign.

Results from an analytical study of the response of composite shells with cutouts and subjected to internal pressure and axial compression are presented. The analytical results are obtained using a geometrically nonlinear finite element code. Results for axial compression and combined internal pressure and axial compression are presented. The effects of varying internal pressure and cutout size on the prebuckling, buckling, and postbuckling responses of the shell are described. Results indicate that the nonlinear interaction between the inplane load distribution and the out-of-plane displacements near the cutout can significantly influence the structural response of the shell. The results also indicate that these local load distributions and displacements can be affected by the size of the cutout and the internal pressure load. Introduction Many modern aerospace shell structures are designed to support combinations of internal pressure and mechanical loads during their service life. With the increasing need to produce lighter weight aerospace structures, the use of advanced composite materials has become more common in the design of these structures. During operation, flight loads and internal cabin pressure are present in all commercial transport aircraft. Some of these loads may be compressive loads and, thus, it is necessary to investigate the buckling characteristics of these structures. In addition, designers will *Ph.D. Candidate, Composite Structures Laboratory, Department of Aerospace Engineering. Student Member, AIAA. tHead, Structural Mechanics Branch. Fellow, AIAA. ^ Associate Professor, Composite Structures Laboratory, Dept. of Aerospace Engineering. Member AIAA. Copyright ©1998 by Mark W. Hilburger. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. often need to incorporate cutouts or openings in the structure to serve as doors, windows, or access ports. It has been shown by a number of authors that a cutout in a shell structure subjected to axial compression can cause a significant reduction in the buckling load of the shell (e.g., Ref. 1-4). The local response near the cutout in a compression-loaded shell is strongly influenced by the local displacement gradients and the internal load distribution. These local displacements and internal load distribution can be affected by the size of the cutout. Recent studies of the response of cylindrical shells with longitudinal cracks and subjected to internal pressure and axial compression loads (e.g., Ref. 5) indicate that the interaction between the internal pressure load and the axial compression load can have a significant effect on the local response of the structure. The results of an analytical study of the response of composite cylindrical shells with cutouts and subjected to internal pressure and axial compression are presented. First, the governing parameters for the buckling of cylindrical shells with a cutout will be defined. The governing parameters will be used to develop the results of a parametric study presented in the paper. These parameters will help provide insight into the effects of changing geometric and laminate parameters on the buckling response of shells. The parametric study will include three cutout sizes and five internal pressure levels to determine the effects of varying the cutout size and internal pressure loads on the compression response. The predicted results are characterized by load-shortening response curves and contour plots of shell displacements and stress resultants. Finally, design curves based on classical parameters for the buckling of shells with cutouts and subjected to internal pressure and axial compression are presented.

This paper proposes a new type of shell, similar to a cylindrical shell, which has significantly higher buckling strength when subjected to an arbitrary combination of uniform external pressure and axial compression. The underlying principle consists in a slight modification of the perfect cylinder in order to counteract the natural deformations which get larger and larger and lead to the collapse of the structure. Such shells are called ASTER shells. The concept has been validated through experiments, then analyzed numerically in order to explain what was observed and to propose avenues for improvements. The shells were made of electrodeposited nickel. The material was characterized. The chosen specimens were carefully measured to characterize their thickness and initial imperfections, then tested under the various types of loading. Then they were analyzed using finite elements. Thus, we were able to compare the finite element predictions with the experimental results. This comparison shows that plasticity has a decisive influence on the critical load and that linear elastic dimensioning leads to a serious overestimation of the experimental critical load. Contrary to perfect cylindrical shells, this type of shell is not significantly affected by geometric imperfections: this is another advantage of this type of design. Finally, we propose a numerical analysis in order to optimize the choice of the shape and propose shapes which resist buckling much better than a smooth cylinder when subjected to uniform external pressure, axial compression or a combination of both.

Nonlinear buckling and postbuckling of heated functionally graded cylindrical shells under combined axial compression and radial pressure

The results of 40 buckling tests on unstiffened welded steel cylindrical shells subjected to combined axial compression and external lateral pressure are compared in the paper with the predictions of theory and various Codes (ASME III, DnV and ECCS). The radius/thickness ratios of the models tested were R/t ≈ 100 and 300 and the length/radius ratios covered the range 0.18 < L/R < 1.45. Three interaction equations were studied, viz. a linear, a quadratic and a linear/quadratic equation suggested recently by Odland. Best agreement with experiment was obtained using the quadratic equation in conjunction with the DnV or ASME III Codes. The ECCS predictions of buckling stress were safe but were more conservative than the other two Codes. Some interactive buckling tests on ring-stiffened cylinders (and conducted recently by other workers) were also compared with the predictions of the above three Codes. The agreement between predicted buckling stresses and test results was broadly similar to that found for the Liverpool models. For very short unstiffened and ring-stiffened cylindrical shells, the theoretical interaction curves were a little unusual. In addition, the test results for external lateral pressure alone on these shells, and obtained by different research groups, did not all agree.

Figure 191 gives several examples of prismatic shells and panels. These are structures the cross sections of which are thin and do not vary in one of the coordinate directions, generally called the axial direction. In this chapter a method will be described in which a computer program for the analysis of shells of revolution can be used to predict buckling of prismatic shells and panels. Results will be given of convergence studies applied to cylindrical shells subjected to external lateral pressure. These studies demonstrate the validity of the technique. The method will then be applied to yield predictions of bifurcation buckling loads of noncircular cylindrical shells under axial compression or external pressure and failure of corrugated and beaded panels under axial compression. The effect of manufacturing processes on buckling and crippling of corrugated semi-sandwich panels of the type from which the rocket payload shroud shown in Fig. 5 is made will be shown.

An analytical model is presented to predict the influence of nonlinearities associated with supersonic fluid flow on the dynamic and stability behavior of thin isotropic cylindrical shells. The method developed is a combination between finite element method, sander’s shell theory and nonlinear aerodynamic theory (third-order piston theory). The shell is subdivided into cylindrical finite elements, the displacements functions are derived from exact solutions of Sanders equations for thin cylindrical shells and the influence of stress stiffening due to internal or external pressure and axial compression is also taken into account. Expressions for the masse and stiffness matrices are determined by exact analytical integration. With the nonlinear dynamic pressure, we develop nonlinear matrices: stiffness, damping and coupling matrices for flow. The nonlinear equation of motion is then solved using a fourth-order Runge-kutta numerical method. Frequency variations are determined with respect to the amplitude of the motion for different cases. This is a powerful model to predict linear, nonlinear vibrations and stability characteristics of cylindrical shells subjected to external supersonic flow that can be applied for the aeroelastic design of aerospace vehicles.

The experience in the Brazilian offshore production systems is to adopt the traditional riser solution composed of unbonded flexible pipes at a free-hanging catenary configuration. In deep waters, the tendency has been to use different pipe length sections (normally two), each of them designed to resist typical loadings. At the bottom, pipe structure is dimensioned against external pressure, axial compression, bending and torsion, for example. The theoretical prediction of riser responses under the crescent combined loading conditions is a key issue at the TDP region. The potential failure modes are buckling of the armour tendons and also rupture of the high resistance tapes. Much effort has been done in order to have available, from the market, larger envelopes of certified methodologies and qualified products, applicable to the Brazilian ultra-deep scenarios. Since 2002, an extensive R&D Program has been conducted (i) to improve current design evaluation tools & criteria and (ii) to establish representative test procedures and scope, for prototype qualification against the potential failure modes associated with combined axial compression, bending and torsion, at the TDP regions of bottom riser sections in ultra-deep water depths. This paper describes the main steps of the R&D Program, as below: I. Improvement of computational tools to better represent the behavior of the tendons, II. Consolidation of a new strategy for structural analysis, under more realistic conditions, III. Issue of a more adequate set of pipe technical specifications, and IV. Review of both theoretical and experimental results obtained from Feasibility Technical Studies and offshore field tests, respectively. Some examples and results are showed to illustrate, step by step, the whole process covered by the cited Program. Finally, the authors document their main conclusions for further discussion.

In order to simulate the seismic behaviour of the prestressed high-strength concrete piles under working state, six full-scale prestressed high-strength concrete piles were tested under combined axial compression and cyclic horizontal loads. Different axial compression levels and prestressing levels of prestressed tendons were studied in this test programme. The failure mode, bending resistance, displacement ductility, stiffness degradation and energy dissipation of the prestressed high-strength concrete piles under different loading scenarios were measured and analysed. Test results indicated that the axial compression ratio and prestressing level of prestressed tendon significantly influenced the seismic performance of prestressed high-strength concrete piles. Theoretical models were developed to predict cracking, yielding and ultimate bending resistances of the prestressed high-strength concrete pile under combined compression and bending. Finite element model was also developed to simulate the ultimate strength behaviour of the prestressed high-strength concrete pile under combined compression and flexural bending. The accuracies of the theoretical and finite element model were checked through validations of their predictions against the reported test results.

Instability of delaminated composite cylindrical shells under combined axial compression and bending

In this paper a deflection function with undetermined coefficients is used to determine analytically the bifurcation buckling load of a cylindrical tube under combined external pressure and axial compression using Donnell's simplified equations. This procedure can be adopted for various types of prescribed boundary conditions. In order to demonstrate the feasibility of this method, only the fixed-end conditions are considered for solution in this paper. The results obtained for the fixed-end conditions indicate that the critical buckling value depends on the ratio of thickness to radius and not on the ratio of radius to length and the critical buckling value decreases as the ratio of circumferential compressive stress to axial compressive stress increases. The buckling interaction curve for combined radial and axial compression for this case appears to follow a straight line indicating a uniform percentage decrease in the axial compressive load from the theoretical classical value for uniform axial compression. di tO 08 __ bi,b2bi,t>2 Cl,C2,Ci,C2 Cij = ij D E ei,e2

Testing of bolted base connections for wide-flange columns under combined axial compression and weak-axis lateral forces