Ring-stiffened Cylinders Research Articles

Numerical modeling of buckling of ring-stiffened cylinders

Numerical modeling of buckling of ring-stiffened cylinders

Damage response of submerged imperfect cylindrical structures to underwater explosion

The effect of the initial geometric imperfections to the damage response of submerged structures is investigated. The type of the submerged structure investigated is the ring-stiffened long circular cylinders submerged in the fluid. The strain hardening mild steel is used in the analysis. The type of the loading is the underwater shock induced by underwater explosions. The modal imperfection concept has been used to simulate the initial geometric imperfections. The numerical analyses were performed to look into the details of damage response of ring-stiffened cylindrical shells. The following models were considered: (i) three-dimensional infinite ring-stiffened cylinder model, and (ii) three-dimensional finite ring-stiffened cylinder model. A finite element hydrocode was used to numerically predict model responses.

Optimal design of imperfect, anisotropic, ring-stiffened cylinders under combined loads

Development of an algorithm to perform the optimal sizing of buckling resistant, imperfect, anisotropic ringstiffened cylinders subjected to axial compression, torsion, and internal pressure is presented. An axisymmetric, geometrically nonlinear prebuckling equilibrium configuration is assumed and both stress and stability constraints are considered. The enforcement of stability constraints is treated in a way that does not require any eigenvalue analysis. Case studies performed using a combination of penalty function and feasible direction optimization methods indicate that the presence of the axisymmetric initial imperfection in the cylinder wall can significantly affect the optimal designs. Weight savings associated with the addition of two rings to the unstiffened cylinder and/or the addition of internal pressure is substantial when torsion makes up a significant fraction of the combined load state.

Composite to Metal Joints for the ARPA Man-Rated Demonstration Article

The design, analysis and testing of composite-to-metal joints for the ARPA Man-Rated Demonstration Article are discussed. The first is a composite-to-titanium sphere joint designed to react sphere membrane stress with block compression loading. A series of uniaxial compression tests to simulate this joint assembly was conducted. Test results successfully demonstrated the ability of the joint to withstand block compression loading even in the presence of assembly fitup gaps. A polymer shimming material (Hysol EA9394) was also evaluated as a means to fill potential fitup gaps and was found to effectively reduce stress concentrations resulting from the gaps. The second joint discussed is one between 120-degree segments that make up a stiffener ring for a ringstiffened composite cylinder. Joint design includes Hysol EA9394, boltedon titanium splice plates, and bondedon thermoset flange straps. 2D joint tests, single stiffener tests, and sub-scale ring-stiffened cylinder hydrostatic tests to validate the joint design are described.

Buckling of imperfect, anisotropic, ring-stiffened cylinders under combined loads

The objective of this study is to develop an anlysis to predict buckling loads of ring-stiffened anisotropic cylinders subject to axial compression, torsion, and internal pressure. This structure is modeled as a branched shell. A nonlinear axisymmetric prebuckling equilibrium state is assumed which is amenable to an exact solution within each branch. Axisymmetric geometric imperfections are included. Buckling displacements are represented by a Fourier series in the circumferential coordination and the finite-element method in the axial coordinate. Application of the Trefftz criterion to the second variation of the total potential energy leads to a nonlinear eigenvalue problem for the buckling load and mode. Results are presented for both unstiffened and ring-stiffened cylinders in the form of buckling interaction diagrams. Imperfections can cause an unexpected buckling mode in the ring web which would not occur for the perfect structure, and pressurization diminishes the benefit of adding rings to the unstiffened shell to increase the buckling load. The implementation of the analysis methodology into a structural sizing algorithm is discussed.

Imperfection Sensitivity of Stiffened Cylindrical Shells Under Interactive Buckling

In this paper some recent advances made in the understanding of the phenomena and computational modelling of the interaction of local and overall instabilities in stiffened cylindrical shells will be reviewed. These relate to two distinct categories of problems: (1) Axially compressed stringer-stiffened shells and (2) Ring-stiffened cylinders subjected to hydrostatic compression. The former have been analyzed with a novel methodology which employs finite elements in which the local buckling information is embedded. Comparisons of the results of the new technique with Abaqus - a well established nonlinear analysis program - reveals the validity of the underlying concepts of the new technique and efficacy of the new approach. It is shown, that provided all the key local buckling modes triggered in the interaction are considered and the modulation of local buckling amplitudes is accounted for, it is justifiable to neglect the mixed second order stresses and strains in the analysis. Imperfection-sensitivity of a stringer stiffened cylindrical shell structure is illustrated. In the case ring-stiffened cylinders subjected to hydrostatic pressure, it is shown that the amplitude modulation is the key factor in the interaction; it performs the function of capturing the contributions of several neighboring modes of the same longitudinal description as the fundamental local mode, but with differing circumferential wave numbers. An examination of the potential energy function indicates that the amplitude modulation is solely responsible for the presence of the nonvanishing cubic terms, which are dominant over the quartic terms. Once again, mixed second order fields evaluated with appropriate orthogonality conditions have little influence on the interaction and can be safely neglected. An example of an orthotropic layered shell under coincident and well separated critical stresses is presented.

Plastic Deformation and Rupture of Ring-Stiffened Cylinders under Localized Pressure Pulse Loading

An analytical solution for the dynamic plastic deformation of a ring-stiffened cylindrical shell subject to high intensity pressure pulse loading is presented. By using an analogy between a cylindrical shell that undergoes large plastic deformation and a rigid-plastic string resting on a rigid-plastic foundation, one derives closed-form solutions for the transient and final deflection profiles and fracture initiation of the shell. Discrete masses' and springs are used to describe the ring stiffeners in the stiffened shell. The problem of finding the transient deflection profile of the central bay is reduced to solving an inhomogeneous wave equation with inhomogeneous boundary conditions using the method of eigenfunction expansion. The overall deflection profile consists of both global (stiffener) and local (bay) components. This division of the shell deflection profile reveals a complex interplay between the motions of the stiffener and the bay. Furthermore, a parametric study on a ring-stiffened shell damaged by a succession of underwater explosions shows that the string-on-foundation model with ring stiffeners described by lumped masses and springs is a promising method of analyzing the structure.

Structural acoustic radiation prediction: Expanding the vibratory response on a functional basis

The theoretical basis of the modal method for acoustic radiation from structures is first presented. It consists of expanding structural responses on a functional basis, truncated for numerical computations. Generally the natural vibration modes of the structure in vacuo are considered, even if it is possible to use other functions. The physical signification of modes allows one to select the modes governing radiation and to truncate the series for efficient computations. In this optimized form, the modal method allows one to calculate radiation of large structures from low to high frequencies within a reasonable computation time. The understanding of the physical phenomena required for mode selection is presented. The characteristics of the fluid-structure coupling are the radiation impedances of modes. Radiation resistances introduce a loss mechanism for the structure associated with radiated power. Radiation reactances are interpreted as added masses. Several examples of radiation impedances are analysed. To be efficient, the modal method requires the knowledge of the modal basis in analytical form. It is thus well adapted to problems involving simple geometric structures, such as rectangular plates or cylindrical shells. It is, however, easy to take into account inhomogeneities such as stiffeners, masses and perforations. The last part of the paper presents the simulation of two complicated problems: the transmission loss of double panels (with absorbing material and mechanical links) separating two rooms, and the radiation, into water, from a ring-stiffened cylinder covered with a coating layer. Finally, the influence of structural defects on radiation, and comparison of theory and experiment are presented.

Plastic Deformation and Rupture of Ring-Stiffened Cylinders under Localized Pressure Pulse Loading

An analytical solution for the dynamic plastic deformation of a ring-stiffened cylindrical shell subject to high intensity pressure pulse loading is presented. By using an analogy between a cylindrical shell that undergoes large plastic deformation and a rigid-plastic string resting on a rigid-plastic foundation, one derives closed-form solutions for the transient and final deflection profiles and fracture initiation of the shell. Discrete masses' and springs are used to describe the ring stiffeners in the stiffened shell. The problem of finding the transient deflection profile of the central bay is reduced to solving an inhomogeneous wave equation with inhomogeneous boundary conditions using the method of eigenfunction expansion. The overall deflection profile consists of both global (stiffener) and local (bay) components. This division of the shell deflection profile reveals a complex interplay between the motions of the stiffener and the bay. Furthermore, a parametric study on a ring-stiffened shell damaged by a succession of underwater explosions shows that the string-on-foundation model with ring stiffeners described by lumped masses and springs is a promising method of analyzing the structure.

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.

TRANSIENT THERMOELASTIC PROBLEM OF RING-STIFFENED HOLLOW CYLINDER HEATED BY A MOVING LINE SOURCE

The transient temperature and thermal stress distributions of a ring-stiffened hollow cylinder are analyzed. The cylinder is heated by a moving line source on its inner boundary and cooled convectively on the exterior surface. To solve this problem, the Laplace transform and finite-element method are adopted. In addition, the inverse Laplace transform is accomplished by utilizing the Fourier series technique. The effects of width and thickness of the stiffening ring on the temperature and thermal stress distributions are the main factors investigated in this article. The results show that the stiffening ring can function as a fin and the axial thermal stress dominates the thermal stress field.

Imperfection sensitivity of stiffened cylinders subjected to external pressure

The effect of initial imperfections on the elastic-buckling behaviour of ring-stiffened cylinders under external pressure is examined using the potential energy approach. Experimental results in the open literature of four ring-stiffened cylinders tested under external pressure were used to compare and verify the theoretical analysis. Both the theoretical and experimental results indicate no apparent influence of initial imperfections on the buckling behaviour within the elastic range. This was so in spite of the presence of an appreciable amount of initial imperfections. The results from this work indicate that less stringent requirements in the manufacturing of ring-stiffened cylinders may be tolerated, leading to possible economy.

Strength formulation for ring-stiffened cylinders under combined axial loading and radial pressure

Abstract After demonstrating how to improve simply the BS 5500 strength formulation for hydrostatically loaded fabricated ring-stiffened cylinders, a simple yet consistent strength formulation is derived for determining their strength when subjected to combined axial loading including tension and radial pressure. The quadratic Merchant-Rankine formula in generalised form as suggested by Odland is adopted as the basis of the proposed formulation. This involves knockdown factors which are derived to provide a good fit with experimental data. Its accuracy is compared with that of the DnV Rules and BS 5500. The effects of boundary conditions and residual stresses are investigated using unstiffened and stress-relieved test data respectively.

Ring‐Stiffened Cylinders Under Interactive Loading

Presented are the results of analyses on ring-stiffened cylinders under combined axial compression and external pressure by rigid plastic mechanism approaches and finite elements. The shell geometries examined lie in the range used for primary members of floating offshore platforms. For each geometry, a series of stiffener sizes is analyzed to determine the limiting stiffener area required to prevent failure in the general collapse mode. The results are presented in the form of design charts. Comparisons between the present results and Det norske Veritas (DnV), European Convention for Constructional Steelwork (ECCS), and American Society of Mechanical Engineers (ASME) design codes have highlighted areas where these codes need to be reassessed.

Interactive Buckling Tests on Cylinders Subjected to External Pressure and Axial Compression

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.

Theoretical and Experimental Results on the Post-Buckling of Ring-Stiffened Cylinders

ABSTRACT The post-buckling behavior of ring-stiffened cylinders subjected to lateral pressure is studied theoretically and experimentally. The theoretical analysis uses the energy method and terms of up to and including fourth order of the buckling displacements are considered. The results of experiments on ten machined ring-stiffened cylinders subjected to lateral pressure and used to verify the theoretical analysis. The theory shows the post-buckling behavior to be stable-symmetric for both the shell and general instability modes. The experimental results are in reasonable agreement with the theory, although they indicate, in general, a lower post-buckling stiffness. For the range of parameters considered, no instability or imperfection sensitivity is found in either the theoretical or the experimental studies.

Buckling behaviour of ring-stiffned cylinders; experimental study

The effect of the number and size of rings on the buckling strength of ring-stiffened cylinders is studied experimentally. The results of ten machined ring-stiffened cylinders subjected to lateral pressure are presented. Five of the cylinders failed by the general instability mode and the rest failed by the shell instability mode. A sample of the experimental results which shows longitudinal and circumferential strains as well as the development of the circularity contours till collapse is presented. Buckling pressures obtained from the experiments are shown to be within ±30% of the corresponding value obtained from the theoretical analysis available in the literature.

A plastic mechanism formulation for the general instability of ring-stiffened cylinders under pressure-dominated loadings

This paper presents a rigid-plastic mechanism approach to investigating the collapse behaviour of ring-stiffened cylinders failing in the general instability mode under pressure-dominated loadings. Experimental data from various sources are used to correlate with the results of the analysis. The influence of initial geometric imperfections on the collapse behaviour is also discussed in detail.

Buckling and sensitivity estimates for ring-stiffened cylinders under external pressure

An analysis of critical and post-critical behaviour of cylinders under external pressure with widely spaced stiffeners is presented. The ring-stiffeners are treated as discrete elements and their torsional plus bending stiffness are taken into account and their effect on the most relevant results are evaluated. Solutions are presented to show the effect of shell and ring geometric parameters on the critical loads and imperfection-sensitivity. Buckling loads are estimated and compared with available test results and recommended design curves.

A mechanism approach for the prediction of the collapse strength of ring-stiffened cylinders under axial compression and external pressure

A mechanism approach is presented for determining the collapse behaviour of ring-stiffened cylindrical shells subjected to axial compression and external pressure. It extends previous work of Alexander, 5 and Andronicou and Walker, 6 incorporating the effect of pressure and calculates failure loads as an upper bound of elastic and mechanism responses. Comparison with recent experiments and a lower bound analysis are given. The paper also discusses the relevance of the results to offshore design.