Elasto-plastic Large Deflection Research Articles

Collapse strength of hatch cover of bulk carrier subjected to lateral pressure load

A series of elastoplastic large deflection FEM analyses has been performed on hatch covers of bulk carriers subjected to lateral load. Two types of hatch covers are considered which are the folding type and the side-sliding type. For the folding-type cover, one size is considered which is for Handy size bulk carrier, whilst for the side-sliding-type cover, two sizes are considered which are for Panamax and Cape size bulk carriers. For each type, two hatch covers are selected which are designed in accordance with the old ICLL rule and new IACS rule, respectively. Calculated collapse strengths are compared with individual design loads, and a strength assessment is performed. On the basis of collapse behaviour observed in FEM analyses, a simple method is proposed to evaluate the collapse strength of a hatch cover subjected to lateral load. It is confirmed that the collapse strength is accurately predicted by the proposed method.

Elastoplastic Large Deflection Analysis of Three-Dimensional Steel Frames

A beam element is presented for analysis of the elastoplastic large deflection of three-dimensional (3D) frames that have steel members with semirigid joints. A plastic hinge type formulation was employed, combining the “modified incremental stiffness method,” the updated Lagrangian formulation, and numerical integration about the end sections of the element. The end sections of the element are discretized into small areas to estimate the plastic deformations of the element. The elastic and plastic deformations of the element are treated separately. The behavior of a semirigid joint is modeled as the element-end compliance. The method can treat comprehensively the plastic deformations due to torsion and warping. Considering the assumptions of the method, a four-element approximation for a member gives excellent results for a 3D analysis of semirigid and pin-connected steel frames as well as for rigid frames. The adequacy of the method is verified by comparing the results with experimental ones obtained by the writer. Some examples are presented to demonstrate the accuracy and efficiency of the method.

Estimation of Ultimate Strength of Continuous Stiffened Plate under Combined Thrust and Lateral Pressure

The authors proposed a set of closed-form simple formulae to estimate ultimate strength of a continuous stiffened plate under combined longitudinal thrust, parallel to stiffener direction, and lateral pressure. This paper extends the application of the formulae to biaxial thrust condition based on a series of elastoplastic large deflection FE analyses. It was found from FEA that the ultimate strength of a continuous stiffened plate under transverse thrust is significantly higher than that of a continuous unstiffened plate simply-supported along stiffener lines because of a stiffener's torsional stiffness. It was also found that there exist two fundamental failure modes; one is local failure mode of plate between stiffener under predominantly transverse thrust and the other is over-all failure mode of stiffened plate under predominantly longitudinal thrust, and that the ultimate strengths corresponding to the respective failure modes can be estimated rather independently, with little interactions. Based on these observations, a set of simple ultimate strength formulae has been derived, and their validity has been confirmed through a comparison with FEA results.

Study on Buckling/Ultimate Strength of Bilge Circle Part and Its Contribution to Ultimate Hull Girder Strength

There are several methods to estimate the ultimate strength of hull girder, among which the method developed by Smith is widely used as a simple and practical method. In this method, the round corners such as a bilge shell part are usually considered as hard corner elements which do not undergo buckling. A series of elastoplastic large deflection analyses were performed to investigate buckling/plastic collapse behaviour of the bilge circle part subjected to uni-axial thrust. Based on the calculated results, simple formulas were derived to simulate buckling/plastic collapse behaviour of the bilge shell. The ultimate strength analyses of hull girder by Smith's method were carried out taking the buckling/plastic collapse behaviour of the bilge shell into account. Through these studies, it has been found that:(1) A bilge structure with a conventional shape and size reaches the ultimate strength by yielding before buckling takes place. After the ultimate strength has been attained, plastic buckling takes place and the capacity decreases with the increase in deflection.(2) The buckling/ultimate strength of the bilge circle part is dominated by design parameters such as radius/thickness ratio, yield stress and length/radius ratio of the bilge circle part.(3) Hard corner elements could be used for bilge circle part to calculate the ultimate hull girder strength applying the Smith's method.(4) However, the influence of buckling of the bilge circle part has to be taken into account for the accurate estimation of the load carrying capacity beyond the ultimate strength when the Smith's method is applied.

Estimation of buckling and ultimate strength of continuous plate with cutout under thrust

A series of buckling eigen-value calculations and elastoplastic large deflection analyses of simply upported continuous plate with cutout under thrust has been performed. Firstly, simple formulae for estimation of elastic buckling strength have been derived based on the results of eigen-value calculations. Secondary, it has been clarified that the buckling strength evaluated by the existing plastic correction methods exceeds the ultimate strength in some combinations of plate thickness and cutout diameter. So, new plastic correction formula considering the yielding effect for estimation of buckling strength of continuous plate with cutout has been proposed. Finally, by focusing on the characteristics of ultimate strength obtained by elastoplastic large deflection analyses, simple formulae for estimation of ultimate strength of continuous plate with cutout have been derived.

Buckling/Ultimate Strength of Perforated Rectangular Plate under Thrust (2nd Report)

Series of elastic eigenvalue analyses and elastoplastic large deflection analyses were performed to investigate into the influence of perforation on the buckling/ultimate strength of rectangular plate subjected to uni-axial and bi-axial thrust. It has been found that : (1) Beyond the ultimate strength, plastic deformation is concentrated around the opening, and elastic unloading takes place in the remaining part in case of long plate subjected to longitudinal thrust.(2) Beyond the ultimate strength, plastic mechanism of a roof mode developes in case of long plate subjected to transverse thrust.(3) Ultimate strength interaction relationship is derived for bi-axial compression, and it was found that general yielding at the perforated cross-section affects the shape of the interaction curve.Simple formulas are proposed to evaluate the elastic buckling strength of a perforated plate under uni-axial thrust. These formulas are used to evaluate the ultimate strength, which showed good correlations with the FEM results.

Elasto-plastic response of uniformly loaded sector plates: full-section yield model predictions and spread of plasticity

The governing equations for an elasto-plastic large deflection analysis of pressure loaded sector plates, based on the Ilyushin full-section yield criterion and the flow theory of plasticity, are presented. An outline of the solution of these equations using a finite difference implementation of the dynamic relaxation algorithm is given. Numerical results are presented for uniformly loaded slender and stocky sector plates with a 60° sector angle. In particular, first yield data are presented as well as the results of two parameter studies. The first study shows the effects of flexural and in-plane edge conditions on the deflections and stress resultants/couples at the centre of the sector plate and the second contrasts the spread of plasticity in slender sector plates with simply supported and clamped in-plane fixed edges.

Buckling/Ultimate Strength of Perforated Rectangular Plate under Thrust

A series of elastoplastic large deflection analyses was performed to investigate into the influence of perforation on the buckling and ultimate strength of rectangular plate under uni-axial thrust. It has been found that : (1) When the plate is subjected to longitudinal thrust, collapse mode varies depending on the aspect ratio of the plate and sometimes differs from the elastic buckling mode.(2) When the plate is subjected to transverse thrust, collapse mode is fundamentally the same regardless of the aspect ratio and is almost the same as the elastic buckling mode.(3) Simple formulas are proposed to evaluate the ultimate strength of a perforated plate under uni-axial thrust both in longitudinal and transverse directions. The evaluated values of the ultimate strength showed good correlations with the FEM results.

Estimation of buckling and ultimate strength of rectangular plate with cutout

A series of buckling eigen-value calculations and elastoplastic large deflection analyses of simply supported rectangular plate with cutout subjected to in-plane loads has been performed. Firstly, advanced simple formulae in practical use for estimation of elastic buckling strength have been derived based on the results of eigen-value calculations. Secondary, relationship between the ultimate strength and the buckling strength evaluated by the existing plastic correction methods has been clarified. By considering the yielding in the effective cross section with cutout, new plastic correction formula for estimation of plastic buckling strength of rectangular plates with cutout has been proposed. Finally, based on the results of elastoplastic large deflection analyses, simple formulae for estimation of ultimate strength of rectangular plate with cutout subject to longitudinal thrust have been derived.

Plastic Collapse Strength of Hatch Cover of Bulk Carrier against Green Sea Load (2nd Report)

After the casualty of M.V.Derbyshire, the strength of a hatch cover of a Bulk Carrier has been discussed at the International Association of Classification Societies (IACS) to prevent the occurrence of similar casualties, and a new unified requirement, S21, came into effect in 1977. In the present paper, elastoplastic large deflection FEM analysis is performed on four hatch covers of a side sliding type designed by the old rule in the International Convention on Load Lines (ICLL, 1966) and the new IACS requirement, respectively. It was found that the hatch cover designed by the new IACS rule has appropriate and enough strength. Based on the simulated collapse behaviour by the FEM, a simplified method is proposed to evaluate the plastic collapse strength of a hatch cover of a side sliding type. It is demonsrated that the proposed method gives accurate collapse load.

Plastic Collapse Strength of Hatch Cover of Bulk Carrier against Green Sea Load (1st Report)

After the casualty of M.V.Derbyshire, United Kingdom insisted to increase the strength of a hatch cover of a Bulk Carrier to prevent the occurrence of similar casualties. This had been discussed at the International Association of Classification Societies (IACS), and a new unified rule, S21, came into effect. In the present paper, elastoplastic large deflection analysis is performed on two hatch covers of a folding type designed by the old rule in the International Convention on Load Lines (ICLL), 1966 and the new IACS rule, respectively. Based on observations on the simulated collapse behaviour by FEM, a simplified method is proposed to evaluate the plastic collapse strength of a hatch cover of a folding type. It is demonstrated that the proposed method gives accurate collapse load. At the end, strength of old and new hatch covers are assessed comparing the evaluated collapse strength with design loads specified by the rules. It is concluded that the hatch cover designed by the new IACS rule has appropriate and enough strength.

Longitudinal and Transverse Thrust

New shape functions for the lateral deflection of rectangular plate elements for the Idealized Structural Unit Method (ISUM) are developed. First, the collapse behaviour of rectangular plates under longitudinal and transverse thrust is studied by elastoplastic large deflection FEM and the characteristics of the collapse modes are highlighted. Based on these characteristic deflection modes, new lateral shape functions for the large ISUM elements are assumed and implemented. Comparisons with FEM results show the applicability and good accuracy of these new ISUM elements. The importance of shape functions simulating the collapse mode accurately is demonstrated by comparing the new formulation with a previous one and by examining the influence of two yield functions.

Strength and behaviour of the corner zones in steel rigid frame columns with shifted beams

This study deals with the “connecting zone” of a thin walled steel column at which two beams for the alternate directions are connected with the different height. A corner zone of a rigid frame structure at which beams are connected is generally subjected to the bending and shear. When two beams are connected to the column with different height, i.e. the beams have a “shift” in their axis, the connected zone is more complicated. In this study, a series of numerical analysis is made on the strength and behaviour of such a structure. Elasto-plastic large deflection FEM is used with the arc-length increment technique, and plate thickness, the magnitude of the “shift” and so on are adopted as parameters. Through the analysis, it is found that the behaviour of a connecting zone of a column with shifted beams has almost completely different from one with no shift, and that the smaller shift reduces the ultimate strength.

Estimation of Ultimate Strength of Continuous Stiffened Plates under Thrust (2nd Report)

The authors presented a simplified method to estimate the ultimate strength of a continuous stiffened plate under uniaxial thrust in the 1 st report. In this method, a continuous stiffened plate is modelled as a double-span beam-column, and the influence of the interaction between adjacent spans and that of the interaction between panel and stiffener on the ultimate strength are taken into account. In the present report, the influence of welding residual stresses produced by the fillet welding along panel/web intersection and/or web/flange intersection is further considered to apply the proposed method to a real welded structure. As for the stiffened plate with flat-bar stiffener, the effective thickness of stiffener is modified to consider the panel/stiffener interactions more correctly. The ultimate strengths estimated by the improved method are compared with the results of elastoplastic large deflection FEM analyses and those of the existing collapse tests for continuous stiffened plates. The comparison with the existing design formula and other estimation method is also carried out. It has been found that the present method can estimate the ultimate strength which is in better agreement with the results of FEM and tested results than the existing methods.

A numerical investigation of tripping

The twin aims of the present study are to investigate numerically the characteristics of tripping failure of flat-bar stiffened panels subject to uniaxial compressive loads and also to study the accuracy of two available design formulations. A special-purpose nonlinear finite element method capable of efficiently analyzing the elasto-plastic large deflection behavior of stiffened panels is developed and used in the study. A benefit of the application of the nonlinear finite element method is that it makes possible a rigorous accounting of the interacting effects of stiffener tripping and plating collapse and also the inclusion of the influence of elasto-plastic rotational restraint at the plate-stiffener intersection prior to and during failure. A parametric series of elasto-plastic large deflection analyses for stiffened panels with flat-bar type of stiffeners under uniaxial compressive loads are carried out varying member proportions and structural parameters. Based on the computed results, a basic investigation of tripping behavior of flat-bars is made, and the accuracy of design formulations is studied. The calculations and comparisons of this paper are for flat-bar stiffened panels under uniaxial compression, but the special-purpose finite element method implemented is considerably more general.

Cyclic Elastoplastic Large Deflection Analysis of Thin Steel Plates

This paper deals with the elastoplastic large deflection analysis of thin steel plates subjected to in-plane cyclic compression and tension using the finite element method. The modified two-surface plasticity model, recently developed by the authors, and the approximate updated Lagrangian description of motion are employed, respectively, for material and geometrical nonlinearities in the elastoplastic finite element formulation for plates. The plate element is implemented in the computer program FEAP used in the analysis. The formulation accounts for important cyclic characteristics of structural steel within the yield plateau and hardening regime, such as the decrease and disappearance of the yield plateau, reduction of the elastic range, and cyclic strain hardening, as well as the spread of plasticity through the thickness and plane of the plate. The cyclic elastoplastic performance of the formulation was found to be good when compared with the results obtained from other material models. Based on the results of an extensive parametric study, the effect of loading history and some important plate parameters on the hysteretic behavior of thin plates is discussed and evaluated.

Post-Ultimate Strength Behaviour of Rectangular Panel under Thrust

In the present paper, post-ultimate strength behaviour of a rectangular panel subjected to uni-axial thrust is discussed based on the results of elastoplastic large deflection analysis by the FEM. It has been found that :(1) When a panel is accompanied by initial deflection of a buckling mode, deflection of a sinusoidal mode gradually changes to that of a periodical roof mode in the post-ultimate strength range except when the panel is very thick.(2) When a panel is accompanied by initial deflection of a hungry-horse mode, plastic deformation is concentrated at a certain part of deflection mode, and unloading takes place in the remaining part. Because of this, capacity after the ultimate strength rapidly decreases.A simple plate element is proposed to simulate the behaviour mentioned in (2), and the calculated results applying the proposed elements show good agreements with those by the FEM. At the end, fundamental idea is described to develop new Idealized Structural Units (ISUM element).

Analysis of Buckling/Plastic Collapse Behaviour of Stiffened Plate under Thrust Using Simple Dynamical Plate Model

A simple and efficient method of buckling/plastic collapse analysis of stiffened plates subjected to uni -axial thrust is presented. Plate part between stiffeners is divided into several plate elements in the stiffener direction. Thebuckling/plastic collapse behaviour of plate element is simulated using a simple dynamical model combining the results of elastic large deflection analysis and rigid plastic mechanism analysis. The influence of a torsional stiffness of stiffeners on the local buckling strength of plate part is taken into account. Stiffener part is modeled by beam-column elements which can simulate a flexural-torsional buckling behaviour of thin-walled beams. Coupling the plate and beamcolumn elements, the buckling/plastic collapse behaviour of stiffened plates accompanied by both local and overall buckling can be analysed. It is also possible to simulate a localisation of plastic deformation in a certain part of panel deflection and a resulting unloading in the remaining part, which have a large influence on the capacity beyond the ultimate strength.Using the proposed method, a series of buckling/plastic collapse analysis of stiffened plates is performed, and the applicability of the proposed method is discussed through a comparison with the ordinary elastoplastic large deflection FEM analysis.

Buckling/Plastic Collapse Strength of Ship Bottom Plating

To clarify the buckling/plastic collapse behaviour and strength of ship bottom plating, a series of elastoplastic large deflection FEM analyses is performed on stiffened plates subjected to combined biaxial thrust and lateral pressure. A part of continuous stiffened plate is considered for analysis taking into account of symmetry conditions. A series of elastic large deflection FEM analyses is also performed on continuous plating without stiffeners to examine the influence of lateral pressure on the buckling behaviour of plating.It has been found that : (1) When initial deflection is in a hungry horse mode, bifurcation buckling takes place. The buckling strength increases with the increase in applied lateral pressure.(2) The buckling strength is increased also by the stiffeners, which constrain the rotation of panel along its edge. An analytical formula is derived to evaluate the local buckling strength of stiffened plate considering the influence of stiffeners.(3) With the increase in applied lateral pressure, the boundary condition of the panel between stiffeners changes from simply supported condition to clamped condition. This change increases the buckling/plastic collapse strength of stiffened plate.(4) With larger lateral pressure, yielding starts earlier. This reduces the buckling/plastic collapse strength of stiffened plate.(5) Owing to the opposite effects described above, the buckling/plastic collapse strength of stiffened plate takes its maximum value at a certain magnitude of lateral pressure, especially when transverse compression is dominant.(6) The formulae by classification societies give conservative buckling strength under bi-axial compression, and the bottom plating has much reserve up to the ultimate strength even when lateral pressure is acting.

Buckling/Plastic Collapse Strength of Wide Rectangular Plate under Combined Pressure and Thrust

A series of elastic/elastoplastic large deflection analyses is performed to clarify buckling/plastic collapse behaviour of a wide rectangular plate as a part of ship bottom plating subjected to combined lateral pressure and transverse thrust. A continuous plating with and without stiffeners is analysed to examine the influences of plate continuity and stiffeners on its buckling/plastic collapse behaviour.Firstly, influence of loading sequence of pressure and thrust loads is examined. The difference between the results of analysis using double bay and triple bay models is also examined for the case of stiffened plate with angle-bar stiffeners.Then, based on the results of elastic large deflection analyses, a semi-empirical formula is derived to evaluate the elastic buckling strength of a wide rectangular plate subjected to combined lateral pressure and transverse thrust considering the influence of plate continuity and stiffeners.At the end, the influences of pattern and magnitude of initial deflection as well as stiffeners on the ultimate strength of a wide rectangular plate are discussed through elastoplastic large deflection analyses on continuous plating with and without stiffeners.