Elasto-plastic Buckling Analysis Research Articles

A new analytical tool for the elastic/plastic buckling design of pressure vessels subjected to external pressure

This paper deals with the elastic/plastic buckling design of pressure vessels under external pressure loading. The objective is to build a simple analytical tool devoted to the elastic and elastoplastic buckling analysis of pressure equipments. This tool is aimed to provide the critical external pressure of cylindrical pressure vessels with ellipsoidal (or possibly hemispherical) heads. Depending on the geometry of the equipment and material parameters, the first buckling pressure may involve either the cylindrical shell or the closure ends, in the elastic or plastic range. The calculation tool will be thus based on a series of exact or approximate analytical solutions of the critical pressure of each part of the considered equipment. In this paper, the elementary shell structures involved in such pressure equipments are first individually examined. The fundamental critical pressures for each of them are recalled or introduced, both in elasticity and plasticity. The new solutions are validated against reference numerical results obtained through finite element computations. Then, approximate solutions of the critical pressure are derived for the same shells, taking account of specific boundary conditions (and not idealized ones, as before) due to the presence of the remaining part of the equipment. In the end, a VBA Excel software is developed. It is able to provide the mappings of the buckling mode type and the corresponding critical pressures for large ranges of geometric and material parameters in a very efficient way. These analytical solutions are finally confronted to numerical calculations performed on complete pressure equipments and they are shown to give quite reliable results. A discussion is also initiated on the use of such a program to update the current design rules in this scope of application.

Parametric study on the assessment of the local buckling behavior of perforated square hollow sections with non-uniform wall thickness under axial compression

The aim of this rigorous parametric study is to explore the influence of perforations on the local buckling behavior of square hollow sections (SHSs) possessing non-uniform wall thickness. A finite element procedure followed in the current study has been first validated against existing test results documented for the local buckling behavior of the perforated SHS with uniform web and flange segment thickness under axial compression. The linear elastic eigenvalue buckling and elastoplastic buckling analyses have been implemented using the Abaqus engineering finite element code. The verification of the numerical procedure has been achieved by favorably comparing the finite element results with the existing test results in terms of the first local buckling mode shape and load-end shortening curves of the perforated SHS with uniform wall thickness. . The verified numerical procedure has been applied to the problem of finding the perforation effect on the local buckling response of the SHS with non-uniform thickness. Finite element analyses have been performed for four various web width-to-perforation diameter ratios ranging from 0.3 to 0.9. Finite element analysis results have revealed that the presence of perforations does not influence the local buckling mode shape of the SHS but considerably affects the critical local buckling loads. The results have put forth that increasing perforation diameter leads to a more pronounced and drastic decrease in the critical local buckling load. The outcomes of the study have also shown that the critical post-buckling load of the SHS with non-uniform wall thickness is less susceptible to perforations compared to the SHS with uniform wall thickness. The results obtained in the context of this parametric study have been made available to practical engineering for use in actual design of the perforated SHSs.

Ultimate strength of hyper-ellipse flanged-perforated plates under uniaxial compression loading

Abstract In order to address the impact of the perforated parameters on the mechanical properties of the plate, the ultimate strength of hyper-ellipse flanged-perforated plates under uniaxial compression stress is numerically investigated in this article. The four edges of the flanged-perforated plate are only supported in the out-of-plane direction while the plate is exposed to uniaxial compressive loads. The impact of the cutout size, flange height, cutout position, rotation angle, and cutout form on the ultimate bearing capacity of the perforated plate with varied thicknesses is investigated and compared through a series of elasto-plastic buckling analyses using the ANSYS software. The structure’s stress and deformation analysis is then used to explain the results of the ultimate strength test. The flange efficiently raises the maximum bearing strength of the structure with cutouts. For the limit strength of thick plate, the cutout size, elliptical shape, cutout rotation angle, and cutout position have considerably more of an impact than they do on the maximum bearing capacity of thin plate. The findings can assist the structural layout of this sort of perforated plate, and the right cutout parameters should be chosen in accordance with the various performance specifications.

Closed-form solutions for the elastic–plastic buckling design of shell structures under external pressure

This paper deals with the elastoplastic buckling analysis of shell geometries traditionally encountered in pressure vessels subjected to external pressure loading. The objective is to propose in a unified way original analytical closed-form solutions giving rise to reliable results, with a good accuracy and a wide range of applications in a straightforward and low time-consuming way, for efficient dimensioning purposes. The present study is based on the plastic bifurcation theory, classically used in the context of conservative systems, where additional terms are incorporated here due to the follower external pressure acting normally to the deformed surface of the shell still after buckling. Cylindrical shells are first considered, which certainly represent the most fundamental components of pressure vessels in practice. Owing to the external pressure also acting on the closure ends of a cylinder, the influence of the induced axial compression is investigated thereafter. It appears to be non-negligible for short cylinders in elasticity and it becomes very significant in the case of plastic buckling. Then, closed-form solutions for the critical external pressure of a complete sphere are also obtained, both in elasticity and plasticity. Finally, all these new closed-form solutions are validated against reference numerical results obtained through finite element computations, and compared to current design rules.

Assessment of the global stability of three-limbed steel tube latticed column using finite element modelling

In order to study the stability performance of the three-limbed steel tube latticed column, the finite element numerical analysis method based on the structural stability theory is adopted. Firstly, the linear analysis of the three-limbed steel tube latticed column without diagonal lacing bar is carried out, and the calculation method of elastic buckling load considering the influence of shear deformation is obtained. Then, the elastic buckling analysis and elastoplastic buckling analysis three-limbed steel tube latticed column with diagonal lacing bar are carried out. The elastic buckling load and elastoplastic buckling load of three-limbed steel tube latticed column with diagonal lacing bar are studied when only the global initial geometric defects, only the member initial geometric defects, and both kinds of defects are considered at the same time. The results show that the direct finite element analysis method can be used to calculate the elastic buckling load of three-limbed steel tube latticed column with diagonal lacing bar, and the error is 6.67%. In the elastic analysis of three-limbed steel tube latticed column with diagonal lacing bar, the column global stability mainly depends on the global initial geometric defects, and the member initial geometric defect is negligible. And when two kinds of defects are applied at the same time, the structural buckling load is reduced by less than 0.20% compared to the global initial geometric defects. In the elastoplastic analysis, the column global stability is determined by both the global initial geometric defect and the member initial geometric defect. When both defects are applied at the same time, the structural buckling load decreases by less than 0.65% compared to the global initial geometric defect only, and 7.60% compared to the member initial geometric defects only. It can be concluded that there is little difference in the overall stability bearing capacity between the two kinds of defects.

In-plane stability of an underground support system with steel corrugated webs: Experimental study, finite element analysis, and design formula

This study proposed an innovative underground support system with I-shaped sections that use steel corrugated webs. The in-plane global buckling behavior of the proposed system was investigated through comprehensive experimental, numerical, and analytical analyses. An experimental test was carried out against a scaled specimen of the proposed support for U-shaped mining roadways when subjected to three concentrated loads. The global asymmetric buckling was identified as the ultimate failure mode. A finite element (FE) model was constructed and verified by comparing its analysis results with the experimental outcomes. Finite element analyses (FEA) first proved that both the stiffness and force capacity of the support with corrugated webs could be much increased when compared with the I-shaped steel that uses flat webs under the same steel consumption. The elastic and elastoplastic buckling analyses from the FEA further indicated that the web height and flange thickness were the influential parameters, from which a closed-form formula was developed to predict the elastic buckling load as a function of the slenderness ratio. Analysis results have shown that the support system will inevitably fail through antisymmetric instability when the slenderness ratio is large, yet the system was not very sensitive to initial imperfections. A design formula for the in-plane compression-bending capacity was derived for the proposed support system by synthesizing and modifying existing relevant design equations. The proposed innovative support system, together with the associated experimental testing, FEA, elastic buckling load formula, and design equation, paves the way to promote its real-world applications as tunnel supports to deal with harsh geological conditions (e.g., soft rocks).

Proposal of the buckling design method by elasto-plastic buckling analysis for steel containment vessel of nuclear power plant

Proposal of the buckling design method by elasto-plastic buckling analysis for steel containment vessel of nuclear power plant

Nonlinear stability analysis of a radially retractable hybrid grid shell in the closed position

The buckling capacity of a radially retractable hybrid grid shell in the closed position was investigated in this paper. The geometrically non-linear elastic buckling and elasto-plastic buckling analyses of the hybrid structure were carried out. A parametric study was done to investigate the effects rise-to-span ratio, beam section, area and pre-stress of cables, on the failure load. Also, the influence of the shape and scale of imperfections on the elasto-plastic buckling loads was discussed. The results show that the critical buckling load is reduced by taking account of material non-linearity. Furthermore, increasing the rise-tospan ratio or the cross-section area of steel beams notably improves the stability of the structure. However, the cross section area and pre-stress of cables pose negligible effect on the structural stability. It can also be found that the hybrid structure is highly sensitive to geometric imperfection which will considerably reduce the failure load. The proper shape and scale of the imperfection are also important.

Buckling of piecewise member composed of steel and high-strength materials in axial compression

The elastic buckling load of an axially compressed piecewise member was derived under various ideal boundary conditions based on the differential element method; then, the result was simplified for a symmetrical member. The theoretical results were found to be consistent with existing formulas for the elastic buckling load of uniform members. Then, the elasto-plastic buckling of an axially compressed piecewise member composed of steel and elastic materials was investigated and found to be quite different from that of a pure steel member, and a theoretical analysis approach was developed. In elasto-plastic buckling analysis, the load-bearing capacity of the steel section in the ultimate state is determined considering initial imperfections and steel hardening. Furthermore, the symmetric method for obtaining the load-bearing capacity of this member was obtained based on the ultimate state of the critical section, which is simple and reparative for design. The theoretical results of the elasto-plastic buckling analysis were consistent with experimental results, therein obtaining an average error of 4%.

Elastoplastic buckling analysis of thin-walled structures

The study is concerned with the elastoplastic buckling of thin-walled beams and stiffened plates, subjected to in-plane, uniformly distributed, uniaxial and biaxial load. The ruling differential equations have been solved analytically by using the Kantorovich technique and the obtained displacement field has been employed in a general procedure that, by using the framework derived by the finite element method, is able to analyze the elastoplastic buckling behavior of prismatic beams and stiffened plates with arbitrary cross-section. The inelastic effect is modeled through a stress–strain law of the Ramberg–Osgood type, and both the incremental deformation theory and the J2 flow theory are here considered. The reliability of the numerical procedure is illustrated for rectangular plates, and the contradicting results obtained by using the two plastic theories are discussed in detail. Finally, the performance of the method is illustrated through the analysis of a C-section and five different closed section columns.

Elastoplastic buckling analysis of rectangular thick plates by incremental and deformation theories of plasticity

In this study, the elastoplastic buckling behavior of thick plates under uniaxial, biaxial compression/tension, pure shear and combined shear, and uniaxial compression loading are analyzed using a stability analysis based on generalized differential quadrature method. Based on first-order shear deformation plate theory and incremental and deformation theories of plasticity, the nonlinear equilibrium equations are developed. Various combinations of clamped, simply supported, and free boundary conditions are considered. The governing equations and solution domain are discretized by the generalized differential quadrature method. The results are compared with known solutions in literature to verify the established methodology and procedures. The effects of aspect, loading and thickness ratios, shear correction factor, different boundary conditions, and behavior of material on the buckling coefficient are discussed. Finally, some mode shapes of various loading and boundary conditions are illustrated.

Force-based FE for large displacement inelastic analysis of two-layer Timoshenko beams with interlayer slips

This paper presents a novel finite element model for the fully material and geometrical nonlinear analysis of shear-deformable two-layer composite planar beam/column members with interlayer slips. We adopt the co-rotational approach where the motion of the element is decomposed into two parts: a rigid body motion which defines a local co-ordinate system and a small deformational motion of the element relative to this local co-ordinate system. The main advantage of this approach is that the transformation matrices relating local and global quantities are independent from the choice of the geometrical linear local element. The effect of transverse shear deformation of the layers is taken into account by assuming that each layer behaves as a Timoshenko beam element. The layers are assumed to be continuously connected and partial interaction is considered by adopting a continuous relationship between the interface shear flow and the corresponding slip. In order to avoid curvature and the shear locking phenomena, the local linear element is derived from the force-based formulation. The present model provides an efficient tool for the elastoplastic buckling analysis of two-layer shear deformable beam/column with arbitrary support and loading conditions. Finally, two numerical applications are presented in order to assess the performance of the proposed formulation.

Non-linear stability analysis of a hybrid barrel vault roof

This paper focuses on the buckling capacity of a hybrid grid shell. The eigenvalue buckling, geometrical non-linear elastic buckling and elasto-plastic buckling analyses of the hybrid structure were carried out. Then the influences of the shape and scale of imperfections on the elasto-plastic buckling loads were discussed. Also, the effects of different structural parameters, such as the rise-to-span ratio, beam section, area and pre-stress of cables and boundary conditions, on the failure load were investigated. Based on the comparison between elastic and elasto-plastic buckling loads, the effect of material non-linearity on the stability of the hybrid barrel vault is found significant. Furthermore, the stability of a hybrid barrel vault is sensitive to the anti-symmetrical distribution of loads. It is also shown that the structures are highly imperfection sensitive which can greatly reduce their failure loads. The results also show that the support conditions pose significant effect on the elasto-plastic buckling load of a perfect hybrid structure.

NONLINEAR STABILITY ANALYSIS OF HYBRID GRID SHELLS

In this paper, we investigate the buckling capacity of a hybrid grid shell, which is made of quadrangular meshes diagonally stiffened by pre-tensioned thin cables. The eigenvalue buckling, geometrical nonlinear elastic buckling and elasto-plastic buckling analyses of the hybrid structure were carried out. Then the influences of the shape and scale of imperfections on the elasto-plastic buckling loads were discussed. Also, the effects of different structural parameters, such as the rise-to-span ratio, cross-section of beams, area and pre-stress of cables and boundary conditions, on the failure load were investigated. The results show that the buckling capacity is reduced when taking into account the material nonlinearity. Furthermore, the hybrid structure is highly imperfection sensitive and the reduction of the failure load due to imperfections can be considerable. The proper shape and scale of the imperfection are also important. It is also shown that there exists an optimal rise-to-span ratio resulting in a relatively high buckling capacity for a specific span. Moreover, the enlarging of the cross-section of steel beams notably improves the stability performance of the structure. However, the area and pre-stress of cables pose small effect on the structural stability.

NONLINEAR STABILITY OF A SINGLE-LAYER HYBRID GRID SHELL

This paper presents a study of a hybrid grid shell, which is made of quadrangular meshes diagonally stiffened by pre-tensioned thin cables. The construction of the hybrid structure by translating a spatial curve against another spatial curve is firstly described. Then the elasto-plastic buckling analyses of the perfect hybrid structure and the corresponding single-layer lattice shell are carried out, and the influence of the asymmetric load on the failure loads is discussed based on a finite element model. Furthermore, the different shapes and sizes of imperfections are considered in this study. Two schemes of imposing imperfections are chosen: the first several eigenvalue buckling modes and the deformed shape of the loaded structure obtained from a geometrical non-linear analysis are chosen as the imperfection shape. Finally, the effects of different structural parameters, such as the rise-to-span ratio, beam section dimension, area and pre-stress of cables and boundary conditions, on the failure loads are investigated.

Elasto-plastic buckling analysis for perforated steel plates subject to uniform compression

This study investigates the elasto-plastic buckling behaviour of simply supported square and rectangular thin steel plates having elliptic cut-outs by means of finite element method. Plates with simply supported in the out-of-plane direction are applied uniform compression in long-edge direction. A50 steel was used in the analysis and the focus was on the effect of plate aspect ratio, elliptical hole size, elliptical hole angle, elliptical hole location and slenderness ratio on buckling behaviour. It was found in the study that as the plate slenderness ratio increases, the critical buckling stress decreases for all the perforated plates.

Elastoplastic buckling analysis of thick rectangular plates by using the differential quadrature method

The paper investigates the elastoplastic buckling behavior of thick rectangular plates by using the Differential Quadrature (DQ) method. Mindlin plate theory is adopted to take the transverse shear effect into considerations. Both incremental theory and deformation theory are employed. Due to the material non-linearity, iteration processes are involved for obtaining solutions. Detailed methodology and procedures are derived. The elastoplastic buckling behavior of thick rectangular plates with ten combinations of boundary conditions and under various loadings is studied. To verify the DQ solution procedures, DQ results are compared with existing analytical solutions for plates with two boundaries simply supported and the others simply supported, clamped, or free. Then the DQ method is used to obtain solutions of rectangular thick plates with other combinations of boundary conditions. Since no analytical solutions for such cases are available, the buckling loads obtained by the DQ method could serve as a reference. The phenomenon reported in the literature, namely, the deformation theory generally gives consistently lower buckling loads than the incremental theory and large discrepancy in predictions between the two theories exists with increasing of plate thickness. E / σ 0 , and c in the Ramberg–Osgood relations, is also observed for the cases studied herein. Apart from the phenomenon reported earlier by Durban that deformation theory predicted a progressively lower in-plane shear modulus as the level of plasticity increased, thus predicted lower buckling loads, another reason is given herein to explain the large discrepancy in predictions for thicker plates with the deformation theory and incremental theory.

Elasto-plastic buckling analysis of laminated plates including interfacial damage

Elasto-plastic buckling of orthotropic laminated plates, which include interfacial damage, is analyzed in detail. Firstly, a novel mixed hardening yield criterion, as an improvement of Hill’s counterpart, is proposed for the orthotropic materials on the basis of the plastic theory. And differing from Hill’s theory, the present yield criterion is related to the spherical tensor of stress. Then, the incremental elasto-plastic constitutive relations of the mixed hardening orthotropic materials are presented. Secondly, the incremental static equilibrium equations for laminated plates including interfacial damage are established based on Von-Karman type theory and the principle of minimum potential energy. Finally, the elasto-plastic buckling of laminated plates are solved by adopting the Galerkin method and iteration scheme. The numerical results show that buckling of the plate occurs easier due to the existence of interfacial damage, and the critical load trends to constant when the interfacial damage approaches a certain degree. Also, the effect of anisotropy on buckling is obvious and the analysis of elasto-plastic buckling is necessary.

A STUDY ON BUCKLING LOAD OF LATTICE DOMES OF TWO-WAY

The present paper proposes an efficient method for evaluating the elasto-plastic buckling loads of two-way single layer lattice domes under vertical loads. The connections are assumed semi-rigid as formed with screwed bolt-to-ball joints. The procedure of the method is composed of the following steps: linear buckling analysis to find the generalized slenderness ratio of the specific member that is the most relevant to their loading capacities; the generalized slenderness ratio is applied to obtain the axial strength for the specific member, based on which the elasto-plastic buckling load is evaluated. The comparison of the evaluated buckling loads with those obtained from FEM elasto-plastic buckling analyses proves that the procedure is valid and efficient enough to be applied in design practice. Based on safety factors, given in some recommendations, the allowable column strength is also proposed for proportioning the members of the single layer lattice domes.

Elastoplastic buckling analyses of rectangular plates under biaxial loadings by the differential qudrature method

The paper investigates the elastoplastic buckling behavior of thin rectangular plates under biaxial loadings by using the differential quadrature (DQ) method for the first time. Both J 2 ′ flow and deformation plasticity theories are adopted and iteration processes are involved due to the material non-linearity. The methodology and procedures are worked out in detail. The buckling behavior of thin rectangular plates with various combinations of boundary conditions and under various loadings is studied. It is found that the DQ results are compared well with existing analytical solutions for plates with two boundaries simply supported and the others either simply supported or clamped. Buckling loads for plates with other combinations of boundary conditions, no analytical solutions are available in such cases, are also presented. The existence of an optimal loading path for the deformation theory model, firstly reported by Durban and Zuckerman, is also observed in such cases. The possible reason is given to explain the large discrepancy in predictions for thicker plates by the J 2 ′ flow theory and deformation plasticity theory.