Search

The various assessment methods of ultimate strength for hull girder of ships or offshore structures might lead to different results and computation time. The nonlinear finite element (FE) analyses include the implicit static analysis and explicit dynamic analysis, which both can consider the large deflection and material nonlinearity during the process of progressive collapse. Comparing with the implicit static analysis, the explicit dynamic analysis can consider the transient influence of time and avoid the convergence issue in iterative procedure. The object of the present paper is to figure out a reliable and suitable FE modelling in the explicit dynamic method, which could keep the balance of the acceptable accurate results and computation resources. Several influential factors on the collapse behaviours of hull girder are discussed including boundary conditions, geometric ranges of finite element model, element types, loading methods and loading time. The results of a Suezmax oil tanker and Reckling models assessed by the explicit dynamic method are compared with that by the other analytical methods or in the experiment. [ABSTRACT FROM AUTHOR]

Various bifurcation behaviors, including asymmetric axial buckling induced by end thrust, bifurcation under external pressure, and eversion without any loading, of a soft circular hollow cylinder (or cylindrical shell) composed of functionally graded incompressible elastomeric material are considered in a unified way. Based on the nonlinear elasticity theory of a deformable continuous body undergoing large deformation and the linearized incremental theory for a superimposed infinitesimal deformation, an efficient approach for buckling analysis is developed and applied to the cylinder subjected to a combination of axial end thrust and internal/external pressure. It is based on the state-space formalism, which naturally avoids the derivatives of instantaneous material constants, enabling a convenient and accurate numerical implementation. Along with the layerwise method, an analytical characteristic equation (i.e. the bifurcation criterion) governing the general asymmetric buckling of the cylinder is derived. Detailed parametric studies are then carried out for a pressurized soft functionally graded hollow cylinder using an incompressible Mooney-Rivlin material model. The effects of material gradient on bifurcation induced either by end thrust or external pressure are discussed through numerical examples. Not only does this study provide an efficient tool for buckling analysis of soft cylinders, some findings that are unique to a functionally graded material are also highlighted. All in all, it is found highly possible to tune the bifurcation behavior of soft elastomeric cylindrical shells by tailoring material composition and/or adjusting the pressures acting on the surfaces of the cylinder. [ABSTRACT FROM AUTHOR]

This note introduces a new computational scheme based on a numerical Picard-like method, which combines successive approximations with differential quadrature rules in order to improve the computational efficiency. Despite of its recursive nature, this scheme can generate the approximate solution in terms of operational matrices and vectors of known quantities. This allows to define explicitly an error functional which can be minimized in order to easily compute the critical load. The performance of this new scheme is examined by means of two application examples. A comparison with the available solutions is carried out, by showing that the method behaves satisfactorily. [ABSTRACT FROM AUTHOR]

Abstract: Based on the modified couple stress theory (MCST), a unified higher order beam theory which contains various beam theories as special cases is proposed for buckling of a functionally graded (FG) microbeam embedded in elastic Pasternak medium. This non-classical microbeam model incorporates the material length scale parameter which can capture the size effect. The non-classical beam model reduces to the classical beam model when the material length scale parameter is set to zero. The material properties of the FG microbeam are assumed to vary in the thickness direction and are estimated through the Mori–Tanaka homogenization technique and the classical rule of mixture. The governing equations and the related boundary conditions are derived using the principal of the minimum total potential energy. The Navier-type solution is developed for simply-supported boundary conditions, and explicit expressions related to each type of beam theory are proposed for the critical buckling load. Numerical results are presented to investigate the influences the material length scale parameter, aspect ratio, different estimation method of material properties, various material compositions, and the parameters of the elastic medium on the critical buckling load. Comparison study is also performed to verify the present formulation. [Copyright &y& Elsevier]

Highlights: [•] An equilibrium method is developed for computing critical equilibrium states. [•] Non-linearly elastic linkages are studied considering large displacements. [•] Statically indeterminate structures and general loadings are dealt with. [•] A global, robust numerical procedure is utilised. [•] Snapping phenomena and structurally unstable equilibrium states are revealed. [ABSTRACT FROM AUTHOR]

Abstract: This paper is a theoretical and numerical study of the uniform growth of a repeating sinusoidal imperfection in the line of a strut on a nonlinear elastic Winkler-type foundation. The imperfection is introduced by considering an initially deformed shape which is a sine function with an half wavelength. The restoring force is either a bi-linear or an exponential profile. Periodic solutions of the equilibrium problem are found using three different approaches: a semi-analytical method, an explicit solution of a Galerkin method and a direct numerical resolution. These methods are found in very good agreement and show the existence of a maximum imperfection size which leads to a limit point in the equilibrium curve of the system. The existence of this limit point is very important since it governs the appearance of localization phenomena. Using the Galerkin method, we then establish an exact formula for this maximum imperfection size and we show that it does not depend on the choice of the restoring force. We also show that this method provides a better estimate with respect to previous publications. The decrease in the maximum compressive force supported by the beam as a function of the imperfection magnitude is also determined. We show that the leading term of the development has a different exponent than in subcritical buckling of elastic systems, and that the exponent values depend on the choice of the restoring force. [Copyright &y& Elsevier]

Abstract: This paper is concerned with an efficient algorithm for the wrinkling with finite strains of very thin structures made of hyperelastic material. In this work, the problem of wrinkling is solved by directly minimizing the total potential energy of the structure. The numerical solution is carried out by the means of an iterative method such as the conjugate gradient algorithm. Although the proposed approach is theoretically equivalent to the traditional finite element method, it proves to be an attractive alternative which is particularly efficient for thin wrinkled structures. [Copyright &y& Elsevier]

Abstract: The elastic-plastic buckling of short and relatively thick unstiffened truncated conical shells subjected to axial compression and external pressure is investigated. This is done using numerical and experimental approach. For the numerical analysis, the finite element code is employed to obtain the domain of combined stability. To validate numerical predictions, thirteen nominally identical laboratory scale cones with 26.56° semi-vertex angle and 3 mm nominal wall thickness with integral top and bottom flanges were CNC machined from 252 mm diameter mild steel billet. Two of the models were subjected to axial compression, with further two subjected to pure lateral external pressure, while the remaining nine cones were subjected to combined action of axial compression and external pressure of different ratio. Experimental results compare well with numerical predictions except for pure axial compression. However, the accuracy of these results is strongly dependent on the approach to modeling of material. Experimental results were compared with predictions of failure loads obtained from ASME code case 2286–2, and with the ECCS design rules for the case of axial compression and lateral pressure. [Copyright &y& Elsevier]

Abstract: In the paper an alternative for horizontal cylindrical tank is presented. The proposed solution has the form of a barrelled tank in which the classical cylindrical shell is replaced by the barrelled one. The geometry of this shape is described. The buckling behaviour of the horizontal barrelled shell filled with liquid is analysed. The liquid level and the negative internal pressure which appear during emptying of the tank are also taken into consideration. On the basis of numerical analyses number of plots as well as analytical formulae are elaborated as a tool for design of barrelled tank with respect of stability criterion. Analyses are made on three families of barrelled shells of different capacities. In each family the capacity and length are constant. Advantages of barrelled tanks in comparison with cylindrical one are discussed. [Copyright &y& Elsevier]

Abstract: The paper considers the buckling of short, and relatively thick, mild steel conical shells subjected to the combined action of external pressure and axial compression. Past results on axially compressed cones and on cones subjected to hydrostatic external pressure are compared with fresh test results on equivalent, axially compressed cylinder and with the equivalent cylinder subjected to external hydrostatic pressure. The paper contains both numerical and experimental results. Details about experiments, numerical modelling and computed estimates of the load carrying capacity of analyzed shells are given. Results of this study suggest that the concept of equivalent cylinders is not applicable to short master-cones. Combined stability plots have also been derived for the master-cone and equivalent cylinders. They provide not only the failure envelopes but also the yield envelopes and spread of plastic zones. The paper also brings into the light a useful design tool proposed by Esslinger and van Impe , and applicable to elastic–plastic buckling of cones subjected to external hydrostatic pressure. [ABSTRACT FROM AUTHOR]

Abstract: Gauge sensitivity indices are a family of techniques for assessing the effect of thickness changes on automotive structural performance. This paper studies the effect of elastic instability on stiffness-based gauge sensitivity indices and demonstrates that as gauge reduction proceeds, the onset of elastic instability results in instantaneous increase in gauges sensitivity. Analysis results are interpreted and validated by a series of numerical examples. The work concludes with application case studies illustrating application of gauge sensitivity for assessing and managing elastic instability present within a light duty truck cab. [Copyright &y& Elsevier]

Abstract: This paper presents a thorough and comprehensive investigation of non-linear buckling and postbuckling analyses of pin-ended shallow circular arches subjected to a uniform radial load and which have equal elastic rotational end-restraints. The differential equations of equilibrium for non-linear buckling and postbuckling are established based on a virtual work approach. Exact solutions for the non-linear bifurcation, limit point and lowest buckling loads are obtained; in particular, exact solutions for the non-linear postbuckling equilibrium paths are derived. The criteria for switching between fundamental buckling and postbuckling modes are developed in terms of critical values of a geometric parameter for an arch, with exact solutions for these critical values of geometric parameter being obtained. Analytical solutions of non-linear buckling and postbuckling problems for arches with rotational end-restraints are of great interest, since they constitute one of the very few closed-form analyses of buckling and postbuckling behaviour of continuous structural systems. These exact solutions are a contribution to the non-linear structural mechanics of arches, as well as providing useful benchmark solutions for verifying non-linear numerical analyses. [Copyright &y& Elsevier]

Abstract: This paper presents a numerical technique to deal with instability phenomena in the context of heterogeneous materials where buckling may occur at both macroscopic and/or microscopic scales. We limit ourselves to elastic materials but geometrical nonlinearity is taken into account at both scales. The proposed approach combines the multilevel finite element analysis and the asymptotic numerical method (ANM). In that framework, the unknown nonlinear constitutive relationship at the macroscale is found by solving a local finite element problem at the microscale. In contrast with , the use of the asymptotic development allows to transform the nonlinear microscopic problems into a sequence of linear problems. Thus, a direct analogy with classical linear homogenization can be made to construct a localization tensor at each step of the asymptotic development, and an explicit macroscopic constitutive relationship can be constructed at each step. Furthermore, the salient features of the ANM allow treating instabilities and limit points in a very simple way at both scales. The method is tested and illustrated through numerical examples involving local instabilities which have significant influence on the macroscopic behaviour. [Copyright &y& Elsevier]

Abstract: The governing equations of elasticity theory for natural vibration and buckling are derived from Hellinger–Reissner’s variational principle with nonlinear strain–displacement relations. Simply supported rectangular laminated plates based on exact theory of elasticity are studied by precise integration method. This method, in contrast to the traditional finite-difference approximation, gives highly precise numerical result, which approaches the full computer precision. So the results for natural vibration and buckling of cross-ply laminated plates, angle-ply laminated plates and hybrid plates presented in the paper can be regarded as analytical solutions. These results can be taken as a standard for both thin plates and moderately thick plates theory considering the effect of shear deformation. The several types of coupling effects, such as coupling between bending and twisting, coupling between extension and bending, etc. when the layer stacking sequence is not symmetric, are considered by only one set of governing equations. [Copyright &y& Elsevier]