SUMMARYMany natural clays have an undisturbed shear strength in excess of the remoulded strength. Destructuration modeling provides a means to account for such sensitivity in a constitutive model. This paper extends the SANICLAY model to include destructuration. Two distinct types of destructuration are considered: isotropic and frictional. The former is a concept already presented in relation to other models and in essence constitutes a mechanism of isotropic softening of the yield surface with destructuration. The latter refers to the reduction of the critical stress ratio reflecting the effect of destructuration on the friction angle, and is believed to be a novel proposition. Both the types depend on a measure of destructuration rate expressed in terms of combined plastic volumetric and deviatoric strain rates. The SANICLAY model itself is generalized from its previous form by additional dependence of the yield surface on the third isotropic stress invariant. Such a generalization allows to obtain as particular cases simplified model versions of lower complexity including one with a single surface and associative flow rule, by simply setting accordingly parameters of the generalized version. A detailed calibration procedure of the relatively few model constants is presented, and the performance of three versions of the model, in descending order of complexity, is validated by comparison of simulations to various data for oedometric consolidation followed by triaxial undrained compression and extension tests on two structured clays.

Of interest here is the influence of imperfections on the stability ofelastic systems. discrete or continuous. with nearly simultaneous modes. The majority of such structures show an extreme sensitivity of their first instability load to the shape of these small amplitude but unavoidable imperfections. The determination of the worst such possible shape is thus a very important issue from the design standpoint. Following a general analysis of the stability of arbitrary elastic systems with nearly simultaneous bifurcation eigenmodes in the presence of imperfections. conditions are given for the determination of the worst imperfection shape which minimizes Ihe first local load manimum. For the case of coincident eigenmodes Ihe answer 10 the worst shape problem is considerably simplified. for it is determined from the equilibrium branch of rhe perfect structure on which the load drops more rapidly. I. lNTRODUCTlON Of interest here is the influence of imperfections on the stability of elastic systems (discrete or continuous) with nearly simultaneous modes. The study of bifurcation and stability in structures with simultaneous or nearly simultancous nwdcs is a classical problem in solid mechanics. AS such it has received a great deal of attolltion in cngincoring literature. ~splklly aI*tcr Koitcr's (1945) pioneering work that put the problem on a sound mathematical basis. In addition to its theoretical interest, and accompanying inherent dilliculties. the problem is also of great practical importance. There is a variety of engineering applications that exhibit multiple bifurcation points at their first buckling loads. Perhaps the best known such examples are the thin walled shell type structures such as thin walled beams, cylinders, cylindrical panels, spheres and spherical caps. The thinner such structures are.the greater the number of buckling modes that appear almost simultaneously near the lowest critical load. Another set of applications contains stitii'ned structures, such as rib stilknsd plates and cylindrical panels iis well iIS large frame type space structures in which a fundamental unit cell can be identified. Due to their particular geometry, both a global and a local buckling mode can occur at, or nearly at, the same load Icvel. The global modes, which have a characteristic wavelength on the order of the dimensions of the structure interact with the local modes whose characteristic wavelength is of the order of the unit cell size. Finally, an additional interesting application pertains to structures that have been optimized with respect to their lowest buckling loads. The optimization procedure leads to overlapping with the next higher buckling load. The higher the number of available design parameters, the more simultaneous modes appear in the optimized structure. For these structures, the first instability point (i.e. the first bifurcation point or local load maximum) can be extremely sensitive to the shape of imperfections. The determination of the worst such possible shape is thus a very important issu...

A SUMMARYMany liquid storage tanks consist of a steel cylindrical shell, which is welded to a base plate, but not fixed to the foundation. When such an unanchored tank is subjected to lateral loads due to earthquake induced hydrodynamic pressures in the liquid, the tank wall tends to uplift locally, pulling the base plate up with it. The contact problem of the partially uplifted base plate and its interaction with the the cylindrical shell is solved in this paper using the finite difference energy method, and a Fourier decomposition of the displacements in the circumferential direction. Non-linearities due to contact, finite displacements and yield of the steel are included in the analysis. However, the equations for the shell are linearized. This uncouples the equations for the Fourier displacement coefficients in the cylindrical shell, and enables the degrees of freedom for the shell to be eliminated by static condensation at very little computational cost.Comparing the analytical results to (for the most part existing) experimental results, produces good agreement in some cases and not so good in others. A number of effects that could give rise to such differences are discussed. In most cases they represent experimental conditions that are not known or modelled in the analysis. The analysis results are also compared to those from a simplified analysis in which the hold-down action of the base plate is modelled by means of nonlinear Winkler springs.

In the last twenty years, experimental tests and FEM-based theoretical studies have been carried out to investigate the buckling mechanisms of thin-walled pipes subject to internal pressure, axial force and bending moment. Unfortunately, these studies do not completely cover the scope relevant for offshore pipelines i.e. outer diameter to thickness ratio lower than 50. In the HotPipe Phase 2 JI Project, full-scale bending tests were performed on pressurized pipes to verify the Finite Element Model predictions from HotPipe Phase 1 of the beneficial effect of internal pressure on the capacity of pipes to undergo large plastic bending deformations without developing local buckling. A total of 4 pipes were tested, the key test parameters being the outer-diameter-to-wall-thickness ratio (seameless pipes with D/t = 25.6, and welded UOE pipes with D/t = 34.2), and the presence of a girth weld in the test section. For comparison a Finite Element Model was developed with shell elements in ABAQUS. The test conditions were matched as closely as possible: this includes the test configuration, the stress-strain curves (i.e. using measured curves as input), and the loading history. The FE results very realistically reproduce the observed failure mechanisms by formation and localization of wrinkles on the compression side of the pipe. Good agreement is also achieved in the moment capacities (with predictions only 2.5 to 8% above measured values), but larger differences arose for the deformation capacity, suggesting that the DNV OS-F101 formulation for the characteristic bending strain (which is based on FE predictions from HotPipe Phase I) may be non-conservative in certain cases.

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Beginning with the work of Koiter in 1945, valuable insights into the postbuckling behavior of structures have been gained by Lyapunov-Schmidt decomposition of the displacements followed by an asymptotic expansion about the bifurcation point. Here this methodology is generalized to include nonlinear prebuckling behavior, as well as multiple, not necessarily coincident buckling modes. The expansion of the reduced equilibrium equations is performed about a reference point (which need not coincide with any of the bifurcation points), and applies no matter whether the modes are coincident, closely spaced, or well separated. From a variety of possible decompositions of the admissible space of displacements, two are incorporated into a finite element program. Theoretical considerations, and numerical examples in which asymptotic results are compared to 'exact' results, indicate that one of the decompositions has some important advantages over the other. Examples include a shallow arch, and a beam on elastic foundation problem exhibiting symmetry-breaking modal interaction.

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This paper presents an explicit, closed-form solution for the Green functions (displacements due to unit loads) corresponding to dynamic loads acting on (or within) layered strata. These functions embody all the essential mechanical properties of the medium and can be used to derive solutions to problems of elastodynamics, such as scattering of waves by rigid inclusions, soil-structure interaction, seismic sources, etc. The solution is based on a discretization of the medium in the direction of layering, which results in a formulation yielding algebraic expressions whose integral transforms can readily be evaluated. The advantages of the procedure are: (a) the speed and accuracy with which the functions can be evaluated (no numerical integration necessary); (b) the potential application to problems of elastodynamics solved by the boundary integral method; and (c) the possibility of comparing and verifying numerical integral solutions implemented in computer codes.