NONSMOOTH MODEL FOR PLASTIC LIMIT ANALYSIS AND ITS SMOOTHING ALGORITHM

By means of Lagrange duality of Hill＇s maximum plastic work principle theory of the convex program, a dual problem under Mises＇ yield condition has been derived and whereby a non-differentiable convex optimization model for the limit analysis is developed. With this model, it is not necessary to linearize the yield condition and its discrete form becomes a minimization problem of the sum of Euclidean norms subject to linear constraints. Aimed at resolving the non-differentiability of Euclidean norms, a smoothing algorithm for the limit analysis of perfect-plastic continuum media is proposed. Its efficiency is demonstrated by computing the limit load factor and the collapse state for some plane stress and plain strain problems.

PLASTIC LIMIT ANALYSIS OF INCOMPATIBLE FINITE ELEMENT METHOD

This paper describes an incompatible finite element model satisfying the consistency condition of energy to solve the numerical precision problem of finite element solution in perfectly plastic analysis. In this paper the reason and criterion of the application of the model to plastic limit analysis are discussed, and an algorithm of computing plastic limit load is given.

Numerical Analyses of Bearing Capacity of Deep-Embedded Large-Diameter Cylindrical Structure on Soft Ground Against Lateral Loads

Presented in this paper is a three-dimensional plastic limit analysis method of bearing capacity of the deeply-embedded large-diameter cylindrical structure in the cross-anisotmpic soft ground. The most likely failure mechanism is assumed to be of a composite rupture surface which is composed of an individual wedge in the passive zone or two wedges in both active and passive zones near the mudline, depending on the separation or bonding state at the interface between the cylindrical structure and neighboring soils in the active wedge, and a truncated spherical slip surface at the base of the cylinder when the structure tends to overturn around a point located on the symmetry axis of the structure. The cylindrical structure and soil interaction system under consideration is also numerically analyzed by the finite element method by virtue of the general-purpose FEM software ABAQUS, in which the soil is assumed to obey tie Hill＇s criterion of yield. Both the failure mechanism assumed and the plastic limit analysis predictions are validated by numerical computations based on FEM. For the K0-consolidated ground of clays typically with anisotropic undrained strength property, it is indicated through a parametric study that limit analysis without consideration of anisotropy of soil overestimates the lateral ultimate bearing capacity of a deeply-embedded cylindrical structure in soft ground in a certain condition.

Prediction of Forming Limit Diagrams for Materials with HCP Structure

The forming limit diagram（FLD） is an important tool to be used when characterizing the formability of metallic sheets used in metal forming processes. Experimental measurement and determination of the FLD is timeconsuming and therefore the analytical prediction based on theory of plasticity and instability criteria allows a direct and efficient methodology to obtain critical values at different loading paths, thus carrying significant practical importance.However, the accuracy of the plastic instability prediction is strongly dependent on the choice of the material constitutive model [1–3]. Particularly for materials with hexagonal close packed（HCP） crystallographic structure, they have a very limited number of active slip systems at room temperature and demonstrate a strong asymmetry between yielding in tension and compression [4, 5]. Not only the magnitude of the yield locus changes, but also the shape of the yield surface is evolving during the plastic deformation [4]. Conventional phenomenological constitutive models of plasticity fail to capture this unconventional mechanical behavior [4, 6]. Cazacu and Plunkett [6] have proposed generic yield criteria, by using the transformed principal stress, to account for the initial plastic anisotropy and strength differential（SD） effect simultaneously. In this contribution, a generic FLD MATLAB script was developed based on Marciniak–Kuczynski analytical theory and applied to predict the localized necking. The influence of asymmetrical effect on the FLD was evaluated. Several yield functions such as von Mises, Hill, Barlat89, and Cazacu06 were incorporated into analysis. The paper also presents and discusses the influence of different hardening laws on the formability of materials with HCP crystal structures. The findings indicate that the plastic instability theory coupled with Cazacu model can adequately predict the onset of localized necking for HCP materials under different strain paths.