Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Constitutive equations for cyclic plasticity and cyclic viscoplasticity

Calculation of potential flow about arbitrary bodies

The finite element method is now recognized as a general approximation process which is applicable to a variety of engineering problems—structural mechanics being only one of these. Boundary solution procedures have been introduced as an independent alternative which at times is more economical and possesses certain merits. In this survey of the field we show how such procedures can be utilized in conventional FEM context.

The coupling of the finite element method and boundary solution procedures

The analogy between potential theory and classical elasticity suggests an extension of the powerful method of integral equations to the boundary value problems of elasticity. A vector boundary formula relating the boundary values of displacement and traction for the general equilibrated stress state is derived. The vector formula itself is shown to generate integral equations for the solution of the traction, displacement, and mixed boundary value problems of plane elasticity. However, an outstanding conceptual advantage of the formulation is that it is not restricted to two dimensions. This distinguishes it from the methods of Muskhelishvili and most other familiar integral equation methods. The presented approach is a real variable one and is applicable, without inherent restriction, to multiply connected domains. More precisely, no difficulty of the order of determining a mapping function is present and unwanted Volterra type dislocation solutions are eliminated a priori. An indication of techniques necessary to effect numerical solution of the resulting integral equations is presented with numerical data from a set of test problems.

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An integral equation approach to boundary value problems of classical elastostatics

I n the plane-strain conditions of a long cylinder in rolling line contact with an elastic-perfectly-plastic half-space an exact shakedown limit has been established previously by use of both the statical (lower bound) and kinematical (upper bound) shakedown theorems. At loads above this limit incremental strain growth or “ratchetting” takes place by a mechanism in which surface layers are plastically sheared relative to the subsurface material. In this paper the kinematical shakedown theorem is used to investigate this mode of deformation for rolling and sliding point contacts, in which a Hertz pressure and frictional traction act on an elliptical area which repeatedly traverses the surface of a half-space. Although a similar mechanism of incremental collapse is possible, the behaviour is found to be different from that in two-dimensional line contact in three significant ways: (i) To develop a mechanism for incremental growth the plastic shear zone must spread to the surface at the sides of the contact so that a complete segment of material immediately beneath the loaded area is free to displace relative to the remainder of the half-space, (ii) Residual shear stresses orthogonal to the surface are developed in the subsurface layers, (iii) A range of loads is found in which a closed cycle of alternating plasticity takes place without incremental growth, a condition often referred to as “plastic shakedown”. Optimal upper bounds to both the elastic and plastic shakedown limits have been found for varying coefficients of traction and shapes of the loaded ellipse. The analysis also gives estimates of the residual orthogonal shear stresses which are induced.

Application of the kinematical shakedown theorem to rolling and sliding point contacts

Shakedown and limit analyses for 3-D structures using the linear matching method

The paper describes a generalisation of the programming method described by Ponter and Carter (1997) for the evaluation of optimal upper bounds on the limit load of a body composed of a rigid/perfectly plastic material. The method is based upon similar principles to the `Elastic Compensation' method which has been used for design calculations for some years but re-interpreted as a non-linear programming method. A sufficient condition for convergence is derived which relates properties of the yield surface to those of the linear solutions solved at each iteration. The method is demonstrated through an application to a Drucker–Prager yield condition in terms of the Von Mises effective stress and the hydrostatic pressure. Implementation is shown to be possible using the user routines in a commercial finite element code, ABAQUS. The examples chosen indicate that stable convergent solutions may be obtained. There are, however, limits to the application of the method if isotropic linear solutions are used for an isotropic yield surface. In an accompanying paper (Ponter and Engelhardt, 2000) the method is extended to shakedown and related problems.

Limit analysis for a general class of yield conditions

The classical torsion problem of St Venant is formulated mathematically as a Neumann boundary-value problem for the warping function. This can be found numerically on the boundary by means of an integral equation method applicable to cross-sections of any shape or form. A single digital computer program assembles and solves the relevant equations, yields the torsional rigidity and boundary shear stress, and evaluates the warping function and stress components at any selected array of points throughout the cross-section. An accuracy of 1% in the torsional rigidity and maximum shear stress can be attained without undue effort.

An integral equation solution of the torsion problem

In previous papers [1,2], a procedure was described for the evaluation of limit loads and shakedown limits for a body subjected to cyclic loading. The procedure was based upon the “Elastic Compensation” method [9,10] where a sequence of linear problems are solved with spatially varying linear moduli. In [1] it was demonstrated that the method may be interpreted as a nonlinear programming method where the local gradient of the upper bound functional and the potential energy of the linear problem are matched at a current strain rate or during a strain rate history. This interpretation may be used to formulate a very general method for evaluating minimum upper bound solutions. Provided certain convexity conditions are satisfied, it is possible to define a sequence of linear problems where the functional monotonically reduces. The sequence then converges to the solution which corresponds to the absolute minimum of the functional, subject to constraints imposed by the class of strain rate histories under consideration. The theoretical basis for the method and convergence proofs are discussed in ref. [3,4].

Alan R.S. Ponter

Papers

Application of the kinematical shakedown theorem to rolling and sliding point contacts

Shakedown and limit analyses for 3-D structures using the linear matching method

Limit analysis for a general class of yield conditions

An integral equation solution of the torsion problem

Shakedown Limits for a General Yield Condition: Implementation and Application for a Von Mises Yield Condition