C.D. Bisbos

Second-order cone programming approaches to static shakedown analysis in steel plasticity

The finite element method discretized static shakedown analysis of steel constructions leads to large, sparse convex optimization problems. Under the von Mises yield criterion, they lead to second-order cone programming problems, for which the most appropriate techniques are Interior Point Methods. Various approaches exploiting the specific characteristics of the shakedown problems are presented and discussed.

Steel T-Stub connections under static loading: an effective 2-D numerical model

Abstract The proposed numerical model concerns the simulation of the structural behaviour of steel bolted T-stub connections in the case where the development of zones of plastification, as well as unilateral contact effects on the interfaces between connection members and bolts, are taken into account. Within such a framework, an effective two-dimensional finite element model capable of describing plasticity, large displacement and unilateral contact effects is proposed. The model constitutes an easy-to-use and accurate numerical model for the analysis of steel connections subjected to tensile loading, and is a simplification of a respective three-dimensional one and aims to reduce in a reliable way the huge computational effort required for the analysis of fine meshes of discretized steel bolted connections. The validity of the assumptions that led to the proposed 2-D model is demonstrated by comparing the numerical results with those obtained by laboratory tests.

Comparison of two methods for the solution of a class of nonconvex energy problems using convex minimization algorithms

Nonmonotone, possibly multivalued stress-strain or reaction-displacement laws give rise to hemivariational inequalities. Due to the lack of convexity and the nonsmoothness of the underlying (super)potentials the problems generally have nonunique solutions (stable or unstable). In this paper we propose two methods for the solution of the hemivariational inequality problem. The first method is based on the decomposition of the nonconvex superpotential into convex constituents. The second one uses an iterative scheme in order to approximate the hemivariational inequality problem with a sequence of variational inequality problems. Both methods are based on the solution of convex subproblems and constitute an effective, reliable and versatile family of numerical algorithms for large scale hemivariational inequalities. Finally, the two methods are applied to solve the same problem and the obtained results are compared.

Unilateral contact stresses at steel pipe saddles

Abstract The topic addressed in the present paper is the computation of the local contact loads acting on a pipe vessel that rests freely on a saddle. The boundary nonlinearity, introduced by the complicated nature of the unilateral contact boundary condition at the saddle, leads to the formulation of a linear complementarity problem (LCP) that governs the behaviour of the discretized pipe shell. This LCP is a direct extension of the force method of structural analysis where the local contact loads are acting as redundants. The flexibility coefficients are obtained through a Fourier series representation. Two algorithms for the solution of the LCP are described. Results for a two-span pipe with an intermediate saddle are given and discussed.

Computing the frictional contact loads of horizontal steel pipes, loosely resting on saddles

Abstract The present paper concerns the computation of the local contact loads acting on a horizontal pipe, loosely resting on saddles in the presence of Coulomb friction. Within the framework of the Flugge shell theory, a discretization in patches and a force-method formulation is accepted, where the local contact loads are acting as redundants. The flexibility coefficients are obtained using a well-known Fourier series representation of local pipe loads. The boundary nonlinearity, introduced by the complicated nature of the unilateral contact-Coulomb friction boundary conditions at the saddle, is treated through an algorithm, consisting of two stages, consecutively executed until convergence is reached. The first stage considers the tangential loads as given and determines the regions of contact and noncontact. In the second stage the normal loads are considered as constant and the sticking/slipping regions are computed. Results are given and discussed for a two-span example.

Unilateral contact, friction and related interactions in cracks. The direct boundary integral method

Abstract The paper presents a theory for the study of cracks having a given geometry by taking into account all types of actions of monotone type like unilateral contact and friction phenomena between the two crack sides. The arising problems are of a non-classical nature, due to the interface conditions expressed in terms of non-differentiable convex superpotentials. The direct B.I.E.M. is extended appropriately in order to treat this type of problem. The developed method is illustrated by a numerical example concerning the calculation of stress intensity factors under the unilateral contact and friction interface conditions.

A computational model for full or partial damage of single or multiple adjacent columns in disproportionate collapse analysis via linear programming

The evaluation of the sensitivity or insensitivity of structures to local damage has been a major research field during the last decades, mainly provoked due to the series of aging structures and infrastructures. Many researchers have described this property as redundancy, others as the resistance to disproportionate collapse or robustness and still others as the ability of structural systems to display alternate load paths in case of a local damage. In any case, the problem for the evaluation of this property is increasingly alarming since many systems experience similar collapses (American Society of Civil Engineers (2009). Proceedings of Structures Congress on the first international symposium on disproportionate collapse. ASCE, Austin, TX). This paper presents the numerical assessment of disproportionate collapse analysis introducing the concept of partial damage of structural elements. Global robustness measures are proposed also for the case of multiple partial losses of adjacent elements. The measures are computed on the basis of a mathematical optimisation problem using collapse load analysis of steel frames with pre-existing damage. Results comparing the cases of partial losses with the full column losses are presented and discussed.

A mathematical programming computational model for disproportionate collapse analysis of steel building frames

Disproportionate collapse analysis aims to assure that frames, a common structural system of buildings, can survive unforeseen local events and a central modeling tool of such abnormal deterioration is the concept of column loss. This paper formulates an appropriate computational model on the basis of mathematical optimization, using the collapse load analysis problem of steel frames with pre-existing damage. A respective collapse load robustness measure is proposed. The model has the ability to consider both full and partial column/node removals. It renders to be a linear programming model, if the US steel design regulations are used. A practical example is presented and several aspects are discussed.

Semidefinite optimization models for limit and shakedown analysis problems involving matrix spreads

Limit and shakedown analysis problems of Computational Mechanics lead to convex optimization problems, characterized by linear objective functions, linear equality constraints and constraints expressing the restrictions imposed by the material strength. It is shown that two important strength criteria, the Mohr–Coulomb and the Tresca criterion, can be represented as systems of semidefinite constraints, leading this way to semidefinite programming problems.

On the parameter identification problem for failure criteria in anisotropic bodies

SummaryThe elliptic paraboloid failure surface criterion (EPFS) is adopted in this paper to describe the failure behaviour of anisotropic bodies. A method is described, based on an inequality-constrained least square problem for the determination of the parameters of the EPFS criterion. After the discussion of the influence of the strength differential effect on the failure behaviour of the material, a neural network learning approach is introduced to the problem of extrapolating the given experimental results beyond the given range of experimental data by establishing an appropriate law of evolution of the failure surface valid for the material up to fracture.