Konstantinos V. Spiliopoulos

Modelling of crack closure for finite-element analysis of structural concrete

Abstract An existing finite element (FE) model of structural concrete is extended so as to also allow for crack closure in localized regions of a structure. The model is used to study the behaviour of structural concrete members under various types of loading, encompassing both proportional and sequential loadings. The analysis is found to yield a close fit to experimental values, and to confirm the view that, while neglecting crack closure has a negligible effect on the predicted behaviour of structural concrete under proportional loading, sequential loading usually requires a proper allowance of crack closure if sensible analytical predictions are to be achieved. Moreover, the results support experimental findings which indicate that compliance with the earthquake-resistant design clauses of the Greek version of the new European code of practice may, in fact, cause, rather than safeguard against, brittle types of failure.

Direct Methods for Limit States in Structures and Materials

Knowing the safety factor for limit states such as plastic collapse, low cycle fatigue or ratcheting is always a major design consideration for civil and mechanical engineering structures that are subjected to loads. Direct methods of limit or shakedown analysis that proceed to directly find the limit states offer a better alternative than exact time-stepping calculations as, on one hand, an exact loading history is scarcely known, and on the other they are much less time-consuming. This book presents the state of the art on various topics concerning these methods, such as theoretical advances in limit and shakedown analysis, the development of relevant algorithms and computational procedures, sophisticated modeling of inelastic material behavior like hardening, non-associated flow rules, material damage and fatigue, contact and friction, homogenization and composites.

On the automation of the force method in the optimal plastic design of frames

It is well known that linear programming provides, computationally, the only solution to the optimal plastic design of plane frames. It is also known that the formulation of the problem by the force method, using kinematic variables, requires for its solution, by the simplex method, much less computation than the corresponding program which uses for its formulation the displacement method. However, the force method is not easily automated. This problem is circumvented in the paper by presenting a new algorithm which automatically selects a subminimal cycle base in any planar graph. Based on a shortest path technique between two points of a connected graph, the algorithm forms cycles by finding the shortest paths between the end nodes of members of the graph. The check for independence is done by fictitiously increasing the lengths of the members that form the cycle. This leads to an easy computer implementation of the algorithm. The algorithm is then used to provide a statical basis for any plane frame. Equilibrium with applied loads is satisfied by the use of cantilevers that follow the shortest load path of each load to the ground. The whole process automates the data generation of the force method and makes possible to use, in a computer program, the same input data as in the displacement method. A few examples of applications are given.

The Residual Stress Decomposition Method (RSDM): A Novel Direct Method to Predict Cyclic Elastoplastic States

Instead of approaching the steady state behavior of an elastic–perfectly plastic structure, under cyclic loading, through time consuming incremental time-stepping calculations, one may alternatively use direct methods. A common feature of these methods is to estimate directly these cyclic states, profiting, thus, big savings in computer time. The elastic shakedown is the most important, in terms of structural safety, cyclic state. Most of the existing methods address this state through the solution of an optimization problem. In this work, a novel direct method that has a more physical understanding and may predict any cyclic steady stress state is exposed. The method is based on the expected cyclic nature of the residual stress distribution at the steady cycle. Having evaluated the elastic stress part of the total stress to equilibrate the external load, the unknown residual stress part is decomposed into Fourier series, whose coefficients are evaluated iteratively by satisfying compatibility and equilibrium with zero loads at time points inside the cycle. A computationally simple way to account for plasticity is considered. The procedure converges uniformly to a residual stress field which is either constant, marking the loading to be below the elastic shakedown limit, or to a cyclic residual stress field, from which possible alternating plasticity or ratcheting conditions may be realized. The procedure is formulated within the finite element method. A von Mises yield surface is typically used. Examples of application to a truss and a two dimensional plate under plane stress or strain are discussed.

Assessment of the Cyclic Behavior of Structural Components Using Novel Approaches

To extend the life of a structure, or a component, which is subjected to cyclic thermomechanical loading history one has to provide safety margins against excessive inelastic deformations that may lead either to low cycle fatigue or to ratcheting. Direct methods constitute a convenient tool towards this direction. Two direct methods that have been named RSDM and RSDM-S have recently appeared in the literature. The first method may predict any cyclic elastoplastic state for a given cyclic loading history. The second method RSDM-S that is based upon RSDM is suggested for the shakedown analysis of structures. Both methods may be directly implemented in any FE code. An elastic perfectly plastic material with a von Mises yield surface has been assumed. In this work both methods are used to undermine their capacity to determine shakedown boundaries and reveal unsafe conditions, through their application to structures that are used as benchmarks in the literature.

Performance Criteria for Liquid Storage Tanks and Piping Systems Subjected to Seismic Loading

In this paper, performance criteria for the seismic design of industrial liquid storage tanks and piping systems are proposed, aimed at defining a performance-based design framework towards reliable development of fragility curves and assessment of seismic risk. Considering “loss of containment” as the ultimate damage state, the proposed performance limits are quantified in terms of local quantities obtained from a simple and efficient earthquake analysis. Liquid storage tanks and the corresponding principal failure modes (elephant’s foot buckling, roof damage, base plate failure, anchorage failure and nozzle damage) are examined first. Subsequently, performance limits for piping systems are presented in terms of local strain at specific piping components (elbows, Tees and nozzles), against ultimate strain capacity (tensile and compressive) and low-cycle fatigue.Modeling issues for liquid storage tanks and piping systems are also discussed, for an efficient analysis that provides reliable estimates of local strain demand. These models are compared successfully with available experimental data. Using those reliable numerical models, the proposed performance limits are applied in two case studies: (a) a liquid storage tank and (b) a piping system, both located in areas of high seismicity.Copyright

AUTOMATIC COLLAPSE LOAD ANALYSIS OF REGULAR PLANE FRAMES USING THE FORCE METHOD

Abstract The limit analysis of regular plane frames consisting of meshes of strictly four members is considered. The inherent difficulty of the force method for automatic geometric data generation is overcome by developing an algorithm which is used to provide a statical basis. Using a shortest path technique between two points of an undirected graph, consecutive cycles are found whose check for independence is done by fictitiously increasing the lengths of the cycles members. Equilibrium with applied loads is satisfied by the use of cantilevers that coincide with the shortest path of each load to the ground. Examples of application are given.

RSDM-S: A Method for the Evaluation of the Shakedown Load of Elastoplastic Structures

To estimate the life of a structure, or a component, which are subjected to a cyclic loading history, the structural engineer must be able to provide safety margins. This is only possible by performing a shakedown analysis that belongs to the class of direct methods. Most of the existing numerical procedures addressing a shakedown analysis are based on the two theorems of plasticity and are formulated within the framework of mathematical programming. A different approach is presented herein. It is an iterative procedure and starts by converting the problem of loading margins to an equivalent loading of a prescribed time history. Inside an iteration, the recently published RSDM direct method is used, which assumes the decomposition of the residual stresses into Fourier series and evaluates its coefficients by iterations. It is proved that a descending sequence of loading factors is generated which converges, from above, to the shakedown load factor when only the constant term of the series remains. An elastic-perfectly plastic with a von Mises yield surface is currently assumed. The method may be implemented in any existing FE code and its efficiency is demonstrated by a couple of applications.

A 3D Solid Finite Element for Reinforced Concrete Analysis Allowing Slippage of Reinforcement

In order to evaluate the safety levels of the design of reinforced concrete structures it is essential to be able to predict their response under any type and level of loading. To this end the finite element method of analysis may be used. For such an analysis to be realistic, one must take into account all aspects of the nonlinear behaviour of reinforced concrete.

Efficient Shakedown Solutions in Complex Loading Domains

To estimate the life of a structure, or a component, which are subjected to a cyclic loading history, the structural engineer must be able to provide safety margins. This is only possible by performing a shakedown analysis which belongs to the class of direct methods. Most of the existing numerical procedures addressing a shakedown analysis are based on the two theorems of plasticity and are formulated within the framework of mathematical programming. A different approach has recently appeared in the literature. It is rather more physical than mathematical as it exploits the physics of the asymptotic steady state cycle. It has been called RSDM-S and has its roots in a previously published procedure (RSDM) which assumes the decomposition of the residual stresses into Fourier series whose coefficients are found by iterations. RSDM-S is a descending sequence of loading factors which stops when only the constant term of the series remains. The method may be implemented in any existing FE code. It is used herein to establish shakedown boundaries for two-dimensional general loadings consisting of mechanical or thermomechanical loads.