Wilfried B. Krätzig

New natural draft cooling tower of 200 m of height

In the years 1999 to 2001 a new natural draft cooling tower has been built at the RWE power station at Niederaussem, with 200 m elevation the highest cooling tower world-wide. For many reasons, such structures can not be designed merely as enlargement of smaller ones, on the contrary, it is full of innovative new design elements. The present paper starts with an overview over the tower and a description of its geometry, followed by an elucidation of the conceptual shape optimization. The structural consequences of the flue gas inlets through the shell at a height of 49 m are explained as well as the needs for an advanced high performance concrete for the wall and the fill construction. Further, the design and structural analysis of the tower is described with respect to the German codified safety concept for these structures. Finally, the necessity of extended durability of this tower is commented, the durability design concept is explained in detail and illustrated by virtue of a series of figures.

Reliability of reinforced concrete structures under fatigue

Abstract This paper focuses on time-variant reliability assessment of deteriorating reinforced concrete structures under fatigue conditions. A strategy combining two time scales, namely the micro-scale of instantaneous structural dynamics (or statics) and the macro-scale of structural lifetime, is proposed. Non-linear response of reinforced concrete structures is simulated by means of the finite element method with adequate material model. A phenomenological fatigue damage model of reinforced concrete is developed and calibrated against experimental results available in the literature. Reliability estimates are obtained within the response surface method using the importance/adaptive sampling techniques and the time-integrated approach. The proposed assessment strategy is illustrated by an example of a concrete arch under fatigue loading. The obtained results show a general inapplicability of local and linear fatigue models to system level of structures.

Best transverse shearing and stretching shell theory for nonlinear finite element simulations

Abstract Convinced of the powerful capability of modern computational techniques the question of ‘best’ physical shell models is re-raised. In the present paper, ‘best’ interior shell equations are derived by mapping a 3-dimensional body, described as a multi-director-continuum, on a Cosserat-surface kinematics. The derived shell equations hold for arbitrarily large deformations and material laws in rate-description, incorporating shear distortions and thickness changes. The optimal character of the developed model — proven by tensor norm bounding techniques — is finally demonstrated by results of numerical simulations of nonlinear shell responses.

Finite-rotation shell elements via mixed formulation

Starting from a tensorial five-parametric finite-rotation shell theory a family of mixed finite elements is developed on the basis of a Reissner-Mindlin type functional. The family developed contains 4-node and 9-node quadrilateral shell elements. In each of them the displacement approximation is combined with various force variable interpolations in order to improve flexibility for numerical applications. The so-called difference vector occurring in the shell theory is expressed in terms of new rotational degrees of freedom which permit a unique determination of this variable in every deformed position. The corresponding constraints are then satisfied at the element level numerically. Due to the underlying theory the numerical models developed are able to predict the physical 2D force variables accurately. Their capability to deal with strongly nonlinear situations is demonstrated by several examples where numerical results due to Kirchhoff-Love type elements are also included for a systematical comparison.

Numerical simulation of serviceability, damage evolution and failure of reinforced concrete shells

Abstract The present paper deals with FE-simulations of damage and failure processes in reinforced concrete structures, with emphasis on the description of suitable material models. For concrete, the generally accepted equivalent strain concept (pseudo-1D) is applied, which allows consideration of arbitrary concrete qualities. In the case of cyclic processes, elastic, plastic as well as micro-damage material phases are considered in an empirical manner, as initially proposed by Bazant and Cedolin [ASCE J. Eng. Mech. 106 (1980) 1287]. Two-dimensionality has been considered by the application of a 2D failure model. Macro-cracking and debonding is treated on the meso-level through special crack elements as computational units of the length of the crack distance. This concept yields crack widths and crack distances with sufficient accuracy and it is also impervious to possible size effects due to the strain localization. The second main issue concentrates on simulation concepts for large structures, elucidating the applied shell elements and the required multi-level-simulation techniques. Finally, exemplary results are presented, demonstrating crack-damage induced response phenomena of a large cooling tower shell up to structural failure.

Automatic adaptive generation of a coupled finite element/element-free Galerkin discretization

In this paper, we present the concept and the implementation issues for an adaptive coupling of the finite element- and the element-free Galerkin discretization. The present algorithm implemented within flexible data structure facilitates the automatic inclusion of meshfree zones and establishes the coupling between the zones with interface elements. The idea is to minimize the expense for a simulation based on a coupled discretization. Two examples at the end of this paper demonstrate the efficiency of the concept.

Multi-layer multi-director concepts for D-adaptivity in shell theory

Abstract Solid mechanics problems use to be formulated in tensor notation in three-dimensional (3D) Euclidean space. But engineering practice favors reduced dimensional models, in order to describe deformation processes in its most natural way by surface- and line-like geometries, mainly for ease of error controling. Modern surface-like structures, e.g. shells, often show a layered structure or are computed––in case of inelastic materials––by use of virtual layers. The present paper thus is devoted to shells in layered representation. After demonstrating the equivalence of six-parameter, 4-noded shell elements with 3D hexahedron elements as fundamental model constituents, the treatment introduces two different layer-wise refinement concepts, one for modeling of complicated stress profiles, the other one for improvement of model deformability. Such concepts admit the simulation of rather arbitrary shell responses including all kinds of perturbations, like thickness jumps, points of single loads or loci of material damage. In order to validate this model, the paper will systematically transform all sets of basic mechanical conditions of a 3D solid of arbitrary material into corresponding two-dimensional sets of a multi-director shell theory. Aim is the evaluation of bounds for the convergence error.

On adaptive remeshing techniques for crack simulation problems

The simulation of fracture processes for discrete crack propagation is well established for linear‐elastic cracking problems. Applying finite element techniques for the numerical formulation, at every incremental macro‐crack step the element mesh has to be adapted such that the crack path remains independent of the initial mesh. The accuracy of the obtained results has to be controlled by suitable error estimators and error indicators. Considering the dependence of the predicted crack path on the precision of the displacement and stress computation, quality measures for the computed results are recommended. In this research the use of the Babuska/Rheinboldt error indicator in combination with linear‐elastic crack propagation problems is demonstrated. Based on this error measure an adaptive mesh refinement technique is developed. In comparison with classical discrete crack propagation simulations the advantages of the new concept can be clearly observed.

Measures of structural damage for global failure analysis

Abstract In building codes, the design of structures is generally based on their virgin state omitting most damage processes and disregarding future physical as well as chemical deterioration. Such concepts of disregard of structural stiffness degradation are in principle incapable of quantifying structural failure and thus of describing important aspects in modern structural engineering. The present paper supposes the modeling of local damage and deterioration phenomena on material point level and its mapping onto structural level. Here, it demonstrates that global damage measures, i.e. measures on structural level, can stringently be deduced from the reduction of the current structural stiffness, up to now an unsettled problem. Damage indicators are thus observable during incremental-iterative solutions of the tangent stiffness equation, where they estimate the distance from the actual structural state to failure varying from 0 to 1. Their applicability is finally demonstrated exemplarily on a reinforced concrete beam and a large shell.

ELASTO - PLASTIC DAMAGE - THEORIES AND ELASTO-PLASTIC FRACTURING THEORIES -A COMPARISON

Abstract In 1979, based on the pioneering work of Dougill (J.W. Dougill, ZAMP 27 (1976) 423–437), Bažant and Kim developed the so-called elasto-plastic-fracturing theory for concrete (Z.P. Bažant, S.-S. Kim, J. Eng. Mech. Div. 105 (3) (1979) 407–428), taking inelastic deformation due to both plastic slip and stiffness degradation into consideration. Independently Simo and Ju (J.C. Simo, J.W. Ju, Int. J. Solids Structures 23 (7) (1987) 821–840) applied in 1987 a theory of elasto-plastic damage to the description of the material behaviour of concrete, using the stiffness tensor itself as an internal variable. In this article the essential identity of this damage theory and the previously mentioned fracturing theory will be proved by theoretical comparison. Furthermore a new kind of combination of plasticity theory with the damage theory has been developed to describe the behaviour of concrete under predominate compression loadings. In this new theory both components – plasticity and damage theory – have been transformed into strain-space. This procedure leads to a simple strain-based elasto-plastic damage theory with only one parameter separating both effects, plastic deformation and stiffness reduction due to material damage. Moreover, the developed theory reproduces favourable experimental results of cyclic uniaxial and biaxial compression tests.