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CONTENTS
Volume 5, Number 6, November 1997
 

Abstract
The damage of concrete subjected to multiaxial complex loading involves strong anisotropy due to its highly heterogeneous nature and the geometrically anisotropic characteristic of the microcracks. A comprehensive description of concrete damage is proposed by introducing a fourth-order anisotropic damage tenser. The evolution of damage is assumed to be related to the principal components of the current states of stress and damage. The unilateral effect of damage due to the closure and opening of microcracks is taken into account by introducing projection tensors that are also determined by the current state of stress. The proposed damage model considers the different kinds of damage mechanisms that result in different failure modes and different patterns of microdefects that cause different unilateral effects. This damage model is embedded in a thermomechanically consistent constitutive equation in which hardening and the triaxial compression caused shear-enhanced compaction can also be taken into account. The validity of the proposed model is verified by comparing theoretical and experimental results of plain and steel fiber reinforced concrete subjected to complex triaxial stress histories.

Key Words
concrete, damage, damage mechanics, constitutive equation, verification

Address
Meyer C, Columbia Univ, Dept Civil Engn & Engn Mech, New York, NY 10027 USA
Columbia Univ, Dept Civil Engn & Engn Mech, New York, NY 10027 USA
Chongqing Univ, Dept Mech Engn, Chongqing, Peoples R China

Abstract
This paper investigates the optimal locations of internal point supports in a symmetric crossply laminated rectangular plate for maximum fundamental frequency of vibration. The method used for solving this optimization problem involves the Rayleigh-Ritz method for the vibration analysis and the simplex method of Nelder and Mead for the iterative search of the optimum support locations. Being a continuum method, the Rayleigh-Ritz method allows easy handling of the changing point support locations during the optimization search. Rectangular plates of various boundary conditions, aspect ratios, composed of different numbers of layers, and with one, two and three internal point supports are analysed. The interesting results on the optimal locations of the point supports showed that (a) there are multiple solutions; (b) the locations are dependent on both the plate aspect ratios and the number of layers (c) the fundamental frequency may be raised significantly with appropriate positioning of the point supports.

Key Words
laminated plates, optimization, point supports, Rayleigh-Ritz method, vibration

Address
Wang CM, Natl Univ Singapore, Dept Civil Engn, Kent Ridge 119260, Singapore
Natl Univ Singapore, Dept Civil Engn, Kent Ridge 119260, Singapore
Univ Western Sydney Nepean, Sch Civil & Environm Engn, Kingswood, NSW 2747, Australia
Univ Queensland, Dept Civil Engn, Brisbane, Qld 4072, Australia

Abstract
The residual thermal stresses at the interface corner between the elastic fiber and the viscoelastic matrix of a two-dimensional unidirectional laminate due to cooling from cure temperature down to room temperature were studied, The matrix material was assumed to be thermorheologically simple. The time-domain boundary element method was employed to investigate the nature of stresses on the interface. Numerical results show that very large stress gradients are present at the interface corner and this stress singularity might lead to local yielding or fiber-matrix debonding.

Key Words
boundary element method, singular thermal stress

Address
Lee SS, Korea Atom Energy Res Inst, Reactor Mech Engn Dept, Taejon 306600, South Korea
Korea Atom Energy Res Inst, Reactor Mech Engn Dept, Taejon 306600, South Korea

Abstract
The aim of this paper is to investigate the secondary buckling behaviour and mode-coupling of spherical caps under uniformly external pressure. The analysis makes use of a rotational finite shell element on the basis of strain-displacement relations according to Koiter\'s shell theory (Small Finite Deflections). The post-buckling behaviours after a bifurcation point are analyzed precisely by considering multi-mode coupling between several higher order harmonic wave numbers: and on the way of post-buckling path the positive definiteness of incremental stiffness matrix of uncoupled modes is examined step by step. The secondary buckling point that has zero eigen-value of incremental stiffness matrix and the corresponding secondary mode are obtained, moreover, the secondary post-buckling path is traced.

Key Words
small finite deflection theory, secondary buckling, mode coupling

Address
Kato S, Toyohashi Univ Technol, Dept Civil & Architectural Engn, Aichi 441, Japan
Toyohashi Univ Technol, Dept Civil & Architectural Engn, Aichi 441, Japan
Hosei Univ, Dept Architecture, Coll Engn, Tokyo 184, Japan
Gifu Natl Coll Technol, Dept Architecture, Gifu 50104, Japan

Abstract
Cracked reinforced concrete in compression has been observed to exhibit lower strength and stiffness than uniaxially compressed concrete. The so-called compression softening effect responsible is thought to be related to the degree of transverse cracking and straining present. It significantly affects the strength, ductility and load-deformation response of a concrete element. A number of experimental investigations have been undertaken to determine the degree of softening that occurs, and the factors that affect it. At the same time, a number of diverse analytical models have been proposed by various this behavior. III this paper, the softened truss model thoery for low-rise structural shearwalls is employed using the principle of the stress and strain transformations. Using this theory the softening parameters for the concrete struts proposed by Hsu and Belarbi as well as by Vecchio and Collins are examined by 51 test shearwalls available in literature. It is found that the experimental shear strengths and ductilities of the walls under static loads are, in average, very close to the theoretical values: however, the experiment shear strengths and ductilities of the walls under dynamic loads with a low (0.2 Hz) frequency are generally less than the theoretical values.


Key Words
softening behavior, structural wall, loading rate, truss model, shear strength, ductility

Address
Mo YL, Natl Cheng Kung Univ, Dept Civil Engn, Tainan 70101, Taiwan
Natl Cheng Kung Univ, Dept Civil Engn, Tainan 70101, Taiwan
Univ Hannover, Inst Struct Anal, Hannover, Germany

Abstract
A three-dimensional constitutive modeling for reinforced concrete is presented for finite element nonlinear analysis of reinforced concrete. The targets of interest to the authors are columns confined by lateral steel hoops, RC thin shells subjected to combined in-plane and out-of-plane actions and massive structures of three-dimensional (3D) extent in shear. The elasto-plastic and continuum fracture law is applied to pre-cracked solid concrete. For post cracking formulation, fixed multi-directional smeared crack model is adopted for RC domains of 3D geometry subjected to monotonic and reversed cyclic actions. The authors propose a new scheme of decomposing stress strain fields into sub-planes on which 2D constitutive laws can be applied. The proposed model for 3D reinforced concrete is experimentally verified in both member and structural levels under cyclic actions.

Key Words
constitutive law, smeared crack, nonlinear analysis, confinement, cyclic action

Address
Maekawa K, Univ Tokyo, Dept Civil Engn, 7-3-1 Hongo, Tokyo 113, Japan
Univ Tokyo, Dept Civil Engn, Tokyo 113, Japan
Nanyang Technol Univ, Sch Civil & Struct Engn, Singapore, Singapore
Univ Tokyo, Dept Civil Engn, Tokyo, Japan

Abstract
Within the framework of anisotropic combined viscoplastic hardening formulation, accounting macroscopically for residual stress as well as texture development at finite deformations of metals, simple shear analyses for the simulation of fixed-end torsion experiments for alpha-Fe, Al and Cu at different strain rates are reviewed with an emphasis on the role of constitutive spins. Complicated responses of the axial stresses with monotonically increasing shear deformations can be successfully described by the capacity of orthotropic hardening part, featuring tensile axial stresses either smooth or oscillatory. Temperature effect on the responses of axial stresses for Cu is investigated in relation to the distortion and orientation of yield surface. The flexibility of this combined hardening model in the simulation of finite inelastic strains is discussed with reference to the variations of constitutive spins depending upon strain rates and temperatures.

Key Words
anisotropic viscoplastic hardening, constitutive, plastic spin, kinematic, orthotropic, distortional, orientational, yield surface

Address
Cho HW, Samsung Corp, Inst Technol Engn & Construct Grp, San 25,Gongse Ri,Giheung Eup, Kyunggi Do 449900, South Korea
Samsung Corp, Inst Technol Engn & Construct Grp, Kyunggi Do 449900, South Korea
Natl Tech Univ Athens, Div Mech, Zorgraphou 15733, Greece
Univ Calif Davis, Dept Civil & Environm Engn, Davis, CA 95616 USA

Abstract
In this paper, three dimensional static behaviors of the self-anchored and partially earth-anchored cable-stayed bridges, with a span of 1400 meters, under wind loading are studied by using a 3D geometrical nonlinear analysis. In this analysis, the bridges both after completion and under construction are dealt with. The wind resistant characteristics of the both cable-stayed systems are made clear. In particular, the characteristics of the partially earth-anchored cable systems, which is expected to be a promising solution for extending the span of the cable-stayed systems further, is presented.

Key Words
cable-stayed bridge, self-anchored bridge, partially earth-anchored bridge, wind load

Address
Xie X, Saitama Univ, Dept Civil & Environm Engn, Urawa, Saitama 338, Japan
Saitama Univ, Dept Civil & Environm Engn, Urawa, Saitama 338, Japan
Nagaoka Univ Technol, Dept Civil Engn, Nagaoka, Niigata 94021, Japan

Abstract
A unified theory is presented for the shape analysis of curved surface with a single layer structure composed by frame, membrane or shell. The shapes produced by the theory have no shear stress in elements, and the stress states in the whole shape are as uniform as possible under an ordinary load. The theory starts from defining an element potential function expressed by the measurement of the element length or the element area. Therefore, the shape analysis can produce various forms according to the definition of the potential function, and each of those form or the cable net form with the potential function of the second power of element length is simply gotten by the linear analysis. The form in tensile stress is mechanically equal to an isotropic tension form.

Key Words
formfinding, shape analysis, tangent stiffness method, geometrically nonlinear analysis

Address
Ijima K, Saga Univ, Dept Civil Engn, 1 Honjo, Saga 840, Japan
Saga Univ, Dept Civil Engn, Saga 840, Japan

Abstract
Reinforced Concrete beams with tension and compression softening material constitutive laws are studied. Energy-based and non-local regularisation techniques are presented and applied to a R.C. element. The element characteristics (sectional tangent stiffness matrix, element tangent stiffness matrix restoring forces) are directly derived from their symbolic expressions through numerical integration. In this way the same spatial grid allows us to obtain a non-local strain estimate and also to sample the contributions to the element stiffness matrix. Three examples show the spurious behaviors due to the strain localization and the stabilization effects given by the regularisation techniques, both in the case of tension and compression softening. The possibility to overestimate the ultimate load level when the non-local strain measure is applied to a non softening material is shown.


Key Words
reinforced concrete structures, softening, localization, continuation methods

Address
Bontempi F, Politecn Milan, Dept Struct Engn, I-20133 Milan, Italy
Politecn Milan, Dept Struct Engn, I-20133 Milan, Italy
Univ Udine, Dept Civil Engn, I-33100 Udine, Italy

Abstract
It is well understood that concentrated forces applied in the plane of a beam or panel (such as a wall or slab) lead to splitting forces developing within a disturbed region forming beyond the bearing zone. In a linearly elastic material the length of the disturbed region is approximately equal to the depth of the member. In concrete structures, however, the length of the disturbed region is a function of the orthotropic properties of the concrete-steel composite. In the detailing of steel reinforcement within the disturbed regions two limit states must be satisfied; strength and serviceability (in this case the serviceability requirement being acceptable crack widths). If the design requires large redistribution of stresses, the member may perform poorly at service and/or overload. In this paper the results of a plane stress finite element investigation of concentrated loads on reinforced concrete panels are presented. Two cases are examined (i) panels loaded concentrically, and (ii) panels loaded eccentrically. The numerical investigation suggests that the bursting force distribution is substantially different from that calculated using elastic design methods currently used in some codes of practice. The optimum solution for a uniformly reinforced bursting region was found to be with the reinforcement distributed from approximately 0.2 times the effective depth of the member (0.2D(e)) to between 1.2D(e) and 1.6D(e). Strut and tie models based on the finite element analyses are proposed herein.

Key Words
strut and tie, splitting, bursting, disturbed regions

Address
Foster SJ, Univ New S Wales, Sch Civil & Environm Engn, Sydney, NSW 2052, Australia
Univ New S Wales, Sch Civil & Environm Engn, Sydney, NSW 2052, Australia
Univ Alberta, Dept Civil & Environm Engn, Edmonton, AB T6G 2G7, Canada

Abstract
In the present contribution an interface crack model is introduced which is capable of modelling crack initialisation and growth in aluminium as well as in Fibre Metal Laminates. Interface elements are inserted in a finite element mesh with a yield function which bounds all states of stress in the interface, Hardening occurs after a state of stress exceeds the yield stress of the material. The hardening branch is bounded by the ultimate stress of the material. Thereafter, the state of stress is reduced to zero while the inelastic deformations grow. The energy dissipated by the inelastic deformations in this process equals the fracture energy of the material. The model is applied to calculate the onset and growth Of cracking in centre cracked plates made of aluminium and GLARE(R). The impact of the model parameters on the performance of the crack model is studied by comparisons of the numerical results with experimental data.

Key Words
interface elements, discrete crack model, mixed-mode cracking, plasticity, fibre metal laminates

Address
Hashagen F, Delft Univ Technol, Dept Civil Engn, PO 5048, NL-2600 GA Delft, Netherlands
Delft Univ Technol, Dept Civil Engn, NL-2600 GA Delft, Netherlands

Abstract
Closed-form solutions are analytically derived for stochastic properties of earthquake ground motion fields, which are conditioned by an observed time series at certain observation sites and are characterized by spectra with uncertainties. The theoretical framework presented here can estimate not only the expectations of such simulated earthquake ground motions, but also the prediction errors which offer important information for the field of engineering. Before these derivations are made, the theory of conditional random fields is summarized for convenience in this study. Furthermore, a method for stochastic interpolation of power spectra is explained.

Key Words
conditional random fields, power spectrum, spectral uncertainties, stochastic interpolation, numerical simulation, conditional probability density function, estimation errors, Fourier coefficients

Address
Morikawa H, Kyoto Univ, Dept Civil Engn Syst, Kyoto 606, Japan
Kyoto Univ, Dept Civil Engn Syst, Kyoto 606, Japan
Kyoto Univ, Disaster Prevent Res Inst, Uji, Kyoto, Japan

Abstract
The design of robust plate and shell elements has been a very challenging area for several decades. The main difficulty has been the shear locking phenomenon in plate elements and the shear and membrane locking phenomena together in the shell elements. Among the various artifices or devices which are used to develop elements free of these problems is the field-consistency approach. In this paper this approach is reviewed, It turns out that not only Mindlin type elements but also elements based on higher-order theories could be developed using the technique.

Key Words
plate elements, shear locking, field-consistency

Address
Prathap G, Natl Aeronaut Lab, Bangalore 560017, Karnataka, India
Natl Aeronaut Lab, Bangalore 560017, Karnataka, India
Jawaharlal Nehru Ctr Adv Sci Res, Bangalore 560064, Karnataka, India

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