H.C. Chan

Mesoscopic study of concrete I: generation of random aggregate structure and finite element mesh

Abstract Concrete is a composite material with a variety of inhomogeneities. Its composite behavior may be studied analytically using the mesoscopic approach which treats the concrete as a three-phase system consisting of coarse aggregate, mortar matrix with fine aggregate dissolved in it, and interfacial zones between the coarse aggregate and the mortar matrix. For such mesoscopic study, it is first necessary to generate a random aggregate structure in which the shape, size and distribution of the aggregate particles resemble real concrete in the statistical sense. Then, if the composite structure is to be analyzed by the finite element method, a mesh for each of the three phases needs to be generated. In this paper, a procedure for generating random aggregate structures for rounded and angular aggregates based on the Monte Carlo random sampling principle is proposed and a method of mesh generation using the advancing front approach is developed. These are combined with a nonlinear finite element method for mesoscopic study of concrete whose methodology and results will be presented in part II of the paper.

Mesoscopic study of concrete II: nonlinear finite element analysis

Abstract At mesoscopic scale, concrete may be regarded as a three-phase composite consisting of coarse aggregate, mortar matrix and interfacial zones. Its composite behavior can be studied by generating a random aggregate structure which resembles the mesoscopic structure of concrete and analyzing the interaction between the three phases using the finite element method. A method of generating random aggregate structures taking into account the size, shape and spatial distributions of aggregate particles has been developed and presented in part I of the paper. Herein, a nonlinear finite element method suitable for mesoscopic study of concrete is developed. Goodman type interface elements are used to model the interfacial zones. Cracking and nonlinear constitutive properties of the materials are taken into account. A failure criterion combining tensile strength and fracture toughness is adopted. Stress relief as cracks propagate is also allowed for. An adaptive incremental displacement controlled iterative scheme which can deal with post–peak behavior is employed. The method is applied to study the strain localization of concrete under uniaxial tension in a numerical example.

Geometrically nonlinear analysis of shallow shells using higher order finite elements

Abstract Based on K. Marguerres shallow shell theory, a family of higher-order finite elements each consisting of 17–25 nodes and with separate in-plane and bending displacement variables has been developed for the geometrically nonlinear analysis of shallow shells subjected to lateral loads. A step-iteration Newton-Raphson scheme has been adopted in solving the final system of recurrent nonlinear equations. Several numerical examples, including a spherical cap and a square shallow shell with surface in double sine curves, are presented to demonstrate the versatility and convenience of the use of higher-order elements in modelling shallow shells and also the sufficient accuracy of the predictions made by the present formulation in the context of geometrically nonlinear analysis.

A family of rectangular bending elements

Abstract By using separate independent transverse and rotational displacement variables in terms of a polynomial it is possible to produce high order conforming elements for plate bending and, at the same time, to include the effect of shear deformation in the analysis. The procedure for constructing a family of conforming rectangular plate bending elements with any number of nodes and the derivation of the stiffness matrix are illustrated. A computer programme is developed to generate the stiffness coefficients of the elements in this family; whereupon the characteristics of elements with as many as 17, 21 or 25 nodes and so on can be investigated. It is demonstrated that accurate results can be obtained for thin and moderately thick plates with various boundary conditions under bending by using just one or a few high order elements in this family. Hence the procedure for solving a problem in plate bending can be much simplified and the total number of nodes in a problem can be much reduced. Highlight in this family is the 17-node element which yields good results without involving too many nodes for many plate bending problems.

Nonlinear modelling of reinforced concrete structures

A nonlinear finite element analytical model for reinforced concrete structures is presented in this paper. In this model, the constitutive relation for concrete is established on the heterogeneous strain hardening plasticity theory and the post-cracking behaviour is governed by a bond stress distribution function proposed by the authors. As an example, the experimental result of a shearwall specimen is employed for comparison with the analytical result obtained by using this nonlinear model. It is demonstrated that the model can be applied to predict the structural response, the crack pattern and ultimate strength of reinforced concrete structures with confidence.

Higher order subparametric elements for large deflection analysis of plates

Abstract A family of higher-order subparamctric elements has been developed for large deflection analysis of flat plates of any geometric shapes subjected to lateral loading. The formulation procedure for these elements with 17–25 nodes involving in-plane as well as bending displacements with subparametric transformation is described and the derivation of the tangential stiffness matrix based on the classical von Karman nonlinear large deflection theory is presented. The Newton-Raphson scheme with modification is used. Several numerical examples of skewed slabs and circular plates are worked out and the results are compared with available data given by other research workers. It is found that these higher-order elements are simple, versatile, economical and convenient to use and give accurate results for large deflection analysis of plates.

High Performance Grade 75–80 Concrete for In-Situ Construction in Hong Kong

Currently, the highest strength concrete being used for in-situ construction in Hong Kong is only of grade 65. In order to develop higher strength concrete, a number of trial concrete mixes made of locally available material were tested. For minimizing the heat of hydration and the creep and shrinkage strains, lire trial mixes were designed to have paste contents as low as possible. During the tests, the effects of fine to local aggregates ratio and the usage. of superplasticizer, pulverized fuel ash and condensed silica fume were investigated. The results show that it is quite possible to produce high performance grade 75 - 80 concrete locally with a paste content of only 30% by volume. It is also found that fairly high dosages of superplasticizer will generally be needed and therefore it is important to select a superplasticizer which can be used at high dosages without producing excessive retardation. Lastly, three alternative mixes for making grade 75 - 80 concrete are recommended.