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CONTENTS
Volume 17, Number 6, June 2004
 

Abstract
This work presents a direct integration scheme, based on a fourth order finite difference approach, for elastodynamics. The proposed scheme was chosen as an alternative for attenuating the errors due to the use of the central difference method, mainly when the time-step length approaches the critical time-step. In addition to eliminating the spurious numerical oscillations, the fourth order finite difference scheme keeps the advantages of the central difference method: reduced computer storage and no requirement of factorisation of the effective stiffness matrix in the step-by-step solution. A study concerning the stability of the fourth order finite difference scheme is presented. The Finite Element Method and the Boundary Element Method are employed to solve elastodynamic problems. In order to verify the accuracy of the proposed scheme, two examples are presented and discussed at the end of this work.

Key Words
direct integration methods; fourth order finite difference method; D-BEM; FEM.

Address
L. A. Souza; CT/UEL - Universidade Estadual de Londrina, Caixa Postal 6001, 86051-990, Londrina, Paran? Brasil
J. A. M. Carrer and C. J. Martins; COPPE/UFRJ - Universidade Federal do Rio de Janeiro, Caixa Postal 68506, 21945-970, Rio de Janeiro, RJ, Brasil

Abstract
This paper extends the use of the hierarchic degenerated shell element to geometric non-linear analysis of composite laminated skew plates by the p-version of the finite element method. For the geometric non-linear analysis, the total Lagrangian formulation is adopted with moderately large displacement and small strain being accounted for in the sense of von Karman hypothesis. The present model is based on equivalent-single layer laminate theory with the first order shear deformation including a shear correction factor of 5/6. The integrals of Legendre polynomials are used for shape functions with p-level varying from 1 to 10. A wide variety of linear and non-linear results obtained by the p-version finite element model are presented for the laminated skew plates as well as laminated square plates. A numerical analysis is made to illustrate the influence of the geometric non-linear effect on the transverse deflections and the stresses with respect to width/depth ratio (a/h), skew angle (b), and stacking sequence of layers. The present results are in good agreement with the results in literatures.

Key Words
geometric non-linearity; laminated skew plates; hierarchic degenerated shell element; integrals of Legendre polynomials; equivalent-single layer laminate theory.

Address
Kwang-Sung Woo and Jin-Hwan Park; Civil Engineering Department, Yeungnam University, Gyeongsan 712-749, Korea
Chong-Hyun Hong; Civil Engineering Department, Tamna University, Seoguipo 697-340, Korea

Abstract
The classical 8-node isoparametric serendipity element uses parametric shape functions for both test and trial functions. Although this element performs well in general, it yields poor results under severe mesh distortions. The distortion sensitivity is caused by the lack of continuity and/or completeness of shape functions used for test and trial functions. A recent element using parametric and metric shape functions for constructing the test and trial functions exhibits distortion immunity. This paper discusses the choice of parametric or metric shape functions as the basis for test and/or trial functions, satisfaction of continuity and completeness requirements, and their connection to distortion sensitivity. Also, the performances of four types of elements, viz., parametric, metric, parametric-metric, and metric-parametric, are compared for distorted meshes, and their merits and demerits are discussed.

Key Words
eight-node plane element; parametric-metric element; unsymmetric finite element; mesh distortion; geometric distortion; higher order completeness.

Address
S. Rajendran; School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798
S. Subramanian; Microwave Tube Research and Development Centre, Jalahalli, Bangalore 560013 India

Abstract
This paper deals with the modal analysis of rotational shell structures by means of the numerical solution technique known as the Generalized Differential Quadrature (G. D. Q.) method. The treatment is conducted within the Reissner first order shear deformation theory (F. S. D. T.) for linearly elastic isotropic shells. Starting from a non-linear formulation, the compatibility equations via Principle of Virtual Works are obtained, for the general shell structure, given the internal equilibrium equations in terms of stress resultants and couples. These equations are subsequently linearized and specialized for the rotational geometry, expanding all problem variables in a partial Fourier series, with respect to the longitudinal coordinate. The procedure leads to the fundamental system of dynamic equilibrium equations in terms of the reference surface kinematic harmonic components. Finally, a one-dimensional problem, by means of a set of five ordinary differential equations, in which the only spatial coordinate appearing is the one along meridians, is obtained. This can be conveniently solved using an appropriate G. D. Q. method in meridional direction, yielding accurate results with an extremely low computational cost and not using the so-called delta-point?technique.

Key Words
shell of revolution; generalized differential quadrature method; modal analysis; numerical method; dynamic analysis.

Address
Erasmo Viola and Edoardo Artioli; D.I.S.T.A.R.T. - Scienza delle Costruzioni, University of Bologna, Viale Risorgimento 2, Bologna, Italy

Abstract
A new process for estimating the natural frequency and the corresponding damping ratio in large structures is discussed. In a practical situation, it is very difficult to analyze large structures precisely because they are too complex to model using the finite element method and too heavy to excite using the exciting force method; in particular, the measured signals are seriously influenced by ambient noise. In order to identify the structural impulse response associated with the information of natural frequency and the corresponding damping ratio in large structures, the analysis process, a so-called

Key Words
structural analysis; the multiresolution blind deconvolution algorithm; Howell-Bunger gate.

Address
Gee-Pinn James Too, Chih-Chung Kenny Wang, and Rumin Chao; Department of System and Naval Mechatronic Engineering, National Cheng Kung University,
Tainan, Taiwan, R.O.C

Abstract
This paper presents a method for the nonlinear analysis of beam elements subjected to the cyclical combined actions of torsion, biaxial flexure and axial forces based on an extension of the disturbed compression field (DSFM). The theoretical model is based on a hybrid formulation between the full rotation of the cracks model and the fixed direction of the cracking model. The described formulation, which treats cracked concrete as an orthotropic material, includes a new approach for the evaluation of the re-orientation of both the compression field and the deformation field by removing the restriction of their coincidence. A new equation of congruence permits evaluating the deformation of the middle line. The problem consists in the solution of coupled nonlinear simultaneous equations expressing equilibrium, congruence and the constitutive laws. The proposed method makes it possible to determine the deformations of the beam element according to the external stresses applied.

Key Words
cyclic loads; reinforced concrete; cracking (fracturing); spatial truss; stress-strain relationships; aggregate interlock; equilibrium; congruence; Mohr

Address
Gian Michele Cocchi and Paolo Tiriaca; Universit?di Ancona, Facolta di Ingegneria, Istituto di Scienza e Tecnica delle Costruzioni, Ancona 60131, Italy

Abstract
Steel corrosion in reinforced concrete structures leads to concrete cover cracking, reduction of bond strength, and reduction of steel cross section. Among theses consequences mentioned, reduction of bond strength between reinforcement and concrete is of great importance to study the behaviour of RC members with corroded reinforcement. In this paper, firstly, an analytical model based on smeared cracking and average stress-strain relationship of concrete in tension is proposed to evaluate the maximum bursting pressure development in the cover concrete for noncorroded bar. Secondly, the internal pressure caused by the expansion of the corrosion products is evaluated by treating the cracked concrete as an orthotropic material. Finally, bond strength for corroded reinforcing bar is calculated and compared with test results.

Key Words
corrosion; bond strength; smeared cracking; corrosion pressure.

Address
Xiaohui Wang and Xila Liu; A0110021#, Department of Civil Engineering, Shanghai Jiaotong University, Minhang, Shanghai, 200240, P.R. China

Abstract
A method of making simply supported girders continuous is described for bridges with spans of 30-45 m. The splicing method takes advantage of an induced secondary moment to transform the self-weight stresses in the precast simply supported girders into values representative of a continuous girder. The secondary moment results from prestressing of continuity tendons and detensioning of temporary tendons in the girders. Preliminary sections are selected for spliced U-girder bridges with a range of span lengths. Use of the proposed technique results in girder depth reductions of 500-800 mm when compared to standard simply supported I-girder bridges. The flexural behavior of an example bridge with 40-m spans is examined to illustrate the necessary considerations for determining the optimum sequence of splicing operations.

Key Words
bridge; continuity method; prestressed concrete; secondary moment; staged prestressing; structural efficiency; U-girder.

Address
Hwan Woo Lee; Department of Civil Engineering, Pukyong National University, San 100, Yongdangdong, Namgu, Busan 608-739, Korea
Robert W. Barnes; Department of Civil Engineering, 238 Harbert Engineering Center, Auburn University, Alabama 36849-5337, U.S.A.
Kwang Yang Kim; Department of Civil Engineering, Pukyong National University, San 100, Yongdangdong, Namgu, Busan 608-739, Korea


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