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Abstract
In this paper, a new method to solve the dynamic response problem for structures with
interval parameters is presented. It is difficult to obtain all possible solutions with sharp bounds even an
optimum scheme is adopted when there are many interval structural parameters. With the interval
algorithm, the expressions of the interval stiffness matrix, damping matrix and mass matrices are
developed. Based on the matrix perturbation theory and interval extension of function, the upper and
lower bounds of dynamic response are obtained, while the sharp bounds are guaranteed by the interval
operations. A numerical example, dynamic response analysis of a box cantilever beam, is given to
illustrate the validity of the present method.

Key Words
interval extension of function; interval characters matrices; matrix perturbation theory; interval of dynamic response.

Address
Su Huan Chen and Hua Dong Lian, Department of Mechanics, Jilin University, Changchun 130025, P.R. China
Xiao Wei Yang, Department of Applied Mathematics, South China University of Technology, Guangzhou 510640, P.R. China

Abstract
In this study, free vibration analysis of Reissner plates on Pasternak foundation is carried out
by mixed finite element method based on the Gateaux differential. New boundary conditions are
established for plates on Pasternak foundation. This method is developed and applied to numerous
problems by Akoz and his co-workers. In dynamic analysis, the problem reduces to the solution of a
standard eigenvalue problem and the mixed element is based upon a consistent mass matrix formulation.
The element has four nodes and bending and torsional moments, transverse shear forces, rotations and
displacements are the basic unknowns. The element performance is assessed by comparison with
numerical examples known from literature. Validity limits of Kirchhoff plate theory is tested by dynamic
analysis. Shear locking effects are tested as far as h/2a =10 -6 and it is observed that REC32 is free from
shear locking.

Key Words
Reissner plate, free vibration, Pasternak, mixed-finite element.

Address
Nihal Eratl and A. Yalcin Akoz, Faculty of Civil Engineering, Istanbul Technical University, 80626 Maslak-Istanbul, Turkey

Abstract
A novel, 6-node, two-dimensional mixed finite element (FE) model has been developed to
analyze laminated composite beams by using the minimum potential energy principle. The model has
been formulated by considering four degrees of freedom (two displacement components u, w and two
transverse stress components sz, txz) per node. The transverse stress components have been invoked as
nodal degrees of freedom by using the fundamental elasticity equations. Thus, the present mixed finite
element model not only ensures the continuity of transverse stress and displacement fields through the
thickness of the laminated beams but also maintains the fundamental elasticity relationship between the
components of stress, strain and displacement fields throughout the elastic continuum. This is an
important feature of the present formulation, which has not been observed in various mixed formulations
available in the literature. Results obtained from the model have been shown to be in excellent agreement
with the elasticity solutions for thin as well as thick laminated composite beams. A few results for a
cross-ply beam under fixed support conditions are also presented.

Key Words
mixed finite element; minimum potential energy principle; laminated composite beam.

Address
Y.M. Desai and G.S. Ramtekkar, Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India

Abstract
The effect of shear coupled with axial force variation on the inelastic seismic behaviour of
reinforced concrete bridge piers is investigated in this paper. For this purpose, a hysteretic axial-shear
interaction model was developed and implemented in a nonlinear finite element analysis program. Thus,
flexure-shear-axial interaction is simulated under variable amplitude reversed actions. Comparative studies
for shear-dominated reinforced concrete columns indicated that a conventional FE model based on flexure-axial
interaction only gave wholly inadequate results and was therefore incapable of predicting the
behaviour of such members. Analysis of a reinforced concrete bridge damaged during the Northridge
(California 1994) earthquake demonstrated the importance of shear modelling. The contribution of shear
deformation to total displacement was considerable, leading to increased ductility demand. Moreover, the
effect of shear with axial force variation can significantly affect strength, stiffness and energy dissipation
capacity of reinforced concrete members. It is concluded that flexure-shear-axial interaction should be
taken into account in assessing the behaviour of reinforced concrete bridge columns, especially in the
presence of high vertical ground motion.

Key Words
reinforced concrete; bridges; columns; hysteretic response; shear deformation; axial force variation

Address
Do Hyung Lee, Department of Civil and Geotechnical Engineering, Paichai University, 439-6 Doma 2 dong, Seo-ku, Daejeon, Korea
Amr S. Elnashai, Structural Engineering, 2129e CEE Department, University of Illinois at Urbana-Champaign, 205 North Mathews Avenue, Urbana, IL 61801-2397, USA

Abstract
The problem of dynamic analysis of truss structures based on probability is studied in this
paper. Considering the randomness of both physical parameters (elastic module and mass density) of
structural materials and geometric dimension of bars respectively or simultaneously, the stiffness and mass
matrixes of the elements and structure have been built. The structure dynamic characteristic based on
probability is analyzed, and the expressions of numeral characteristics of inherence frequency random
variable are derived from the Rayleigh

Key Words
truss structure; physical parameter; geometric dimension; random variables; dynamic characteristic analysis.

Address
J.J. Chen, J.W. Che, H.A. Sun, H.B. Ma and M.T. Cui, School of Electronic Mechanical Engineering, Xidian University, Xi

Abstract
The objective of this study is to investigate the dynamic behavior of elastic beams subjected
to moving loads. Although analytical methods are available, they have limitations with respect to
complicated structures. The use of computer technology in recent years is an effective way to solve the
problem; thus using the latest technology this study establishes a finite-element solution procedure to
investigate dynamic behaviors of a typical elastic beam having a set of constant geometric properties and
various span lengths. Both the dead load of the beam and traffic load are applied in which the traffic load
is considered a concentrated moving force with various traveling passage speeds on the beam. Dynamic
behaviors including deflection, shear, and bending moment due to moving loads are obtained by both
analytical and finite element methods; for simple structures, they have an excellent agreement. The
numerical results show that based on analytical methods the fundamental mode is good enough to
estimate the dynamic deflection along the beam, but is not sufficient to simulate the total response of the
shear force or the bending moment. The linear dynamic behavior of the elastic beams subjected to
multiple exciting loads can easily be found by linear superposition, and the geometric nonlinear results
caused by large deformation and axial force of the beam are always underestimated with only a few
exceptions which are indicated. In order to make the results useful, they have been nondimensionalized
and presented in graphical form.

Key Words
dynamic; characteristics; beams; bridges; moving loads; traffic loads.

Address
Chia-Chih Tang, Department of Civil Engineering, Chinese Military Academy, 1 Wei-Wu Rd. Feng-Shan, 83000, Taiwan, R.O.C.
Yang-Cheng Wang, Academic Affairs Development Office, National Defense University, 156 Chung-Shin Rd. Lung-Tang, 32500, Tao-Yuan, Taiwan, R.O.C.

Abstract
The infrastructure system in the United States has been aging faster than the resource
available to restore them. Therefore decision for allocating the resources is based in part on the condition
of the structural system. This paper proposes to use neural network to predict the overall rating of the
structural system because of the successful applications of neural network to other fields which require a


Key Words
infrastructure; systems; evaluation; bridges; ratings; neural networks.

Address
Augusto V. Molina, Parson Transportation Group, New York, U.S.A.
Karen C. Chou, Department of Mechanical & Civil Engineering, Minnesota State University, Mankato, MN 56001, U.S.A.

Abstract
In this study, a new functional is obtained for folded plates with geometric (kinematic) and
dynamic (natural) boundary conditions. This functional is the combination of two different functionals.
Both functionals are obtained for thick plates which carry in-plane and lateral forces. A new mixed finite
element is developed with 4

Key Words
Reissner plate; folded plate; mixed-finite element.

Address
Nihal Eratli and A. Yalcin Akoz, Faculty of Civil Engineering, Istanbul Technical University, 80626 Maslak-Istanbul,Turkey

Abstract
Static and dynamic penetration tests of reinforced concrete (RC) slab specimens are described
and discussed. The experimental study was aimed at a better understanding of mechanisms that are
involved in dynamic penetration, through their identification in static tests, and by establishing their
relative influence in similar dynamic cases. The RC specimens were 80

Key Words
impact; penetration; perforation; reinforced concrete barriers.

Address
Avraham N. Dancygier and David Z. Yankelevsky, Department of Civil Engineering and National Building Research Institute, Technion, Technion City, Haifa 32000, Israel

Abstract
This paper presents the convected material frame approach to study the nonlinear behavior of
inelastic frame structures. The convected material frame approach is a modification of the co-rotational
approximation by incorporating an adaptive convected material frame in the basic definition of the
displacement vector and strain tensor. In the formulation, each discrete element is associated with a local
coordinate system that rotates and translates with the element. For each load increment, the corresponding
strain-displacement and nodal force-stress relationships are defined in the updated local coordinates, and
based on the updated element geometry. The rigid body motion and deformation displacements are
decoupled for each increment. This modified approach incorporates the geometrical nonlinearities through
the continuous updating of the material frame geometry. A generalized nonlinear function is used to
derive the inelastic constitutive relation and the kinematic hardening is considered. The equation of
motion is integrated by an explicit procedure and it involves only vector assemblage and vector storage in
the analysis by assuming a lumped mass matrix of diagonal form. Several numerical examples are
demonstrated in close agreement with the solutions obtained by the ANSYS code. Numerical studies show
that the proposed approach is capable of investigating large deflection of inelastic planar structures and
providing an excellent numerical performance.

Key Words
convected material frame approach; explicit finite element analysis; inelastic frame structures.

Address
Yaw- Jeng Chiou, Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan 701, R.O.C.
Yeon-Kang Wang, Department of Civil Engineering, Chung-Cheng Institute of Technology, National Defense University, Taoyuan, Taiwan 335, R.O.C.
Pang-An Hsiao and Yi-Lung Chen, Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan 701, R.O.C.

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