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CONTENTS
Volume 20, Number 4, July10 2005
 

Abstract
In the present paper it is aimed to perform the stochastic dynamic analysis of fluid and fluid-structure systems by using the Lagrangian approach. For that reason, variable-number-nodes two-dimensional isoparametric fluid finite elements are programmed in Fortran language by the authors and incorporated into a general-purpose computer program for stochastic dynamic analysis of structure systems, STOCAL. Formulation of the fluid elements includes the effects of compressible wave propagation and surface sloshing motion. For numerical example a rigid fluid tank and a dam-reservoir interaction system are selected and modeled by finite element method. Results obtained from the modal analysis are compared with the results of the analytical and numerical solutions. The Pacoima Dam record S16E component recorded during the San Fernando Earthquake in 1971 is used as a ground motion. The mean of maximum values of displacements and hydrodynamic pressures are compared with the deterministic analysis results.

Key Words
fluid-structure interaction; stochastic dynamic analysis; Lagrangian approach; fluid finite element.

Address
Karadeniz Technical University, Department of Civil Engineering, 61080, Trabzon, Turkey

Abstract
In this paper, a hybrid/mixed nonlinear shell element is developed in polar coordinate system based on Hellinger/Reissner variational principle and the large-deflection theory of plate. A numerical solution scheme is formulated using the hybrid/mixed finite element method (HMFEM), in which the nodal values of bending moments and the deflection are the unknown discrete parameters. Stability of the present element is studied. The large-deflection analyses are performed for simple supported and clamped circular plates under uniformly distributed and concentrated loads using HMFEM and the traditional displacement finite element method. A parametric study is also conducted in the research. The accuracy of the shell element is investigated using numerical computations. Comparisons of numerical solutions are made with theoretical results, finite element analysis and the available numerical results. Excellent agreements are shown.

Key Words
circular plate; geometric nonlinear; hybrid/mixed finite element.

Address
School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia

Abstract
In this paper, the finite element method is applied to investigate the effect of the lateral boundary in homogenous soil on the seismic response of a superstructure. Some influencing factors are presented and discussed, and several parameters are identified to be important for conducting soil-structure interaction experiments on shaking tables. Numerical results show that the cross-section width L, thickness H, wave propagation velocity and lateral boundaries of soil layer have certain influences on the computational accuracy. The dimensionless parameter L/H is the most significant one among the influencing factors. In other words, a greater depth of soil layer near the foundation should be considered in shaking table tests as the thickness of the soil layer increases, which can be regarded as a linear relationship approximately. It is also found that the wave propagation velocity in soil layer affects the numerical accuracy and it is suggested to consider a greater depth of the soil layer as the wave propagation velocity increases. A numerical study on a soil-structure experimental model with a rubber ring surrounding the soil on a shaking table is also conducted. It is found the rubber ring has great effect on the soil-structure interaction experiments on shaking table. The experimental precision can be improved by reasonably choosing the elastic parameter and width of the rubber ring.

Key Words
soil-structure interaction; finite element method; earthquake engineering; shaking table test.

Address
Z. N. Li; College of Civil Engineering, Hunan University, Changsha, Hunan, 410082, China
College of the Architectural and Civil Engineering, Wenzhou University, Wenzhou, 325027, China

Q. S. Li; Department of Building and Construction, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China

M. L. Lou; State Key Laboratory for Disaster Reduction in Civil Engineering, Research Institute of Structural
Engineering and Disaster Reduction, Tongji University, Shanghai 200092, China

Abstract
Here, the dynamic instability characteristics of aero-thermo-mechanically stressed functionally graded plates are investigated using finite element procedure. Temperature field is assumed to be a uniform distribution over the plate surface and varied in thickness direction only. Material properties are assumed to be temperature dependent and graded in the thickness direction according to simple power law distribution. For the numerical illustrations, silicon nitride/stainless steel is considered as functionally graded material. The aerodynamic pressure is evaluated based on first-order high Mach number approximation to the linear potential flow theory. The boundaries of the instability region are obtained using the principle of Bolotin? method and are conveniently represented in the non-dimensional excitation frequency-load amplitude plane. The variation dynamic instability width is highlighted considering various parameters such as gradient index, temperature, aerodynamic and mechanical loads, thickness and aspect ratios, and boundary condition.

Key Words
functionally graded plate; forced vibration frequency; aspect ratio; temperature; gradient index; aerodynamic pressure; periodic load; instability width.

Address
T. Prakash; Department of Applied Mechanics, Indian Institute of Technology Delhi, India
M. Ganapathi; FEA Group, Institute of Armament Technology, Girinagar, Pune-411025, India

Abstract
Structural members commonly employed in marine and off-shore structures are usually fabricated from plates and shells. Collision of this class of structures is usually modeled as plate and shell structures subjected to dynamic impact loading. The understanding of the dynamic response and energy transmission of the structures subjected to low velocity impact is useful for the efficient design of this type of structures. The transmissions of transient energy flow and dynamic transient response of these structures under low velocity impact are presented in the paper. The structural intensity approach is adopted to study the elastic transient dynamic characteristics of the plate structures under low velocity impact. The nine-node degenerated shell elements are adopted to model both the target and impactor in the dynamic impact response analysis. The structural intensity streamline representation is introduced to interpret energy flow paths for transient dynamic response of the structures. Numerical results, including contact force and transient energy flow vectors as well as structural intensity stream lines, demonstrate the efficiency of the present approach and attenuating impact effects on this type of structures.

Key Words
dynamic response; finite element method; low velocity impact; plate and shell structures; structural intensity.

Address
Z. S. Liu; Computational Solid Mechanics, Institute of High Performance Computing, 1 Science Park Road, #01-01, Singapore Science Park II, 117528, Singapore
S. Swaddiwudhipong; Department of Civil Engineering, National University of Singapore, Kent Ridge, 119260, Singapore
C. Lu; Computational Solid Mechanics, Institute of High Performance Computing, 1 Science Park Road, #01-01, Singapore Science Park II, 117528, Singapore
J. Hua; Department of Civil Engineering, National University of Singapore, Kent Ridge, 119260, Singapore

Abstract
Free vibration of orthotropic functionally graded beams, whose material properties can vary arbitrarily along the thickness direction, is investigated based on the two-dimensional theory of elasticity. A hybrid state-space/differential quadrature method is employed along with an approximate laminate model, which allows us to obtain the semi-analytical solution easily. With the introduction of continuity conditions at each fictitious interface and boundary conditions at the top and bottom surfaces, the frequency equation for an inhomogeneous beam is derived. A completely exact solution of an FGM beam with material constants varying in exponential way through the thickness is also presented, which serves a benchmark to verify the present method. Numerical results are performed and discussed.

Key Words
functionally graded beams; differential quadrature; state space method; approximate laminate model; exact solution.

Address
Chao-Feng Lu; Department of Civil Engineering, Zhejiang University, Hangzhou 310027, P. R. China
W. Q. Chen; State Key Lab of CAD & CG, Zhejiang University, Hangzhou 310027, P. R. China
Department of Civil Engineering, Zhejiang University, Hangzhou 310027, P. R. China

Abstract
In case of Mindlin plate, not only the bending deformation but also the shear behavior is allowed. While the bending and shear stiffness are given in the same order in terms of elastic modulus, they are in different order in case of plate thickness. Accordingly, bending and shear contributions have to be dealt with independently if the stochastic finite element analysis is performed on the Mindlin plate taking into account of the uncertain plate thickness. In this study, a formulation is suggested to give the response variability of Mindlin plate taking into account of the uncertainties in elastic modulus as well as in the thickness of plate, a geometrical parameter, and their correlation. The cubic function of thickness and the correlation between elastic modulus and thickness are incorporated into the formulation by means of the modified auto- and cross-correlation functions, which are constructed based on the general formula for n-th joint moment of random variables. To demonstrate the adequacy of the proposed formulation, a plate with various boundary conditions is taken as an example and the results are compared with those obtained by means of classical Monte Carlo simulation.

Key Words
stochastic FEM; weighted integral method; plates; modified cross- and auto-correlation function; response variability; Monte Carlo simulation.

Address
Hyuk Chun Noh; Department of Civil Engineering and Engineering Mechanics, Columbia University,New York, NY 10027, USA
Chang Koon Choi; Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea


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