Browsing by Author "LIOU, GS"

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ANALYTIC SOLUTION FOR DYNAMIC LOADING ON HALF-SPACE MEDIUM
(1991-07-01)
LIOU, GS
;
LEE, GC
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KETTER, RL
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土木工程學系
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Department of Civil Engineering
A systematic procedure for generating impedance matrices for foundations resting on an elastic half-space medium is presented. The prescribed harmonic loading due to the foundation is decomposed into an infinite Fourier series with respect to the azimuth. For each Fourier component an analytic solution is found. Then, provided that the interaction stresses due to excitation of the foundation can be assumed to be piecewise linear in the r-direction of the cylindrical coordinates, the impedance matrix of the foundation can be generated using the variational principle and the reciprocal theorem. A simple example of a rigid circular plate, rigidly attached to the half-space medium, and subjected to torsional, vertical, rocking, and horizontal exitation is used to demonstrate the effectiveness and efficiency of the procedure.
ANALYTIC SOLUTIONS FOR SOIL STRUCTURE INTERACTION IN LAYERED MEDIA
(1989-07-01)
LIOU, GS
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交大名義發表
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土木工程學系
;
National Chiao Tung University
;
Department of Civil Engineering
DYNAMIC STIFFNESS MATRICES FOR 2 CIRCULAR FOUNDATIONS
(1994-02-01)
LIOU, GS
;
交大名義發表
;
土木工程學系
;
National Chiao Tung University
;
Department of Civil Engineering
A systematic procedure is presented for generating dynamic stiffness matrices for two independent circular foundations on an elastic half-space medium. With the technique reported in References 1-3, the analytic solution of three-dimensional (3D) wave equations satisfying the prescribed traction due to the vibration of one circular foundation can be found. Since there are two analytic solutions for two prescribed tractions due to the vibrations of two circular foundations, the principle of superposition must be used to obtain the total solution. The interaction stresses (prescribed tractions) are assumed to be piecewise linear in the r-directions of both cylindrical co-ordinates for the two circular foundations. Then, the variational principle and the reciprocal theorem are employed to generate the dynamic stiffness matrices for the two foundations. In the process of employing the variational principle, a co-ordinate transformation matrix between two cylindrical co-ordinate systems is introduced. Some numerical results of dynamic stiffness matrices for the interaction of two identical rigid circular foundations are presented in order to show the effectiveness and efficiency of the present method, and some elaborations for its future extensions are also discussed.
EFFECT OF FLEXIBILITY ON IMPEDANCE FUNCTIONS FOR CIRCULAR FOUNDATION
(1994-07-01)
LIOU, GS
;
HUANG, PH
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交大名義發表
;
土木工程學系
;
National Chiao Tung University
This paper investigates the effect of foundation rigidity on impedance functions for a circular foundation on a viscoelastic soil medium. In addition to vertical and rocking impedances, the paper also investigates the influence of coupling impedance for horizontal and rocking motions of foundation and horizontal impedance. To generate impedance functions for flexible foundation, a substructure technique is used. For the substructure of the flexible foundation. classical plate theory with neglecting inertial force is employed to obtain the deformation of the foundation due to the interaction stress. For the substructure of the soil medium, the technique, which can deal with wave equations in cylindrical coordinates with arbitrarily prescribed boundary conditions, is employed to obtain the displacement field in the soil medium due to the interaction stresses. Then, with the help of the variational principle, the displacement continuity condition of both substructures is imposed to generate the impedances for the flexible foundation. To demonstrate the effectiveness of the presented procedure, comparison with some previous numerical results is made. Selected numerical results of the presented procedure are presented. Also, comparison between results with and without the assumption of relaxed stress condition is given in order to show the significance of the assumption.
IMPEDANCE MATRICES FOR 2 AXIAL SYMMETRICAL FOUNDATIONS ON LAYERED MEDIUM
(1994-09-01)
LIOU, GS
;
交大名義發表
;
土木工程學系
;
National Chiao Tung University
;
Department of Civil Engineering
An attempt is made to generate impedance matrices for two independent axial symmetric foundations on an elastic layered medium. The analytic solution of three dimensional wave equations for a layered medium with the prescribed traction due to vibration of one axial symmetric foundation can be found using the technique developed in Refs. [3,4,5]. Two analytic solutions for two prescribed tractions due to the vibrations of two axial symmetric foundations are found separately. The principle of superposition is then used to obtain the final solution. The interaction stresses at the interfaces between the foundations and layered soil medium are assumed to be piecewise linear in r-directions of both cylindrical coordinates for two axial symmetric foundations. Then, the variational principle and reciprocal theorem are employed to generate the impedance matrices for both foundations. Some numerical results of impedance matrices for the interaction of two closely spaced circular foundations are presented, in order to show the effectiveness and efficiency of the presented method and the effect of layered stratum on the vibrations of two independent foundations. Discussion and conclusions are made.
NONLINEAR RESPONSES OF A BUILDING STRUCTURE TO EARTHQUAKE EXCITATION
(1992-11-03)
LIOU, GS
;
KANG, YY
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交大名義發表
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土木工程學系
;
National Chiao Tung University
A simplified stick model for the nonlinear dynamic analysis of a building structure is presented. Based on the strong-column weak-beam design philosophy, similar deformation shapes for all the columns in the same storey of a building structure is assumed. Therefore, while subjected to horizontal earthquake excitation, the inflection points of beam elements of building structures are assumed at either the middle of the spans or the locations of the plastic hinges in beam elements. After stacking all the column lines of the building structure and making use of the technique of static condensation for the stiffness matrices of beam elements, the simplified stick model with intermediate rotational constraints at all the floor levels can be set up. Bilinear behavior for beam and column elements is adopted for the nonlinear analysis. The advantage of using the proposed stick model for nonlinear dynamic analysis is to slash the computational cost, since the number of the degrees of freedom for each floor level is only two and the bandwidth of the stiffness matrix for total structure system is four. Some numerical results and some comparisons with the results of DRAIN-TABS are presented in order to show the effectiveness of the simplified model, and some possible extentions of the stick model are also discussed.
VIBRATION OF SURFACE FOUNDATIONS OF ARBITRARY SHAPES
(1991-12-01)
LIOU, GS
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交大名義發表
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土木工程學系
;
National Chiao Tung University
;
Department of Civil Engineering
Presented is a systematic procedure for generating impedance (or compliance) matrices for foundations with arbitrary shapes, resting on an elastic half-space medium. A technique to decompose prescribed harmonic tractions on the half-space medium is employed to solve analytically the differential wave equations in cylindrical coordinates. However, the interaction stresses due to the vibration of a foundation with arbitrary shape are described in rectangular coordinates, and assumed to be piecewise constant in the region of the arbitrary shape. A coordinate transformation matrix is introduced for the piecewise constant tractions in order to use the solution of the differential wave equations in cylindrical coordinates. Finite element modelling is assumed in rectangular coordinates for the foundation itself. The impedance matrix is then obtained for the finite element model, using a variational principle and the reciprocal theorem. A simple example of a rigid square plate resting on a half-space medium and subjected to vertical excitation is used to demonstrate the efficiency and effectiveness of the procedure. Some numerical aspects are investigated and some possible extensions of the procedure are also discussed.