Showing papers by "Qiusheng Li published in 2001"

Exact solutions for buckling of non-uniform columns under axial concentrated and distributed loading

Abstract: In this paper, the buckling problem of non-uniform columns subjected to axial concentrated and distributed loading is studied. The expression for describing the distribution of flexural stiffness of a non-uniform column is arbitrary, and the distribution of axial forces acting on the column is expressed as a functional relation with the distribution of flexural stiffness and vice versa. The governing equation for buckling of a non-uniform column with arbitrary distribution of flexural stiffness or axial forces is reduced to a second-order differential equation without the first-order derivative by means of functional transformations. Then, this kind of differential equation is reduced to Bessel equations and other solvable equations for 12 cases, several of which are important in engineering practice. The exact solutions that represent a class of exact functional solutions for the buckling problem of non-uniform columns subjected to axial concentrated and distributed loading are obtained. In order to illustrate the proposed method, a numerical example is given in the last part of this paper.

Multi-level design model and genetic algorithm for structural control system optimization

Abstract: The integrated optimum problem of structures subjected to strong earthquakes and wind excitations, optimizing the number of actuators, the configuration of actuators and the control algorithms simultaneously, is studied. Two control algorithms, optimal control and acceleration feedback control, are used as the control algorithms. A multi-level optimization model is proposed with respect to the solution procedure of the optimum problem. The characteristics of the model are analysed, and the formulation of each suboptimization problem at each level is presented. To solve the multi-level optimization problem, a multi-level genetic algorithm (MLGA) is proposed. The proposed model and MLGA are used to solve two multi-level optimization problems in which the optimization of the number of actuators, the positions of actuators and the control algorithm are considered in different levels. In problem 1, an example structure is excited by strong wind, and in problem 2, an example structure is subjected to strong earthquake excitation. Copyright © 2001 John Wiley & Sons, Ltd.

An explosive seismic sounding profile across the transition zone between west Kunlun Mts. and Tarim Basin

Abstract: The explosive seismic sounding profile across the transition zone from the west Kunlun Mts. to the Tarim Basin revealed the complex deep structure formed by continent-continent collision on the northern margin of the Tibetan Plateau. The profile shows that the attitude of the Moho is in agreement with that of the crystalline basement in the Tarim Basin and the whole crust dips as a thick slate southwards with an angle from 5° to 7°. Meanwhile, the Moho depth increases from 40 km to 57 km within a distance of 150 km in the southern Tarim region, depicting the subduction of the crust of this region towards the west Kunlun Mts. The crust of the northern slope of the west Kunlun Mts. shows an evident compressed and shortened feature, that is, the basement is uplifted, the interface dips northwards and the Moho rises abruptly to become flat, so that the lower crust is as thick as 20 km.

Negative Shear Lag Effect in Box Girders with Varying Depth

Abstract: A study on negative shear lag effects in box girders with varying depth is performed using a modified finite segment method developed by the writers. Three types of structuressimply supported, cant...

Dynamic behavior of multistep cracked beams with varying cross section

Abstract: An analytical method for free-vibration analysis of a multistep nonuniform cracked beam is presented. Special solutions for five different types of nonuniform beams are given first. The procedure for determining the fundamental solutions that satisfy the normalization conditions is proposed. The problem of free vibration of a multistep beam, each step beam being nonuniform and having an arbitrary number of cracks and concentrated masses, can be conveniently solved based on the fundamental solutions and recurrence formulas developed in this paper. The eigenvalue equation of such a multistep cracked beam with any kind of two end supports can be established from a determinant of order 2.

Vibratory characteristics of multistep nonuniform orthotropic shear plates with line spring supports and line masses.

Abstract: A new exact approach for free-vibration analysis of multistep nonuniform orthotropic shear plates with line spring supports and line masses is presented. The governing differential equation for free vibrations of an orthotropic shear plate with variably distributed mass and stiffness is established. It is proved that it is possible to separate a shear plate as two independent shear beams for free-vibration analysis. The jkth natural frequency of a shear plate is equal to the square root of the square sum of the jth natural frequency of a shear beam and the kth natural frequency of another shear beam. The jkth mode shape of the shear plate is the product of the jth mode shape of a shear beam and the kth mode shape of another shear beam. In this paper, the function for describing the distribution of mass of each step plate can be selected as an arbitrary one, and the distribution of shear stiffness is expressed as a functional relation with the mass distribution, and vice versa. The exact solutions of one-step shear plates with varying cross section are obtained first for eight cases. Then, the derived exact solutions are used to establish the frequency equation of a multistep nonuniform orthotropic shear plate with spring supports and line masses using the transfer matrix method and the recurrence method developed in this paper. The numerical example shows that the calculated results are in good agreement with the experimental data, and the proposed procedure is an exact and efficient method.

Exact solutions for free vibration of shear-type structures with arbitrary distribution of mass or stiffness.

Abstract: In this paper, shear-type structures such as frame buildings, etc., are treated as nonuniform shear beams (one-dimensional systems) in free-vibration analysis. The expression for describing the distribution of shear stiffness of a shear beam is arbitrary, and the distribution of mass is expressed as a functional relation with the distribution of shear stiffness, and vice versa. Using appropriate functional transformation, the governing differential equations for free vibration of nonuniform shear beams are reduced to Bessel’s equations or ordinary differential equations with constant coefficients for several functional relations. Thus, classes of exact solutions for free vibrations of the shear beam with arbitrary distribution of stiffness or mass are obtained. The effect of taper on natural frequencies of nonuniform beams is investigated. Numerical examples show that the calculated natural frequencies and mode shapes of shear-type structures are in good agreement with the field measured data and those determined by the finite-element method and Ritz method.

Classes of exact solutions for several static and dynamic problems of non-uniform beams

Abstract: In this paper, an analytical procedure for solving several static and dynamic problems of non-uniform beams is proposed. It is shown that the governing differential equations for several stability, free vibration and static problems of non-uniform beams can be written in the from of a unified self-conjugate differential equation of the second-order. There are two functions in the unified equation, unlike most previous researches dealing with this problem, one of the functions is selected as an arbitrary expression in this paper, while the other one is expressed as a functional relation with the arbitrary function. Using appropriate functional transformation, the self-conjugate equation is reduced to Bessel`s equation or to other solvable ordinary differential equations for several cases that are important in engineering practice. Thus, classes of exact solutions of the self-conjugate equation for several static and dynamic problems are derived. Numerical examples demonstrate that the results calculated by the proposed method and solutions are in good agreement with the corresponding experimental data, and the proposed procedure is a simple, efficient and exact method.

Evaluation of vertical dynamic characteristics of cantilevered tall structures

Abstract: In this paper, cantilevered tall structures are treated as cantilever bars with varying cross-section for the analysis of their free longitudinal (or axial) vibrations. Using appropriate transformations, exact analytical solutions to determine the longitudinal natural frequencies and mode shapes for a one step non-uniform bar are derived by selecting suitable expressions, such as exponential functions, for the distributions of mass and axial stiffness. The frequency equation of a multi-step bar is established using the approach that combines the transfer matrix procedure or the recurrence formula and the closed-form solutions of one step bars, leading to a single frequency equation for any number of steps. The Ritz method is also applied to determine the natural frequencies and mode shapes in the vertical direction for cantilevered tall structures with variably distributed stiffness and mass. The formulae proposed in this paper are simple and convenient for engineering applications. Numerical example shows that the fundamental longitudinal natural frequency and mode shape of a 27-storey building determined by the proposed methods are in good agreement with the corresponding measured data. It is also shown that the selected expressions are suitable for describing the distributions of axial stiffness and mass of typical tall buildings.

Stochastic Transient Variational Principle in Vibration Analysis

Abstract: Publisher Summary The stochastic transient variational principle (STVP) is developed based on the second order perturbation techniques. This chapter discusses the dependence of virtual displacements on real displacements hence on the material properties and loading conditions of the structures. For stochastic structures involved with physical and/or geometrical stochastic parameters, the virtual displacements are regarded as stochastic quantities. Therefore, a general purposes version of STVP is developed for vibration analysis of linear continuum. Probabilistic distributions of random parameters are consistently incorporated. Stochasticity of all random quantities, as well as their variations, is taken into consideration. The second-order perturbation techniques are employed to expand all the random quantities involved in the energy functional. Accordingly, a set of deterministic recursive equations is obtained as the alternative expressions of the STVP. On the basis of the STVP, the stochastic finite element method (SFEM) is developed for vibration analysis so that the roundabout procedures for formulations of the SFEM are avoided.