F.T.K. Au

Robust design of structures using convex models

Robust design aims to achieve a state of robustness so that the performance of a design is least sensitive to the variability of uncertain variables. In this paper, a novel method of robust design is proposed using the convex model with the help of the unsatisfactory degree functions. The robustness of the objective function is achieved by minimizing the worst value of unsatisfactory degree functions of the uncertainty parameters while the feasibility robustness is ensured by a sub-optimization conducting the worst-case analysis. The proposed model is a nested optimization and a decomposition technique is then employed to relieve computational burdens. The robust design of a 10-bar aluminium truss and a 25-bar steel truss under uncertain loads are carried out based on the proposed model as numerical examples.

On the determination of natural frequencies and mode shapes of cable-stayed bridges

Abstract An accurate analysis of the natural frequencies and mode shapes of a cable-stayed bridge is fundamental to the solution of its dynamic responses due to seismic, wind and traffic loads. In most previous studies, the stay cables have been modelled as single truss elements in conventional finite element analysis. This method is simple but it is inadequate for the accurate dynamic analysis of a cable-stayed bridge because it essentially precludes the transverse cable vibrations. This paper presents a comprehensive study of various modelling schemes for the dynamic analysis of cable-stayed bridges. The modelling schemes studied include the finite element method and the dynamic stiffness method. Both the mesh options of modelling each stay cable as a single truss element with an equivalent modulus and modelling each stay cable by a number of cable elements with the original modulus are studied. Their capability to account for transverse cable vibrations in the overall dynamic analysis as well as their accuracy and efficiency are investigated.

Effects of random road surface roughness and long-term deflection of prestressed concrete girder and cable-stayed bridges on impact due to moving vehicles

The effects of random road surface roughness and long-term deflection of prestressed concrete bridges on the impact effects due to moving vehicles are investigated. The concrete bridges studied include multi-span girder bridges and cable-stayed bridges. The random road surface roughness is described by a zero-mean stationary Gaussian random process, while the long-term deflection of the concrete deck is represented as a kind of global roadway surface roughness in the study. The bridge is modelled by finite element method. Each moving vehicle is idealised as a one-foot dynamic system, in which a mass is supported by a spring and a dashpot. Numerical results show that the effect of random road surface roughness on the impact induced by moving vehicles is significant in the girder bridges, while that of the long-term deflection of concrete deck is small to moderate. The impact effects of the random road surface roughness and the long-term deflection of concrete deck on a cable-stayed bridge vary a lot depending on the location. In general, such effects on the bridge deck are more significant at sections closed to the bridge towers. Such effects on the bending moment at the tower base are also significant. The effects on the stay cables vary much, with significant effects on the short cables and negligible effects on the longest cables.

Parameter identification of vehicles moving on continuous bridges

Abstract This paper describes a method for the identification of parameters of vehicles moving on multi-span continuous bridges. Each moving vehicle is modelled as a 2-degree-of-freedom system that comprises four components: an unsprung mass and a sprung mass, which are connected together by a damper and a spring. The corresponding parameters of these four components, namely, the equivalent unsprung mass and sprung mass, the damping coefficient and the spring stiffness are identified based on dynamic simulation of the vehicle–bridge system. The identification process makes use of acceleration measurements at selected stations on the bridge. In the study, the acceleration measurements are simulated from the solution to the forward problem of a continuous beam under moving vehicles, together with the addition of artificially generated measurement noise. The identification is carried out through a robust multi-stage optimization scheme based on genetic algorithms, which searches for the best estimates of parameters by minimizing the errors between the measured accelerations and the reconstructed accelerations from the moving vehicles. This multi-stage optimization scheme reduces the variable search domains stage by stage using the identified results of the previous stage. Besides the basic operators in simple genetic algorithms, some advanced genetic operators and techniques are adopted here. Therefore, it makes the proposed identification procedure much more efficient than other traditional optimization methods. The identification procedure is then verified with a few test cases. The estimated vehicle parameters can also be used to get the time varying contact forces between the vehicles and bridge surface.

Finite strip method for the free vibration and buckling analysis of plates with abrupt changes in thickness and complex support conditions

Abstract The free vibration problem of a stepped plate supported on non-homogeneous Winkler elastic foundation with elastically mounted masses is formulated based on Hamiltons principle. The stepped plate is modelled by finite strip method. To overcome the problem of excessive continuity of common beam vibration functions at the location of abrupt change of plate thickness, a set of C 1 continuous functions have been chosen as the longitudinal interpolation functions in the finite strip analysis. The C 1 continuous functions are obtained by augmenting the relevant beam vibration modes with piecewise cubic polynomials. As these displacement functions are built up from beam vibration modes with appropriate corrections, they possess both the advantages of fast convergence of harmonic functions as well as the appropriate order of continuity. The method is further extended to the buckling analysis of rectangular stepped plates. Numerical results also show that the method is versatile, efficient and accurate.

Vibration and stability of non-uniform beams with abrupt changes of cross-section by using C1 modified beam vibration functions

Abstract A unified method is presented for the analysis of vibration and stability of axially loaded non-uniform beams with abrupt changes of cross-section. The beam may also be supported on Winkler elastic foundation, and both the axial force and the foundation stiffness can be varied arbitrarily. The method is based on the Euler–Lagrangian approach using a family of C 1 admissible functions as the assumed modes. The assumed modes comprise essentially the vibration modes of a single span hypothetical prismatic beam with the same end supports but without the intermediate supports, modified by piecewise C 1 cubic polynomials. The chosen admissible functions therefore possess both the advantages of fast convergence of the eigenfunctions and the appropriate order of continuity at the location of abrupt change of cross-section. The method allows extensive use of matrix notations and programming is rather straightforward. Numerical results also show that the method is versatile, efficient and accurate.

Isoparametric spline finite strip for degenerate shells

Abstract The isoparametric spline finite strip method for degenerate shells is presented. In the formulation, both the geometry and the displacement field are represented by uniform cubic B-spline curves. In this paper, the general theory of isoparametric spline finite strip for analysis of shell structures is outlined. The method, when applied to most problems, yields a relatively narrow band matrix and requires little computational effort. Solutions of a number of problems using this method are compared with other available analytical and numerical solutions, and in all cases very good agreement is observed.

Identification of masses moving on multi-span beams based on a genetic algorithm

This paper describes a theoretical study on the identification of masses moving on a multi-span continuous beam using the acceleration measurements. In the study, the acceleration measurements are simulated from the solution to the forward problem of a continuous beam under moving masses, together with the addition of artificially generated measurement noise. In particular, the forward problem for the simulation is solved using the modified beam vibration functions. A simple dynamic force identification procedure using pseudo-inverse and singular value decomposition is first employed to arrive at rough approximations of the moving masses. A genetic algorithm is then used to find the best estimated values of the moving masses by minimizing the errors between the measured accelerations and the reconstructed accelerations from the moving masses in each generation. Five numerical examples are given to demonstrate the robustness of this method. Various possible sources of error including the effects of measurement noise and surface roughness are also discussed.

Free vibration and stability analysis of shells by the isoparametric spline finite strip method

The isoparametric spline finite strip method has been applied to the free vibration and stability analysis of shells. The convergence of the method is reviewed critically. Additional numerical examples on shells of different geometry are also employed to demonstrate the efficiency, accuracy and versatility of the method.

Analysis of deep beams and shear walls by finite strip method with C0 continuous displacement functions

This paper presents a new finite strip method for the analysis of deep beams and shear walls. The essence of the method lies in the adoption of displacement functions possessing the right amount of continuity at the ends as well as at locations of abrupt changes of thickness. The concept of periodic extension in Fourier series is utilized to improve the accuracy of the stresses at the strip ends. The equilibrium conditions at locations of abrupt changes of thickness are taken into account by the incorporation of piecewise linear correction functions. As these displacement functions are built up from harmonic functions with appropriate corrections, they possess both the advantages of fast convergence of harmonic functions as well as appropriate order of continuity. Numerical results also show that the method is versatile, efficient and accurate.