Hae Sung Lee

Analysis of target configurations under dead loads for cable-supported bridges

Abstract This paper presents a rigorous approach for analyzing the target configurations of cable-supported structures under dead loads by the Newton–Raphson method. A linearized equilibrium equation of a cable element, which includes the nodal coordinates and the unstrained element length as unknowns, is formulated using the analytical solution of an elastic catenary cable. An incremental equilibrium equation for a single cable is formed with the proposed equilibrium matrices of cable elements. The geometry of the target configuration of a cable-supported structure under dead loads is utilized to solve the incremental equilibrium equation. Detailed procedures to analyze the target configurations of suspension bridges and cable-stayed bridges are presented. The efficiency and the accuracy of the proposed method are demonstrated through numerical examples.

Optimal pile arrangement for minimizing differential settlements in piled raft foundations

This paper presents an optimal pile placement scheme to minimize the differential settlements of piled raft systems. A raft is modelled as a plate based on the Mindlin theory, and soils and piles are modelled as the Winkler springs and single springs, respectively. Interactions between piles are neglected. The pile spring constant is obtained by the method proposed by Randolph and Wroth, and the frmula is adopted to obtain the Winkler spring constant. The raft is discretized by isoparameteric finite element. The object function for the optimization is derived from the area of the deflected surface of a raft, and the locations of piles are selected as design variables. Inequality constraints are imposed to keep all piles completely inside of the raft. The recursive quadratic programming is adopted to minimize the nonlinear object function with respect to the design variables. The direct differentiation method is used to obtain the sensitivity of displacement. The validity and effectiveness of the proposed method are demonstrated by three numerical examples.

A NEW SPATIAL REGULARIZATION SCHEME FOR THE IDENTIFICATION OF THE GEOMETRIC SHAPE OF AN INCLUSION IN A FINITE BODY

This paper presents a system identification scheme to determine the geometric shape of an inclusion in a finite body. The proposed algorithm is based on the minimization of the least-squared errors between the measured displacement field and calculated displacement field by the finite element model. The domain parameterization technique is adopted to manipulate the shape variation of an inclusion. To stabilize the optimization process, a new regularization function defined by the length of the boundary curve of an inclusion is added to the error function. A variable regularization factor scheme is proposed for a consistent regularization effect. The modified Newton method with the active set method is adopted for optimization. Copyright

Identification of geometric shapes and material properties of inclusions in two-dimensional finite bodies by boundary parameterization

A system identification scheme based on the boundary element method (BEM) is proposed to determine geometric shape and elastic material properties of an inclusion in a finite body. The proposed algorithm is based on the minimization of least squared errors between measured displacement and calculated displacement by a boundary element model. A regularization function that consists of the geometric term and material property term is added to the error function to overcome ill-posedness of inverse problems. To deal with the shape variation of an inclusion during the optimization process, the boundary parameterization technique is applied to the BEM. The recursive quadratic programming (RQP) technique with line search is used for optimization.

Finite element formulation for the analysis of turbulent wind flow passing bluff structures using the RNG k−ε model

Abstract This paper presents a stable finite element formulation to predict behaviors of high-speed wind passing bluff structures using the Reynolds averaged Navier–Stokes equation and the k – e model. To incorporate the k – e model with the finite element framework, a stable and accurate solution strategy is proposed. The streamline-upwind/Petrov–Galerkin scheme is adopted to stabilize the Reynolds averaged Navier–Stokes equation as well as the k – e equations. The re-normalization group k – e model is employed to reduce the turbulence over-production around the stagnation points on the upwind side of structures. Detailed discussions on the flow behaviors around the bluff structures are made through examples of wind flows passing a square cylinder and actual bridge sections to validate the proposed formulation. It is shown that the periodicity and magnitude of unsteady forces acting on the square cylinder are well predicted. Aerodynamic forces acting on bridge girder sections with complex geometry are presented for high-speed wind with the Reynolds number over 10 7 , and compared with experimental results.

Design of accelerometer layout for structural monitoring and damage detection

The paper presents an algorithm for designing a layout of accelerometers for structural monitoring and damage detection. The maximum likelihood approach has been applied as a mathematical basis for the algorithm. Fisher information matrix is formulated in terms of mode shape sensitivity with respect to structural parameters. A scheme of an effective independence distribution vector has been applied to determine optimal locations of accelerometers. Singular value decomposition scheme has been applied to overcome the rank deficiency problem in the computed sensitivity matrix. The adequacy of the proposed algorithm has been examined by estimating structural parameters through a frequency-domain system identification. The identification results using the response data measured at the locations selected by the proposed algorithm are compared with those at arbitrary locations. In addition to the design of accelerometer layout for a structural monitoring of general purpose, the paper proposes another algorithm of layout design for damage detection with the assumption that some members critical for the structural safety are pre-determined. Damage possibility of each member computed from the static strain energy has been implemented as a weighting factor in the algorithm. Simulation studies have been carried out on a two-span multigirder bridge to examine the proposed algorithms.

An incremental formulation of the moving-grid finite element method for the prediction of dynamic crack propagation

Abstract This paper presents an incremental formulation of the moving-grid finite element method based on the Eulerian-Lagrangian Lagramatic description (ELD) to predict dynamic crack propagation in brittle materials. The variational statement of the equations of motion based on the ELD and an integral form of the energy balance criterion for crack growth are used to form the governing equations for the prediction problems of dynamic crack propagation. The resulting governing equations for the present formulation are nonlinear with respect to two unknowns, displacement and crack-tip position. An iterative solution scheme for the present formulation is proposed. The unknown crack-tip position is computed directly in the solution procedure. Numerical results of the prediction of mode I dynamic crack propagation are presented and compared with experimental results and other numerical solutions.

A regularization scheme for displacement reconstruction using acceleration data measured from structures

This paper present a new displacement reconstruction scheme using only acceleration measured from a structure. For a given set of acceleration data, the reconstruction problem is formulated as a boundary value problem in which the acceleration is approximated by the second-order central finite difference of displacement. The displacement is reconstructed by minimizing the least squared errors between measured and approximated acceleration within a finite time interval referred to as a time window. An overlapping time window is introduced to improve the accuracy of the reconstructed displacement. The displacement reconstruction problem becomes ill-posed because the boundary conditions at both ends of each time window are not known a priori. Furthermore, random noise in measured acceleration causes physically inadmissible errors in the reconstructed displacement similar to the conventional time integration schemes. A Tikhonov regularization scheme is adopted to alleviate the ill-posedness. The validity of the proposed method is demonstrated through two laboratory experiments.

Evaluation of Impulse Response Functions for Convolution Integrals of Aerodynamic Forces by Optimization with a Penalty Function

AbstractThis paper presents a new algorithm for evaluating impulse response functions for the convolution integrals of the aerodynamic forces of bridge decks. The impulse response functions formed by measured flutter derivatives are modified to satisfy causality conditions through optimization. The error function in the object function is defined as the least square errors between the measured and the modified transfer function, and the causality condition is imposed as a penalty function. The modified transfer functions are interpolated with the cubic spline. The selection of the optimal penalty number is presented for obtaining a balanced solution between the effects of the error function and the penalty function. The proposed method is verified using two numerical examples. Time-domain aeroelastic analyses are performed with the proposed method for a thin rectangular section and a bluff H-type section, and the results are compared to values obtained by the rational function approximation (RFA) and the ...

Optimal Accelerometer Locations for Structural Health Monitoring Using Time-Domain System Identification

The paper presents two algorithms for determining optimal accelerometer locations for structural health monitoring when structural condition is assessed by a system identification scheme in time-domain. The accelerometer locations are determined by ranking the components of an effective independent distribution vector computed from a Fisher information matrix. One of the proposed algorithms formulates a Fisher information matrix by multiplying acceleration matrix with its transpose and the other as a Gauss-Newton Hessian matrix composed of acceleration sensitivities with respect to structural parameters. Since the structural parameters cannot be known exactly in an actual application, a statistical approach is proposed by setting an error bound between the actual and the baseline values. To examine the algorithm, simulation studies have been carried out on a two-span planar truss. The results using locations selected by the two algorithms were compared.