Browsing by Author "Yang, Judy P."

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A gradient reproducing kernel collocation method for boundary value problems
(2013-03-30)
Chi, Sheng-Wei
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Chen, Jiun-Shyan
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Hu, Hsin-Yun
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Yang, Judy P.
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土木工程學系
The earlier work in the development of direct strong form collocation methods, such as the reproducing kernel collocation method (RKCM), addressed the domain integration issue in the Galerkin type meshfree method, such as the reproducing kernel particle method, but with increased computational complexity because of taking higher order derivatives of the approximation functions and the need for using a large number of collocation points for optimal convergence. In this work, we intend to address the computational complexity in RKCM while achieving optimal convergence by introducing a gradient reproduction kernel approximation. The proposed gradient RKCM reduces the order of differentiation to the first order for solving second-order PDEs with strong form collocation. We also show that, different from the typical strong form collocation method where a significantly large number of collocation points than the number of source points is needed for optimal convergence, the same number of collocation points and source points can be used in gradient RKCM. We also show that the same order of convergence rates in the primary unknown and its first-order derivative is achieved, owing to the imposition of gradient reproducing conditions. The numerical examples are given to verify the analytical prediction. Copyright (c) 2012 John Wiley & Sons, Ltd.
A Novel Approach for Buckling Analysis of Pretwisted Spatially Curved Beams by State Equations
(2016-06)
Kuo, S. R.
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Yang, Judy P.
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Yang, Y. B.
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土木工程學系
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Department of Civil Engineering
Based on force equilibrium and rigid body considerations, a novel approach is proposed for deriving the state equations and then the buckling equations of pretwisted spatially curved beams. Based on statical consideration of an infinitesimal element from the last calculated configuration C-1 to the current configuration C-2, a set of condition equations for the state matrix is derived. Next, by enforcing the rigid body rule for the beam, another set of condition equations for the state matrix is derived. From these two sets of equations, the state matrix of the beam is derived that leads directly to the buckling differential equations. The merit of the proposed approach is that it only requires simple differential and matrix operations. No hidden errors are possible because no higher-order terms need to be treated. In addition, a direct link is established between the straight and curved beam theories. Finally, examples are provided to demonstrate the application of the theory to the buckling analysis of various curved beams, including the helical ones.
A qualified plate theory for rigid rotation in postcritical nonlinear analysis
(2018-12-10)
Kuo, S. R.
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Yang, Judy P.
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Yang, Y. B.
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土木工程學系
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Department of Civil Engineering
A new, simple method is presented for deriving the instability potential of thin plates, based on the equilibrium conditions and constitutive law for incremental forces considering the geometric nonlinear effect. First, the equations of equilibrium are established for the plate at the last calculated C-1 and current deformed C-2 states, from which the equilibrium equations for the incremental forces at C-2 are derived. Then, the incremental forces are derived as the summation of two parts: (1) the part from the increase of the Cauchy stresses at C-1 to the 2nd Piola-Kirchhoff stresses at C-2, which are related to the strain increments and derivable from the linear constitutive; and (2) the part by the difference between the 2nd Piola-Kirchhoff and 1st Piola-Kirchhoff stresses, which are related to the cross-sectional forces at C-1 and rigid displacements. Based on the previous concept, the rigid body rule and coordinate indifference of tensor expressions, the constitutive law for incremental forces including the geometric nonlinear effect is derived. Further, by the variational principle, the following instability potentials are derived: delta U-GB caused by the balance conditions for initial forces, delta U-GC caused by the constitutive law for incremental forces, and delta U-GR caused by the rotation of boundary moments. Consequently, the total instability potential is presented for the plate in the virtual work form. The present approach is self-explanatory, which requires only simple integration operations. Moreover, the two essential conditions are satisfied: equilibrium conditions for incremental forces and rigid body rule. Numerical examples are presented to demonstrate the rationality of the present plate theory compared with the conventional one.
Damping Effect of a Passing Vehicle for Indirectly Measuring Bridge Frequencies by EMD Technique
(2018-01-01)
Yang, Judy P.
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Lee, Wei-Chun
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土木工程學系
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Department of Civil Engineering
The indirect approach for measuring bridge frequencies from a passing vehicle has become an attractive method recently because it provides mobility, reliability, and safety for setting up sensors in comparison with the traditional method for measurement. In the vehicle-bridge interaction system, it is realized that the bridge frequencies can be identified from the spectral analysis of the passing vehicle. However, there exist many factors affecting the identified results of bridge frequencies, and one key factor is the vehicle damping. This study investigates the effect of vehicle damping on the identification of the first bridge frequency for three different levels of road surface roughness by the empirical mode decomposition (EMD) technique. The numerical experimentation shows the following properties that can be utilized in a field measurement: (1) higher vehicle damping tends to suppress the vehicle frequency, and (2) the use of vehicle damping helps to suppress the effect of rough surface roughness and make the first bridge frequency visible.
Detecting Inverse Boundaries by Weighted High-Order Gradient Collocation Method
(2020-08-01)
Yang, Judy P.
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Lam, Hon Fung Samuel
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土木工程學系
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Department of Civil Engineering
The weighted reproducing kernel collocation method exhibits high accuracy and efficiency in solving inverse problems as compared with traditional mesh-based methods. Nevertheless, it is known that computing higher order reproducing kernel (RK) shape functions is generally an expensive process. Computational cost may dramatically increase, especially when dealing with strong-from equations where high-order derivative operators are required as compared to weak-form approaches for obtaining results with promising levels of accuracy. Under the framework of gradient approximation, the derivatives of reproducing kernel shape functions can be constructed synchronically, thereby alleviating the complexity in computation. In view of this, the present work first introduces the weighted high-order gradient reproducing kernel collocation method in the inverse analysis. The convergence of the method is examined through the weights imposed on the boundary conditions. Then, several configurations of multiply connected domains are provided to numerically investigate the stability and efficiency of the method. To reach the desired accuracy in detecting the outer boundary for two special cases, special treatments including allocation of points and use of ghost points are adopted as the solution strategy. From four benchmark examples, the efficacy of the method in detecting the unknown boundary is demonstrated.
Investigation of Multiply Connected Inverse Cauchy Problems by Efficient Weighted Collocation Method
(2020-01-01)
Yang, Judy P.
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Lin, Qizheng
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土木工程學系
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Department of Civil Engineering
This work introduces an efficient weighted collocation method to solve inverse Cauchy problems. As it is known that the reproducing kernel approximation takes time to compute the second-order derivatives in the meshfree strong form method, the gradient approach alleviates such a drawback by approximating the first-order derivatives in a similar way to the primary unknown. In view of the overdetermined system derived from inverse Cauchy problems with incomplete boundary conditions, the weighted gradient reproducing kernel collocation method (G-RKCM) is further introduced in the analysis. The convergence of the met hod is first demonstrated by the simply connected inverse problems, in which the same set of source points and collocation points is adopted. Then, the multiply connected inverse problems are investigated to show that high accuracy of approximation can be reached. The sensitivity and stability of the method is tested through the disturbance added on both Neumann and Dirichlet boundary conditions. From the investigation of four benchmark problems, it is concluded that the weighted gradient reproducing kernel collocation method is more efficient than the reproducing kernel collocation method.
Investigation of Radial Basis Collocation Method for Incremental-Iterative Analysis
(2016-02)
Yang, Judy P.
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Su, Wan-Ting
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土木工程學系
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Department of Civil Engineering
We propose an incremental-iterative algorithm by using the strong form collocation method for solving geometric nonlinear problems. As nonlinear analyses concerning large deformation have been relied on the weak form-based methods such as the finite element methods and the reproducing kernel particle methods, the recently developed strong form collocation methods could be new research directions in that the mesh control and quadrature rule are abandoned in the collocation methods. In this work, the radial basis collocation method is adopted to perform the nonlinear analysis. The corresponding parameters affecting the deformation paths such as the increment of applied traction and shape parameter of the radial basis function are discussed. We also investigate the possibility of using the weighted collocation methods in the nonlinear analysis.
Resonance and Cancellation in Torsional Vibration of Monosymmetric I-Sections Under Moving Loads
(2018-09-01)
Yang, Y. B.
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Li, Mei
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Zhang, Bin
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Wu, Yuntian
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Yang, Judy P.
This paper is concerned with the lateral and torsional coupled vibration of monosymmetric I-beams under moving loads. To this end, a train is modeled as two subsystems of eccentric wheel loads of constant intervals to account for the front and rear wheels. By assuming the lateral and torsional displacements to be restrained at the two ends of the beam, both the lateral and torsional displacements are approximated by a series of sine functions. The method of variation of constants is adopted to derive the closed-form solution. For the most severe condition when the last wheel load is acting on the beam, both the conditions of resonance and cancellation are identified. Once the condition of cancellation is enforced, the resonance response can always be suppressed, which represents the optimal design for the beam. Since the condition for suppressing the torsional resonance is exactly the same as that for the vertical resonance, this offers a great advantage in the design of monosymmetric I-beams, as no distinction needs to be made between the suppression of vertical or torsional resonance.
Rigid-Mass Vehicle Model for Identification of Bridge Frequencies Concerning Pitching Effect
(2019-02-01)
Yang, Judy P.
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Chen, Bo-Lin
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土木工程學系
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Department of Civil Engineering
The concept of vehicle-bridge interaction (VBI) was originally developed to investigate the dynamic behavior of bridges subjected to moving loads such as high-speed trains. In recent years, the VBI system was introduced to further explore the possibility of identifying bridge frequencies in order to monitor the health of bridges via the use of passing vehicles. Among the models of test vehicles, the sprung mass vehicle model with a single-degree-of-freedom vehicle body is the most common adopted one due to its simplicity. Nevertheless, for a test vehicle moving over the uneven pavement, the pitching effect arising from the vertical and rotational movements of the vehicle actually influences the identification of bridge frequencies. As such, a rigid-mass vehicle model is proposed in this work to improve the sprung mass vehicle model by including both vertical and rotational deflections. The analytical solutions to the rigid-mass VBI system are derived to verify the proposed model, and the numerical examples are provided to investigate the dynamic behavior of the VBI system subjected to road irregularity.
Seismic Analysis of Twin Tunnels by a Finite/Infinite Element Approach
(2017-09-01)
Lin, Szu-Yun
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Hung, Hsiao-Hui
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Yang, Judy P.
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Yang, Y. B.
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土木工程學系
The two-dimensional (2D) dynamic response of horizontally aligned, cylindrical twin tunnels subjected to vertically incident seismic waves was simulated by a finite/infinite element approach. A rational approach was proposed for imposing the earthquake forces using free-field recorded data. First, the earthquake motion recorded on the free field was transferred to that on the boundary of the near field using the one-dimensional (1D) wave theory. Second, the motion data were computed as the equivalent seismic forces and applied on the near-field boundary in the frequency domain. In this study, the data from the 1999 Chi-Chi earthquake recorded at the TAP003 station were adopted. The accuracy of the procedure for imposing the free-field earthquakes was first verified. Then, a parametric study was performed to investigate the effects of spacing between the twin tunnels, depths of tunnels, and stiffness of tunnel lining under seismic excitation. The results of the analysis indicate that although the depth and spacing of the twin tunnels have less effect on ground response, they are important parameters for the seismic responses of the tunnels. (C) 2017 American Society of Civil Engineers.
Seismic analysis of underground tunnels by the 2.5D finite/infinite element approach
(2016-06)
Lin, K. C.
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Hung, H. H.
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Yang, Judy P.
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Yang, Y. B.
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土木工程學系
A procedure for the seismic analysis of underground tunnels using recorded free-field earthquakes based on the 2.5D finite/infinite element approach is presented. The near and far fields of the half space are modeled by finite and infinite elements, respectively. Using the 1D wave theory, the nodal force and displacement on the near-field boundary are computed for each spectral frequency of the earthquake. Then, equivalent seismic forces are computed for the near-field boundary for the earthquake spectrum. By assuming the soil-tunnel system to be uniform along the tunnel axis, the 2.5D approach can account for the wave transmission along the tunnel axis, which reduces to the 2D case for infinite transmission velocity. The horizontal and vertical components of the 1999 Chi-Chi Earthquake (TCU068) are adopted as the free-field motions in the numerical analysis. The maximal stresses and distribution patterns of the tunnel section under the P- and SV-waves are thoroughly studied by the 2.5D and 2D approaches, which should prove useful to the design of underground tunnels. (C) 2016 Elsevier Ltd. All rights reserved.
Solving Inverse Laplace Equation with Singularity by Weighted Reproducing Kernel Collocation Method
(2017-07-01)
Yang, Judy P.
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Guan, Pai-Chen
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Fan, Chia-Ming
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土木工程學系
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Department of Civil Engineering
This work introduces the weighted collocation method with reproducing kernel approximation to solve the inverse Laplace equations. As the inverse problems in consideration are equipped with over-specified boundary conditions, the resulting equations yield an overdetermined system. Following our previous work, the weighted collocation method using a least-squares minimization has shown to solve the inverse Cauchy problems efficiently without using techniques such as iteration and regularization. In this work, we further consider solving the inverse problems of Laplace type and introduce the Shepard functions to deal with singularity. Numerical examples are provided to demonstrate the validity of the method.
State-of-the-Art Review on Modal Identification and Damage Detection of Bridges by Moving Test Vehicles
(2018-02-01)
Yang, Y. B.
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Yang, Judy P.
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土木工程學系
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Department of Civil Engineering
In 2004, Yang and co-workers proposed the extraction of bridge frequencies from the dynamic response of a moving test vehicle [Y. B. Yang, C. W. Lin and J. D. Yau, Extracting bridge frequencies from the dynamic response of a passing vehicle, J. Sound Vib. 272 (2004) 471-493] and verified the technique by a field test [C. W. Lin and Y. B. Yang, Use of a passing vehicle to scan the bridge frequencies - An experimental verification, Eng. Struct. 27(13) (2005) 1865-1878]. This technique was extended to construction of mode shapes [Y. B. Yang, Y. C. Li and K. C. Chang, Constructing the mode shapes of a bridge from a passing vehicles: A theoretical study, Smart Struct. Syst. 13(5) (2014) 797-819] and damage identification of bridges. It was referred to as the indirect method for bridge measurement because no vibration sensors are needed for installation on the bridge, but it only requires one or few vibration sensors on the test vehicle. When compared with the conventional direct method that relies fully on the response of the bridge fitted with vibration sensors, the advantage of the indirect method is clear: mobility, economy, and efficiency. Over the past years, many research studies were conducted along the lines of the indirect method for bridge measurement. Significant advances have been made on various aspects of application. This paper represents a state-of-the-art review of the related research works conducted worldwide. Comments and recommendations will be made at proper places, while concluding remarks including future research directions will be presented at the end of the paper.
Strong-Form Formulated Generalized Displacement Control Method for Large Deformation Analysis
(2017-10-01)
Yang, Judy P.
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Chen, Jian-Yu
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土木工程學系
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Department of Civil Engineering
The traditional analysis of geometric nonlinearity is mostly based on the weak-formulated Galerkin method such as the finite element method. The element nature has limited its application as a result of numerical integration in the governing equation and quality control of deformed mesh. In the middle of 1990s, the meshfree methods have been developed and become one leading research topic in computational mechanics. Especially, the strong form collocation methods require no additional efforts to process numerical integration and impose Dirichlet boundary condition, thereby making the collocation methods computationally efficient. In the incremental-iterative process, how to accurately reflect the change in the slope of the load-deflection curve of the structure and remain numerically stable are of major concerns. Thus, we propose a strong-form formulated generalized displacement control method to analyze geometric nonlinear problems, where the radial basis collocation method is adopted. The numerical examples demonstrate the ability of the proposed method for large deformation analysis.
Two-Mass Vehicle Model for Extracting Bridge Frequencies
(2018-04-01)
Yang, Judy P.
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Chen, Bo-How
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土木工程學系
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Department of Civil Engineering
The dynamic response of a moving vehicle has been utilized to extract the frequencies of the supporting bridge. In most previous studies, the vehicle was modeled as a single-degree-of-freedom sprung mass moving over a simple beam, which suffers from the drawback that the sprung mass may be affected by the vehicle motion. To overcome this drawback, this paper presents a two-mass vehicle model for extracting the bridge frequencies, which contains a sprung mass (vehicle body) and an unsprung mass (axle mass). By using the response of the unsprung mass, the bridge response can be more realistically extracted. The main findings of the present study are as follows: (1) the use of unsprung mass in the vehicle model can faithfully reveal the dynamic responses of both the vehicle and bridge, (2) the increase in the unsprung mass can effectively help the extraction of bridge frequencies, including the second frequency, (3) under high levels of road roughness, the proposed model can identify the bridge frequencies, while the single-mass model cannot, and (4) in the presence of vehicle damping, the proposed model can identify the bridge frequencies under high levels of road roughness without additional techniques of processing.
Wave Number-Based Technique for Detecting Slope Discontinuity in Simple Beams Using Moving Test Vehicle
(2017-08-01)
Yau, J. D.
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Yang, Judy P.
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Yang, Y. B.
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土木工程學系
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Department of Civil Engineering
The wavelength characteristic is a useful clue for locating and assessing the severity of slope discontinuity in beams. In this study, the slope discontinuity of a beam is represented by an internal hinge restrained by elastic springs, and the wavelength of the beam is calculated indirectly from the vertical response of a test vehicle during its travel over the beam. The key parameters of the problem at hand are first unveiled using an approximate, closed-form solution for the response of the vehicle moving at low speeds over the bridge. Then a two-beam element model with slope discontinuity is formulated for the vehicle-bridge interaction (VBI) system for use in numerical simulation. In the examples, the wavenumber-based response of the test vehicle is used to identify the location and severity of the discontinuity in the beam. It is demonstrated that the wavelength-based technique presented herein by using the moving test vehicle as a moving sensor system offers a promising, alternative approach for damage detection in girder type bridges.
Weighted Reproducing Kernel Collocation Method and Error Analysis for Inverse Cauchy Problems
(2016-04)
Yang, Judy P.
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Guan, Pai-Chen
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Fan, Chia-Ming
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土木工程學系
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Department of Civil Engineering
In this work, the weighted reproducing kernel collocation method (weighted RKCM) is introduced to solve the inverse Cauchy problems governed by both homogeneous and inhomogeneous second-order linear partial differential equations. As the inverse Cauchy problem is known for the incomplete boundary conditions, how to numerically obtain an accurate solution to the problem is a challenging task. We first show that the weighted RKCM for solving the inverse Cauchy problems considered is formulated in the least-squares sense. Then, we provide the corresponding error analysis to show how the errors in the domain and on the boundary can be balanced with proper weights. The numerical examples demonstrate that the weighted discrete systems improve the accuracy of solutions and exhibit optimal convergence rates in comparison with those obtained by the traditional direct collocation method. It is shown that neither implementation of regularization nor implementation of iteration is needed to reach the desired accuracy. Further, the locality of reproducing kernel approximation gets rid of the ill-conditioned system.
Weighted reproducing kernel collocation method based on error analysis for solving inverse elasticity problems
(2019-10-01)
Yang, Judy P.
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Hsin, Wen-Chims
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土木工程學系
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Department of Civil Engineering
For inverse problems equipped with incomplete boundary conditions, a simple solution strategy to obtain approximations remains a challenge in the fields of engineering and science. Based on our previous study, the weighted reproducing kernel collocation method (W-RKCM) shows optimal convergence in solving inverse Cauchy problems. As such, this work further introduces the W-RKCM to solve inverse problems in elasticity. From mathematical error estimate and numerical convergence study, it is shown that the weighted least-squares formulation can properly balance the errors in the domain and on the boundary. By comparing the approximations obtained by W-RKCM with those obtained by the direct collocation method, the reproducing kernel shape function can retain the locality without using a large support size, and the corresponding approximations exhibit extremely high solution accuracy. The stability of the W-RKCM is demonstrated by adding noise on the boundary conditions. This work shows the efficacy of the proposed W-RKCM in solving inverse elasticity problems as no additional technique is involved to reach the desired solution accuracy in comparison with the existing methods in the literature.
Wheel size embedded two-mass vehicle model for scanning bridge frequencies
(1970-01-01)
Yang, Judy P.
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Cao, Cheng-Yi
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土木工程學系
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Department of Civil Engineering
A novel vehicle model is proposed to scan bridge frequencies effectively by incorporating both the size of wheel and the unsprung mass in the formulation of an vehicle-bridge interaction element. For the single-degree-of-freedom sprung mass vehicle model commonly adopted in the literature, either the wheel has been treated as a point or the unsprung mass has been neglected due to simplicity. Nevertheless, when a test vehicle is moving on the uneven pavement, the wheels of finite size and mass cannot avoid suffering a bumpy journey, i.e., the wheels are elevated and lowered. As such, the advanced two-mass vehicle model concerning wheel size comes out for realistic application. It is shown that the bridge frequencies can be scanned up to the fifth frequency with desired accuracy even under a high class of road surface roughness in the presence of vehicle damping, whereas the two-mass vehicle model can identify no more than the first two bridge frequencies in the absence of vehicle damping.