Judy P. Yang

Finite element modeling of passive material influence on the deformation and force output of skeletal muscle

The pattern of deformation of different structural components of a muscle-tendon complex when it is activated provides important information about the internal mechanics of the muscle. Recent experimental observations of deformations in contracting muscle have presented inconsistencies with current widely held assumption about muscle behavior. These include negative strain in aponeuroses, non-uniform strain changes in sarcomeres, even of individual muscle fibers and evidence that muscle fiber cross sectional deformations are asymmetrical suggesting a need to readjust current models of contracting muscle. We report here our use of finite element modeling techniques to simulate a simple muscle-tendon complex and investigate the influence of passive intramuscular material properties upon the deformation patterns under isometric and shortening conditions. While phenomenological force-displacement relationships described the muscle fiber properties, the material properties of the passive matrix were varied to simulate a hydrostatic model, compliant and stiff isotropically hyperelastic models and an anisotropic elastic model. The numerical results demonstrate that passive elastic material properties significantly influence the magnitude, heterogeneity and distribution pattern of many measures of deformation in a contracting muscle. Measures included aponeurosis strain, aponeurosis separation, muscle fiber strain and fiber cross-sectional deformation. The force output of our simulations was strongly influenced by passive material properties, changing by as much as ~80% under some conditions. The maximum output was accomplished by introducing anisotropy along axes which were not strained significantly during a muscle length change, suggesting that correct costamere orientation may be a critical factor in the optimal muscle function. Such a model not only fits known physiological data, but also maintains the relatively constant aponeurosis separation observed during in vivo muscle contractions and is easily extrapolated from our plane-strain conditions into a three-dimensional structure. Such modeling approaches have the potential of explaining the reduction of force output consequent to changes in material properties of intramuscular materials arising in the diseased state such as in genetic disorders.

State-of-the-Art Review on Modal Identification and Damage Detection of Bridges by Moving Test Vehicles

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...

Key Considerations in Tracing the Postbuckling Response of Structures with Multi Winding Loops

The postbuckling response of structures with multi winding loops is characterized by the appearance of multi adjacent equilibrium paths, which often makes the iterations difficult to converge to the desired path. In this paper, some key issues for tracing the postbuckling response of a structure using an incremental-iterative approach are discussed. Concerning the finite element equations used, it is essential that the corrector used for recovering the element forces from the element displacements be made as accurate as possible, and that the predictor for computing the structural displacements under given load increments, which are approximate by nature due to linearization involved, be accurate to the level not to misguide the iterations. As for the incremental-iterative scheme, it is required to be: (1) numerically stable when encountering the limit points, (2) adjustable in load increments to reflect the stiffness variation, and (3) self-adaptive in changing the loading direction. To demonstrate the ideas involved, some examples with highly complicated postbuckling responses will be solved in this paper.

Wave Number-Based Technique for Detecting Slope Discontinuity in Simple Beams Using Moving Test Vehicle

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.

Investigation of Radial Basis Collocation Method for Incremental-Iterative Analysis

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.

Damping Effect of a Passing Vehicle for Indirectly Measuring Bridge Frequencies by EMD Technique

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 a...

Weighted Reproducing Kernel Collocation Method and Error Analysis for Inverse Cauchy Problems

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.

Resonance and Cancellation in Torsional Vibration of Monosymmetric I-Sections Under Moving Loads

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 disti...

Two-Mass Vehicle Model for Extracting Bridge Frequencies

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, ...

Solving Inverse Laplace Equation with Singularity by Weighted Reproducing Kernel Collocation Method

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.