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The Second Kind Chebyshev Wavelet Method for Fractional Differential Equations with Variable Coefficients
No full textIn this article, the second kind Chebyshev wavelet method is presented for solving a class of multi-order fractional differential equations (FDEs) with variable coefficients. We first construct the second kind Chebyshev wavelet, prove its convergence and then derive the operational matrix of fractional integration of the second kind Chebyshev wavelet. The operational matrix of fractional integration is utilized to reduce the fractional differential equations to a system of algebraic equations. In addition, illustrative examples are presented to demonstrate the efficiency and accuracy of the proposed method
A Benchmark Problem for Comparison of Vibration-Based Crack Identification Methods
No full textThe vibration-based crack identification problem insists of finding a measured vibration parameter from a complete crack-detection-database constructed by numerical simulation. It is one of the classical optimization problems. Many intelligence methods, such as neural network (NN), genetic algorithm (GA), determinant transformation (DT), and frequency contour (FC) etc., have been extensively employed as optimization tools to achieve this task. The aim of this paper is to propose a benchmark problem to compare these extensive-used optimization methods in terms of crack identification precision and computational time. The merit and demerits for each method are discussed. The results suggest that FC is a visualized, stable and easily applied method for detecting crack in practice. The conclusions of current studies are useful to investigators in deciding which method should be chosen in their crack inspections
Three-dimensional Fluid Flow Simulations Using GPU-based Particle Method
Get PDFThe application of a GPU-based particle method to three-dimensional incompressible viscous fluid flow problems is presented. The particle approach is based on the MPS (Moving Particle Semi-implicit) scheme using logarithmic weighting function to stabilize the spurious oscillatory solutions for solving the Poisson equation with respect to the pressure fields by using GPU-based SCG (Scaled Conjugate Gradient) method. Numerical results demonstrate the workability and the validity of the present approach through the dam-breaking flow problem and flow behavior in a liquid ring pump with rotating impeller blades
Topological Design of Structures Using a Cellular Automata Method
Get PDFTopological design of continuum structures usually involves numerical instabilities, such as checkerboards and mesh-dependency, which degenerate the manufacturability, the efficiency and the robustness of the optimal design. This paper will propose a new topology optimization method to suppress numerical instabilities occurred in the topology optimization of continua, according to the principle of error amplifier and feedback control in the control system. The design variables associated with topological design are updated based on the Cellular Automata (CA) theory. A couple of typical numerical examples are used to demonstrate the effectiveness of the proposed method in effectively suppressing numerical instabilities occurred in the numerical procedure of topology optimization
On Static Analysis of Composite Plane State Structures via GDQFEM and Cell Method
Get PDFIn this paper, an advanced version of the classic GDQ method, called the Generalized Differential Quadrature Finite Element Method (GDQFEM) is formulated to solve plate elastic problems with inclusions. The GDQFEM is compared with Cell Method (CM) and Finite Element Method (FEM). In particular, stress and strain results at fiber/matrix interface of dissimilar materials are provided. The GDQFEM is based on the classic Generalized Differential Quadrature (GDQ) technique that is applied upon each sub-domain, or element, into which the problem domain is divided. When the physical domain is not regular, the mapping technique is used to transform the fundamental system of equations and all the compatibility conditions. A differential problem defined on the regular master element in the computational domain is turned into an algebraic system. With respect to the very well-known Finite Element Method (FEM), the GDQFEM is based on a different approach: the direct derivative calculation is performed by using the GDQ rule. The imposition of the compatibility conditions between two boundaries are also used in the CM for solving contact problems. Since the GDQFEM is a higherorder tool connected with the resolution of the strong formulation of the system of equations, the compatibility conditions must be applied at each disconnection in order to capture the discontinuity between two boundaries, without losing accuracy. A comparison between GDQFEM, CM and FEM is presented and very good agreement is observed
A Self-regularization Technique in Boundary Element Method for 3-D Stress Analysis
Get PDFThe self-regularization technique in the Boundary Element Method (BEM) originally proposed by Cruse and Richardson (1996, 1999) in their work for two-dimensional (2-D) stress analysis is extended to three-dimensional (3-D) elastostatics in this paper. The regularization scheme addresses the issue of accurate numerical evaluation of the integrals due to the singularity of the kernel functions of the integral equations. It is first implemented for the determination of displacements and stresses at interior points of the solution domain, and very accurate results are obtained even when these points are very close to the surface of the domain. A self-regularized traction-BIE is then implemented with two different approaches to deal with the requirement of continuity of the displacement-gradients across element boundaries. The examples presented suggest that when corners are present, this smoothness requirement for the traction-BIE must be met if convergence of the solution is to be assured. Finally, a self-regularized displacement-BIE is developed which can treat thin-body problems by eliminating the near-singularity issues encountered in conventional BEM. This is demonstrated by numerical examples
Numerical and Experimental Investigations of Jet Impingement on a Periodically Oscillating-Heated Flat Plate
Get PDFIn the present paper, the impingement of air jet on a heated flat plate subjected to a periodic oscillation is numerically and experimentally investigated. The motivation of the present research is the desire to enhance the heat transfer characteristics during the cooling process of a heated flat plate which can be found in many relevance industrial applications. In order to improve the heat transfer characteristics, a novel idea is utilized, where a periodical oscillation movement in form of sine wave produced from a Scotch yoke mechanism is applied to the heated flat plate. The obtained numerical results showed a good agreement with the performed experimental measurements. Moreover, an increase of the Nusselt number is obtained from an oscillated plate in comparison with that obtained from a fixed plate. This reveals the enhancement of the heat transfer characteristics of a heated flat plate as a result of the applied periodic oscillation movement
Application of the Time-Domain Boundary Element Method to Analysis of Flow-Acoustic Interaction in a Hole-tone Feedback System with a Tailpipe
Get PDFThis paper is concerned with a mathematical model of a simple axisymmetric silencer-like model, consisting of a hole-tone feedback system equipped with a tailpipe. The unstable shear layer is modeled via a discrete vortex method, based on axisymmetric vortex rings. The aeroacoustic model is based on the Powell- Howe theory of vortex sound. Boundary integrals are discretized via the boundary element method; but the tailpipe is represented by the exact (one-dimensional) solution. It is demonstrated though numerical examples that this numerical model can display lock-in of the self-sustained flow oscillations to the resonant acoustic oscillations
Cell Migration and Cell-Cell Interaction in the Presence of Mechano-Chemo-Thermotaxis
Get PDFAlthough there are several computational models that explain the trajectory that cells take during migration, till now little attention has been paid to the integration of the cell migration in a multi-signaling system. With that aim, a generalized model of cell migration and cell-cell interaction under multisignal environments is presented herein. In this work we investigate the spatio-temporal cell-cell interaction problem induced by mechano-chemo-thermotactic cues. It is assumed that formation of a new focal adhesion generates traction forces proportional to the stresses transmitted by the cell to the extracellular matrix. The cell velocity and polarization direction are calculated based on the equilibrium of the effective forces associated to cell motility. It is also assumed that, in addition to mechanotaxis signals, chemotactic and thermotactic cues control the direction of the resultant traction force. This model enables predicting the trajectory of migrating cells as well as the spatial and temporal distributions of the net traction force and cell velocity. Results indicate that the tendency of the cells is firstly to reach each other and then migrate towards an imaginary equilibrium plane located near the source of the signal. The position of this plane is sensitive to the gradient slope and the corresponding efficient factors. The cells come into contact and separate several times during migration. Adding other cues to the substrate (such as chemotaxis and/or thermotaxis) delays that primary contact. Moreover, in all states, the average local velocity and the net traction force of the cells decrease while the cells approach the cues source. Our findings are qualitatively consistent with experimental observations reported in the related literature
Challenge of Biomechanics
Get PDFThe application of mechanics to biology – biomechanics – bears great challenges due to the intricacy of living things. Their dynamism, along with the complexity of their mechanical response (which in itself involves complex chemical, electrical, and thermal phenomena) makes it very difficult to correlate empirical data with theoretical models. This difficulty elevates the importance of useful biomechanical theories compared to other fields of engineering. Despite inherent imperfections of all theories, a well formulated theory is crucial in any field of science because it is the basis for interpreting observations. This is all-the-more vital, for instance, when diagnosing symptoms, or planning treatment to a disease. The notion of interpreting empirical data without theory is unscientific and unsound. This paper attempts to fortify the importance of biomechanics and invigorate research efforts for those engineers and mechanicians who are not yet involved in the field. It is not aimed here, however, to give an overview of biomechanics. Instead, three unsolved problems are formulated to challenge the readers. At the microscale, the problem of the structural organization and integrity of the living cell is presented. At the meso-scale, the enigma of fingerprint formation is discussed. At the macro-scale, the problem of predicting aneurysm ruptures is reviewed. It is aimed here to attract the attention of engineers and mechanicians to problems in biomechanics which, in the author’s opinion, will dominate the development of engineering and mechanics in forthcoming years