Authors: Wei Wei Zhang, Zhi Hua Wang, Hong Wei Ma

Abstract: The objective of this study is to show the potential of the crack detection method based on Wavelet Packet Transform (WPT), which is depending on the response at a single point on a beam subject to moving load. In this paper, an ANSYS model of a cracked beam is established. The moving load is transient analyzed by shifting the point of the concentrated force. The response at mid-span of the beam is calculated and wavelet packet transformed. The crack on the beam can be found by the abnormal signal in WPT branches. The size is also estimated by a defined damage index (Dindex) which relates to the energy of the abnormal signal. Finally, the effects of both crack location and wavelet selection on Dindex are discussed in detail.

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Authors: Jing Yan, Ya Wu Zeng, Rui Gao

Abstract: For the research of beam’s deformation, material mechanics uses equation of small deflection curve which neglects 1^{st}^{ }order derivative of deflection and regards bending moment M is merely a function of abscissa x, and then gets the approximate solution of vertical displacement. However in some case, small deflection curve isn’t efficacious, so two methods come up in this paper to solve the accurate differential equation of beam’s deformation. This paper takes a slightness beam from temperature controlling device as an example and shows detailed process of mathematical modeling and solving. For iteration, firstly governing equations are founded, then an initial value is put into it to work out a new value, next see the new value as a new initial value and calculate again, by doing the operation repeatedly steady-state solution will be got in the end. For functional analysis, deflection equation is assumed as a kind of function containing some undetermined coefficients, then make it satisfy all the boundary conditions, and establish residual fonctionelle, by partial derivative operation to make the fonctionelle minimum, undetermined coefficients are estimated and deflection curve is got. At the end, impacts of gravity and axial deformation are discussed.

6144

Abstract: The equation of large deflection of functionally graded beam subjected to arbitrary loading condition is derived. In this work assumed that the elastic modulus varies by exponential and power function in longitudinal direction. The nonlinear derived equation has not exact solution so shooting method has been proposed to solve the nonlinear equation of large deflection. Results are validated with finite element solutions. The method will be useful toward the design of compliant mechanisms driven by smart actuators. Finally the effect of different elastic modulus functions and loading conditions are investigated and discussed.

4705

Authors: P.V. Jeyakarthikeyan, R. Yogeshwaran, Karthikk Sridharan

Abstract: This paper presents about generating elemental stiffness matrix for quadrilateral elements in closed form solution method for application on vehicle analysis which is convenient and simple as long as Jacobian is matrix of constant. The interpolation function of the field variable to be found can integrate explicitly once for all, which gives the constant universal matrices A, B and C. Therefore, stiffness matrix is no longer integration of the given functional, it is simple calculation of universal matrices and local co-ordinates of the element. So time taken for generation of element stiffness can be reduced considerably compared to Gauss numerical integration method. For effective use of quadrilateral elements hybrid grid generation is recommended that contains all interior element edges are parallel to each other (rectangle or square elements) and outer boundary elements are quadrilaterals with distortion. So in the Proposed method, the closed form and Gauss numerical method is used explicitly for interior elements and outer elements respectively. The time efficiency of proposed method is compared with conventional Gauss quadrature that is used for entire domain. It is found that the proposed method is much efficient than Gauss Quadrature.

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