Authors: Shu Yuan Zhang, Yun Xin Wu

Abstract: A mathematical model has been developed to predict the residual stresses level in pre-stretched aluminum alloy plate. This is based on force balances of the residual stress, theory of plastoelasticity and a new conception of free length. The model is relatively simple because only rolling direction residual stress is taken into account, but provides a clear illustration of stress relief mechanism in stretching process. With this model, residual stress distributions of stretched beam can be determined directly by knowing the specimen dimensions, material properties and the original stress. The model offers an useful tool to show the effect of varying tension ratio on the final residual stress level, thus makes it possible to predict stress relief and control residual stresses. An example of using the model is presented by applying published data while showing mechanism of stress relief during stretching. Analysis indicates that it is stretch-caused convergence of the free lengths of strips in beam that lead to reduction in the residual stresses.

3187

Abstract: By using of closed-form solution for predicting fatigue crack initiation life of a beam subjected to the transverse bending load in large range damage， fatigue crack initiation life of backup roll of four high mill is predicted. The method adopted in this paper is simple and effective. A new method is provided for predicting fatigue crack initiation life backup roll of four high mill.

1469

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: Abstract: The article presents the optimized design of the strains transducer elastic component with double cantilever beam. The calculation has been made by the methods of differential equations in the mechanics of material and the finite element methods.We get the maximum strain range and the best gauge position of the strains transducer. The results by the finite element methods are in accordance with the one that calculated by the differential equations. The output sensitivity of the transducer has been analysed. The load electrical capacity output of the material testing machine has been calculated.

1746

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