The Application of Iteration and Functional Analysis in Numerical Calculation of Beams with Large Deformation
For the research of beam’s deformation, material mechanics uses equation of small deflection curve which neglects 1st 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.
Chaohe Chen, Yong Huang and Guangfan Li
J. Yan et al., "The Application of Iteration and Functional Analysis in Numerical Calculation of Beams with Large Deformation", Advanced Materials Research, Vols. 243-249, pp. 6144-6149, 2011