I have been going through your paper titled "beam models". I have a question regarding the formulation which you have done in the variational asymptotic method. After deriving the first expression you have perturbed it and hence got an energy expression with the newly added variables. The doubt which i am facing here is that you have considered the potential with respect to v2 and v3 to go to absolute 0 where as taken the variation of the energy corresponding to the v1 terms to go to 0. But we have considered the order of v1 v2 and v3 to be the same. So why the difference?
I took a shortcut here for v2 and v3 as we know that take the variations with respect to v2 and v3 will give you the same result. Please refer to my paper Yu, W. and Hodges, D. H.: "Elasticity Solutions versus Asymptotic Sectional Analysis of Homoge-neous, Isotropic, Prismatic Beams," Journal of Applied Mechanics, vol. 71, no. 1, 2004, pp. 15-23 which used the variation with respect to v2 and v3 goes to zero yielding the same results. The basic reason is that the minimum of the quadratic form involving v2 and v3 is zero (energy is at least zero) can be reached by those conditions listed on the paper. However, it is impossible for energy related with v1 reach zero, thus we must use calculation of variation to solve for it.
Ankit Deo @ on — Edited @ on
Respected Dr. Wenbin Yu,
I have been going through your paper titled "beam models". I have a question regarding the formulation which you have done in the variational asymptotic method. After deriving the first expression you have perturbed it and hence got an energy expression with the newly added variables. The doubt which i am facing here is that you have considered the potential with respect to v2 and v3 to go to absolute 0 where as taken the variation of the energy corresponding to the v1 terms to go to 0. But we have considered the order of v1 v2 and v3 to be the same. So why the difference?
Ankit Deo
Wenbin Yu @ on
I took a shortcut here for v2 and v3 as we know that take the variations with respect to v2 and v3 will give you the same result. Please refer to my paper Yu, W. and Hodges, D. H.: "Elasticity Solutions versus Asymptotic Sectional Analysis of Homoge-neous, Isotropic, Prismatic Beams," Journal of Applied Mechanics, vol. 71, no. 1, 2004, pp. 15-23 which used the variation with respect to v2 and v3 goes to zero yielding the same results. The basic reason is that the minimum of the quadratic form involving v2 and v3 is zero (energy is at least zero) can be reached by those conditions listed on the paper. However, it is impossible for energy related with v1 reach zero, thus we must use calculation of variation to solve for it.