The general expressions of finite Hankel transform are naturally deduced with the help of the property of Bessel functions.The equations in this paper can degenerate into three kinds of boundaries since all the coeffi...The general expressions of finite Hankel transform are naturally deduced with the help of the property of Bessel functions.The equations in this paper can degenerate into three kinds of boundaries since all the coefficients in the boundary conditions are taken into consideration.The results can be adopted in solving physics problems involving the finite Hankel transform.展开更多
This work is a supplement to the work of Sneddon on axisymmetric Boussinesq problem in 1965 in which the distributions of interior-stress fields are derived here for a punch with general profile.A novel set of mathema...This work is a supplement to the work of Sneddon on axisymmetric Boussinesq problem in 1965 in which the distributions of interior-stress fields are derived here for a punch with general profile.A novel set of mathematical procedures is introduced to process the basic elastic solutions(obtained by the method of Hankel transform,which was pioneered by Sneddon)and the solution of the dual integral equations.These processes then enable us to not only derive the general relationship of indentation depth D and total load P that acts on the punch but also explicitly obtain the general analytical expressions of the stress fields beneath the surface of an isotropic elastic half-space.The usually known cases of punch profiles are reconsidered according to the general formulas derived in this study,and the deduced results are verified by comparing them with the classical results.Finally,these general formulas are also applied to evaluate the von Mises stresses for several new punch profiles.展开更多
基金supported by the National Natural Scientific Foundation of China (Grant Nos.10972103 and 10902055)the National Science Foundation for Postdoctoral Scientists of China (Grant No.20070411046)
文摘The general expressions of finite Hankel transform are naturally deduced with the help of the property of Bessel functions.The equations in this paper can degenerate into three kinds of boundaries since all the coefficients in the boundary conditions are taken into consideration.The results can be adopted in solving physics problems involving the finite Hankel transform.
基金The authors would like to acknowledge the partial supports provided by the National Natural Science Foundation of China(Nos.51575090,11272083,and 11502049)the Fundamental Research Funds for the Central Universities(Nos.ZYGX2014Z004 and ZYGX2015J084)+1 种基金the China Postdoctoral Science Foundation Grant(No.2016M590873)the National Youth Top-Notch Talent Support Program。
文摘This work is a supplement to the work of Sneddon on axisymmetric Boussinesq problem in 1965 in which the distributions of interior-stress fields are derived here for a punch with general profile.A novel set of mathematical procedures is introduced to process the basic elastic solutions(obtained by the method of Hankel transform,which was pioneered by Sneddon)and the solution of the dual integral equations.These processes then enable us to not only derive the general relationship of indentation depth D and total load P that acts on the punch but also explicitly obtain the general analytical expressions of the stress fields beneath the surface of an isotropic elastic half-space.The usually known cases of punch profiles are reconsidered according to the general formulas derived in this study,and the deduced results are verified by comparing them with the classical results.Finally,these general formulas are also applied to evaluate the von Mises stresses for several new punch profiles.
