The crucial effect of compressibility of rods on their instability is novelly demonstrated via singularity theory. It is shown that the critical load of compressible rod is always greater than the one of the Euler rod...The crucial effect of compressibility of rods on their instability is novelly demonstrated via singularity theory. It is shown that the critical load of compressible rod is always greater than the one of the Euler rod, and a subcritical pitchfork bifurcation, which cannot occur for the Euler rod, may occur for a compressible rod. A whole bifurcation diagram of compressible rods is as follows ： when the original slenderness ratio of a compressible rod, $o is smaller than （1 ＋ v/3 √3π/2,, the rod does not buckle; when So∈ [1＋ v/3）3√3π/2 ,（1＋v/5）5 5√5π/4）,the rod may undergo a subcritical pitchfork bifurcation and a collapse may occur; when So ∈ [1＋ v/5）5√5π/4 ＋ ∞）, the rod may undergo a supercritical pitchfork bifurcation. The deformation of cross section of rods causes a little shift of bifurcation points towards to the one corresponding to larger slenderness ratio.展开更多
Continuous roll forming(CRF) is a novel forming process for three-dimensional surface parts,in which a pair of bendable forming rolls is used as sheet metal forming tool.By controlling the gap between the upper and lo...Continuous roll forming(CRF) is a novel forming process for three-dimensional surface parts,in which a pair of bendable forming rolls is used as sheet metal forming tool.By controlling the gap between the upper and lower forming rolls,sheet metal is non-uniformly extended in the longitudinal direction while it is bent in the transverse direction during the rolling process.As a result,longitudinal bending is gained and a doubly curved surface is formed.With the rotations of the forming rolls,the sheet metal is deformed consecutively,and a three-dimensional surface part is shaped continuously.In this paper,the mechanism of the three-dimensional surface formation in CRF is set forth.Through theoretical analysis of the CRF process,the governing equations for the bending deformation in rolling process are presented.Based on the simplification on the deformation and material model,the formulation to calculate the longitudinal bending deformation is derived,and the methods to design the compression ratio and the roll gap are given,the effects of compression ratio of rolling and the width of blank sheet on the longitudinal bending curvature are analyzed.The forming experiments on typical surface parts and measured results show that forming results with good precision can be obtained by CRF process.展开更多
基金Supported by National Natural Science Foundation of China(No. 10272079)joint grant from National Natural Science Foundation of Chinathe Royal Society of UK under their Joint Project Scheme
文摘The crucial effect of compressibility of rods on their instability is novelly demonstrated via singularity theory. It is shown that the critical load of compressible rod is always greater than the one of the Euler rod, and a subcritical pitchfork bifurcation, which cannot occur for the Euler rod, may occur for a compressible rod. A whole bifurcation diagram of compressible rods is as follows ： when the original slenderness ratio of a compressible rod, $o is smaller than （1 ＋ v/3 √3π/2,, the rod does not buckle; when So∈ [1＋ v/3）3√3π/2 ,（1＋v/5）5 5√5π/4）,the rod may undergo a subcritical pitchfork bifurcation and a collapse may occur; when So ∈ [1＋ v/5）5√5π/4 ＋ ∞）, the rod may undergo a supercritical pitchfork bifurcation. The deformation of cross section of rods causes a little shift of bifurcation points towards to the one corresponding to larger slenderness ratio.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51275202 and 51075186)
文摘Continuous roll forming(CRF) is a novel forming process for three-dimensional surface parts,in which a pair of bendable forming rolls is used as sheet metal forming tool.By controlling the gap between the upper and lower forming rolls,sheet metal is non-uniformly extended in the longitudinal direction while it is bent in the transverse direction during the rolling process.As a result,longitudinal bending is gained and a doubly curved surface is formed.With the rotations of the forming rolls,the sheet metal is deformed consecutively,and a three-dimensional surface part is shaped continuously.In this paper,the mechanism of the three-dimensional surface formation in CRF is set forth.Through theoretical analysis of the CRF process,the governing equations for the bending deformation in rolling process are presented.Based on the simplification on the deformation and material model,the formulation to calculate the longitudinal bending deformation is derived,and the methods to design the compression ratio and the roll gap are given,the effects of compression ratio of rolling and the width of blank sheet on the longitudinal bending curvature are analyzed.The forming experiments on typical surface parts and measured results show that forming results with good precision can be obtained by CRF process.
