Shallow spheroidal shell segments have been press formed from rectangular plates by stamping between a die and matching punch that have two degrees of curvature. Experiments on mild steel, copper and aluminium plates that were not clamped in the die have measured the punch force, contact regions and final curvature distribution; and have observed plate buckling for a range of die curvature ratios and plate sizes. An analysis based on a rigid/plastic material idealization and decoupled in-plane forces and bending moments has been correlated with these experiments. The sequence of deformation modes has been identified; initially these are bending but in later stages, in-plane forces predominate.
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References
1.
JohnsonW.The mechanics of some industrial pressing, rolling and forging processes. In Mechanics of solids: the Rodney Hill 60th anniversary volume, (Eds. HopkinsH. G.SewellM. J.), 1982, 303–356, Pergamon, Oxford.
2.
YuT. X.JohnsonW.StrongeW. J.Stamping and spring-back of circular plates deformed in hemispherical dies. Int. J. Mech. Sci., 1984, 26, 131–148.
3.
JohnsonW.SinghA. N.Springback in circular blanks. Metallurgia, 1980, 275–280.
4.
JohnsonW.YuT. X.Springback after the biaxial elastic-plastic pure bending of a rectangular plate—I. Int. J. Mech. Sci., 1981, 23, 619–630.
YuT. X.JohnsonW.Experiments on the cylindrical bending of metal strips. Metal Technology, 1983, 10, 439–447.
7.
CalladineC. R.The static-geometric analogy in the equations of thin steel structures. Math Proc. Camh. Phil. Soc., 1977, 82, 335–351.
8.
JohnsonW.MellorP. B.Engineering plasticity, 1973, Van Nostrand Reinhold Co., London.
9.
JohnsonW.Upper bounds to the load for the transverse bending of flat rigid-perfectly plastic plates. Int. J. Mech. Sci., 1969, 11, 913–938.
10.
YuT. X.JohnsonW.A theoretical analysis of the bending into cylindrical dies of metal strips, Proc. Instn. Mech Engrs, 1984, 198, Part C, No. 8, 99–108.
11.
TimoshenkoS.Woinowsky-KriegerS.Theory of plates and shells, 1959, 2nd Edition, McGraw-Hill, New York.
12.
HilbertD.Cohn-VosshenS.Geometry and imagination, 1952, 193–204, Chelsea Pub. Co., New York.
13.
CasparD. L. D.KlugA.Physical principles in the construction of regular viruses. Cold Spring Harbour Symposia on Quantitative Biology, 1962, 27, 1–24.
14.
CalladineC. R.Thin-walled elastic shells analysed by a Rayleigh method. Int. J. Solids Structures, 1977, 13, 515–530.
