The Studys And Applications Of Springback Variational Theory Of Beam And Thin Plate

At present, the research on springback feature of material shaping is anadvanced subject in scientific and technical field, and also a research hotspot.In order to adapt to new requests of more comprehensive and higher accuracydevelopment for modern technology like cars and airplanes, it is imperativeunder the situation to research into the springback feature of material.Therefore, it is of a great importance and value for both economy and scienceto outspread the research on springback feature of material. At present, thisresearch in the world still rests on a numerical simulation stage, and thesimulation accuracy of springback is in very low level. Now, there is noaccurate theory of material shaping springback, so this research onspringback feature of material shaping is an creative origination.This article first applied the non-coupled equation of finite deformationspringback and method of weighted residual to establish the variationalprinciple of finite deformation springback, by introduce the non-coupledsystems and non-coupled equation of finite deformation springback. Then,the method of Lagrange arithmetic operators is applied in variationalprinciple of finite deformation springback to establish the springbackvariational principle and the gen-eralized springback variational principle .Springback potential energy principle and comp-lementary energy principleof the larger deflection for straight beam shaping, Generalized springbackpotential energy principle and springback complementary energy principle ofthe large deflection for straight beam shaping are established. SpringbackFinite-element method of large deflection for straight beam shaping isestablished on the Springback potential energy principle of large deflectionfor straight beam shaping.springback potential energy principle andcomplementary energy principle of compound bending plate are establishedon Springback non-coupled equation of finite deformation and weightedresidual method. Both of Springback potential energy principle for largedeflection of bending thin plate and the method of Springback finite-elementfor large deflection of bending thin plate are established.At last, the Springback of large deflection bending straight beam shapingis calculated by applying the Springback finite-element method. Both of theSpringback energy principle and the Springback finite-element method areverified by a Springback test of simply supported beam. And, Springback oflarge deflection bending straight beam shaping is simulated by finite-elementuniversal calculating program software ANSYS.Springback amount of automobile door material is calculated by applyingthe method of Springback finite-element for large deflection of plate shaping.And, a corresponding Springback test of pressed plate is carried. Springbackpotential energy principle and the method of Springback finite-element forlarge deflection of bending thin plate are verified by a cylindrical bendingtest of rectangular plate.Therefore, Springback potential energy principle and complementaryenergy principle for large deflection of bending straight beamshaping,Generalized springback potential energy principle and springbackcomplementary energy principle, Springback potential energy principle andcomplementary energy principle of compound bending plate, and Springbackpotential energy principle for large deflection of bending thin plate areestablished theoretically in the article. And, the Springback finite elementmethod for large deflection of bending straight beam and bending thin plate isprovided. Also, a new Springback-calculating method of large deflectionbending beam and bending thin plate is provided. Thanks to the new method,the force and deflection curve equation and the boundary condition of beamor plate shaping are only needed to know Springback amount of beam or plate.It is a kind of convenient and suitable computing method to be applied on theproject directly and it provide necessary theory to guide production and toincrease economic efficiency.