Tube hydroforming is an attractive manufacturing technology which is now widely used in many industries, especially the automobile industry. The purpose of this study is to develop a method to analyze the effects of the forming parameters on the quality of part formability and determine the optimal combination of the forming parameters for the process. The effects of the forming parameters on the tube hydroforming process are studied by finite element analysis and the Taguchi method. The Taguchi method is applied to design an orthogonal experimental array, and the virtual experiments are analyzed by the use of the finite element method (FEM). The predicted results are then analyzed by the use of the Taguchi method from which the effect of each parameter on the hydroformed tube is given. In this work, a free bulging tube hydroforming process is employed to find the optimal forming parameters combination for the highest bulge ratio and the lowest thinning ratio. A multiobjective optimization approach is proposed by simultaneously maximizing the bulge ratio and minimizing the thinning ratio. The optimization problem is solved by using a goal attainment method. An example is given to illustrate the practicality of this approach and ease of use by the designers and process engineers.
The temperature behaviour of meson condensates < σ 0 > and < σ 8 > is calculated in the SU (3) × SU (3)-linear sigma model. The couplings of the Lagrangian are fitted to the physical π, K, η, η ′ masses, the pion decay constant and a O + (I = 0) scalar mass of m σ = 1.5 GeV. The quartic terms of the mesonic interaction are converted to a quadratic term with the help of a Hubbard-Stratonovich transformation. Effective mass terms are generated this way, which are treated self-consistently to leading order of a 1/Nexpansion. We calculate the light and strange -quark condensates using PCAC relations between the meson masses and condensates. For a cut-off value of 1.5 GeV we find a first-order chiral transition at a critical temperature T c ∼ 161 MeV. At this temperature the spontaneously broken subgroup SU (2) × SU (2) is restored. Entropy density, energy density and pressure are calculated for temperatures up to and slightly above the critical temperature. To our surprise we find some indications for a reduced contribution from strange mesons for T ≥ T c .
Traditionally, the finite element technique has been applied to static and steady-state problems using implicit methods. When nonlinearities exist, equilibrium iterations must be performed using Newton-Raphson or quasi-Newton techniques at each load level. In the presence of complex geometry, nonlinear material behavior, and large relative sliding of material interfaces, solutions using implicit methods often become intractable. A dynamic relaxation algorithm is developed for inclusion in finite element codes. The explicit nature of the method avoids large computer memory requirements and makes possible the solution of large-scale problems. The method described approaches the steady-state solution with no overshoot, a problem which has plagued researchers in the past. The method is included in a general nonlinear finite element code. A description of the method along with a number of new applications involving geometric and material nonlinearities are presented.
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