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To solve the design problems of engineering structures with multiple conflicting performance indices under uncertainties, a non-probabilistic optimization model which takes into consideration the correlation of uncertainties was proposed in this paper. The multidimensional parallelepiped model was utilized to describe the uncertainties and deal with their correlation. Further, a novel concept of feasible discriminant of interval constraints was proposed to identify the feasible solutions, and a competitive strategy for design vectors was proposed to achieve equilibrium design of structures. To improve the efficiency of optimization and promote its applications in engineering, a direct solution framework was constructed in this paper. This framework was based on response surface model and integrated the interval analysis with the genetic algorithm. The effectiveness and superiority of the proposed approach were illustrated by two numerical examples. Finally, the proposed method was applied to structural design of the upper and lower beams of forming machine, and the design of lightweight and equilibrium were achieved. This structural design example demonstrated the applicability and effectiveness of the proposed method in engineering.

A clear understanding of temperature variation of the sheet metal in immersion quenching process is indispensable for microstructural evolution of the metal material. It means specimen temperature variation in immersion quenching process remains to be further investigated. This work focuses on temperature variation of the 7075 aluminum alloy sheet in the immersion quenching process with the consideration of thermal radiation, boiling process and thermal convection. The proposed mathematical model was validated by the experiment data under different specimen positions and quenchant temperatures. Furthermore, the effects of the instability coefficient α in film boiling stage and the wetting parameter wp in transition boiling stage on temperature variation in boiling process were theoretically investigated. Both the experiment results and the theoretical prediction indicated that the temperature variation curves of different measuring points in boiling process are parallel during the quick immersion quenching process, and the temperature change rate in quenching procedure only depends on the quenchant temperature and the boiling stage.

This work is aimed at introducing a novel technology for forming large-scale and small-curvature aluminum alloy sheet using pulsed electromagnetic force. This method is named electromagnetic superposed forming (EMSF). Two basic experiments are carried out to demonstrate practical methodology of this newly proposed method. The electromagnetic force is applied on a sheet that is placed above a punch matrix. It results in local shallow dome-shaped and/or bowl-shaped plastic deformations according to spherical ends of punches and spaces between the punches. Positioning the coil and punch matrix along sheet surface incrementally, a uniformly distributed deformation matrix is generated. Two doubly curved specimens are obtained. One specimen bends towards the punch whereas the other bends towards the coil. Based on bending theory of thin plate, forming mechanism of this method is carried out using analytical analyses and numerical simulations. The results show that final macroscopic deformation of the sheet depends on superposition of those local plastic deformations. The relative magnitude of spherical radius which is between local dome-shaped deformation and bowl-shaped deformation determines macroscopic bending direction of specimen. In other words, small radius leads to high plastic deformation and bending direction of the specimen is in accordance with local deformation with small bending radius.

Electromagnetic superposed forming (EMSF) is a novel forming method which is aimed at forming large scale sheet specimens using pulsed electromagnetic (EM) force and multi-point punch matrix. A large number of computational resources are then needed for corresponding numerical simulations. This paper introduces the modeling strategies for predicting the specimen deformation in EMSF. The large size specimen is substituted by a small specimen that is wide enough to cover the electromagnetic field during solving the EM forces. The forces are then translated and applied to specific locations of the large specimen where the coil works. For deformation analysis, the shell elements are used to model the dynamic behavior of the specimens, which has not been studied in the former simulations of electromagnetic forming (EMF). The results show that the strategies are valid and dramatic time-saving in simulating the forming procedures. The relative deviation between simulations and experiments is less than 5% and the decrement of computational time-cost is approximately equal to 90%. The numerical hourglass which is an outstanding problem in bending simulation could be inhibited by using shell elements.

To explore the formability of larger size pre-stressed aluminum alloy sheet, a novel forming method named the electromagnetic superposed forming (EMSF) is proposed in this paper. The electromagnetic force is incrementally applied to the aluminum alloy sheet which is elastically pre-bended with a 1D curved die matrix. Specimens were formed and their shapes macroscopically curved due to superposition of the many weeny dome-shaped deformations. The feasibility of electromagnetic superposed forming of pre-stressed aluminum alloy sheet has been verified. The results show that the larger the discharge voltage has been given, the bigger deflection will have been obtained.

Electromagnetic superposed forming (EMSF) is a newly proposed method for forming large-scale aluminum alloy sheets with small curvature. The forming principle is based on superposition of local shallow deformations generated by the coaction of a flat spiral coil and a punch matrix. This paper emphasizes the deformation controllability, which is a basic research for developing the EMSF into a mature process of forming aircraft skins. The study is conducted via forming experiments in which the sheet blanks with different length-width ratio are entirely or partially subjected to the pulsed electromagnetic force. Finally, two pieces of S-shaped specimens are trail-produced. Waviness and surface finish of the specimens are analyzed. The results show that obtaining spherical specimen by EMSF is feasible. When a square blank is uniformly loaded, the specimen shape is approximately spherical. It is also feasible to obtain the major deformation perpendicular to loading paths in EMSF. The controllability of deformation during the EMSF process can be ensured. The S-shaped specimens show potential application of the EMSF in forming parts with complex shape. Besides, the specimen waviness is suitable for aircraft skins.

Limited by strength of electromagnetic coil, discharging energy of capacitor bank and some other auxiliary tools, electromagnetic forming (EMF) researches are mainly focused on regular size specimens. This paper demonstrates forming procedure of a large size AA2524-T3 sheet specimen with one-dimensional curvature, which expands application of electromagnetic force and intends to explore a new forming technology for aircraft skin manufacturing. It is based on the superposition of shallow local dome-shaped and bowl-shaped deformations which are generated by a coaction of electromagnetic driving force and punch matrix restraining. The results show that the sheet in size of 1840 mm × 810 mm × 2.5 mm is formed to be a macroscopically one-dimensional curved specimen. Curvature radius of the specimen varies from 6115.4 to 6328.3 mm. The maximum deflection of the specimen reaches 79.4 mm. Feasibility of this method in forming specimen with large size and one-dimensional curvature is verified.

In this paper, the stress relaxation tests were performed on Ti-6Al-4V alloy sheet with different initial total strains and different temperatures. Based on the experimental data, a novel empirical equation for predicting the stress versus time curves was proposed, and then an explicit constitutive model for describing the stress relaxation behaviours was further developed. The average prediction error was less than 8.27%, proving the proposed prediction curves were valid. In addition, two material constants which depend on initial stresses and total strains were introduced to accurately describe the stress relaxation curves. Then the methods for solving these two material constants under different initial conditions were presented. Finally, a simple method for dividing the stress relaxation stages was proposed. There are three stages in the stress relaxation curve studied in this paper, including the loading stage, stress relaxation-I and stress relaxation-II. A symbol called ηi which represents the normalized ratio of instantaneous stress to initial stress was used. When time τ is equal to α, the ratio of instantaneous normalized stress to normalized initial stress is reduced to η1 = 1/e, and the instantaneous plastic strain at this moment is (1 − η1) of the total plastic strain.