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The orthogonal experiment was established to reduce the wrinkling of convex flange rubber forming with 2A12 aluminum alloy sheet. The impact factors consisted of the feed of master-cylinder, the hardness of the rubber, and the radius of the die. The rubber forming was simulated for the quantities, widths, and heights of the wrinkles in ABAQUS software, where the results was analyzed by gray correlation. Theoretically the greatest influence on the wrinkles is the feed of master-cylinder that the more the feed is, the smaller the wrinkles are. However, neither in the simulation nor in the experiment, all the wrinkles of the convex flanged parts still could not be flattened when the master-cylinder was fed to the rubber's compression limit. Aiming to further eliminate wrinkling, a new method called multi-stage rubber forming was proposed, in which four extra-cylinders were added to the broadside of the container to enhance the forming force. Both the numerical simulation and experiment were taken into the multi-stage rubber forming, proving that multi-stage rubber forming could effectively reduce the wrinkling in rubber forming of the convex flange, as the feed of the extra-cylinders increased risks of the wrinkles. When the feed of the extra-cylinders was set 8 mm while the master-cylinder 34 mm, the wrinkle of the convex curve bending edge could be eliminated smoothly.

The solution of large matrix eigenvalues and complex linear equations limits the Fourier modal method (FMM) application in ultrathin metallic gratings (UMG) analysis. This paper proposes an efficient and explicit FMM method for analyzing UMG. The proposed method avoids solving complex linear equations and eigenvalues of eigenmatrix in the conventional method by simplifying the implementation equations. Two numerical examples then verify the reliability of the proposed method compared with CST simulations and the conventional method. The proposed method is proven efficient in decreasing the CPU time by over 80% and demanding significantly less memory.