Inverse problem of ribbed panel shape formation

An algorithm for solving an inverse problem of shaping of a ribbed panel made of the AK4-1 alloy (analog of the AA2018 and Al-Cu$_2$-Mg$_2$-Ni$_1$ alloys) at a temperature of 200$^{\circ}$С is proposed. The problem is reduced to solving auxiliary direct problems on the stress-strain states of the elements of the panel structure. The structural elements are taken to be T-beams subjected to pure bending. The resultant moment for obtaining a desired shape is calculated by the Nelder–Mead optimization method. Two methods of obtaining target-shaped articles are considered: deformation under the plastic flow condition and under the creep condition. The material models used in the study take into account the difference in the mechanical properties under tension and compression, as well as the presence of accumulated damage in the material. The calculations are performed with allowance for elastic spring unloading of the article after load removal.