Optimal design of bars under nonuniform tension with respect to mixed creep rupture time

The first attempt of finding of optimal shape for bars in presence of body forces with respect to mixed creep rupture is made. For given volume of the bar, distribution of initial cross-section, ensuring the longest life-time to mixed rupture is sought. The finite strain theory and physical law in form of Norton's law generalized for true stresses and logarithmic strains are applied. Using the method of parametric optimization, the best of linear and quadratic functions describing the initial shape of the bar are found. The shape of initial strength is corrected in a way leading to longer life-time. Results of both approaches are compared.

► In present paper as the optimization criterion serves the mixed rupture theory.
► For given volume of the bar, distribution of initial cross-section, ensuring the longest life-time to mixed rupture is sought.
► The finite strain theory and Norton's law here generalized for true stresses and logarithmic strains are applied.
► Using the method of parametric optimization, the initial shape of the bar are found.
► The shape of initial strength is corrected in a way leading to longer life-time. Results of both approaches are compared.