Abstract
A mathematical model was intricately devised to explore the influence of continuous variations in thickness and mechanical properties on the performance of tailor rolled blanks (TRB) and tailor rolled tubes (TRT). Through the integration of analytical and numerical techniques, it was discerned that these variations play a pivotal role in modulating stress distribution and strain localization, thereby inducing a spectrum of plastic instability behaviors within the structures. The introduction of an 'equivalent strength' metric as a novel means to quantify structural performance shed light on strategic material distribution to enhance durability and mechanical efficiency. Moreover, the insights garnered from this research deepen the understanding of the mechanical responses of tailor-rolled constructs under varying loads, offering valuable perspectives for the development and fabrication of engineered materials with bespoke properties. This study not only contributes to bridging a knowledge gap in the realm of tailored material engineering but also fosters the advancement of design methodologies in the construction of high-performance engineered structures.