An Intrinsic Material Tailoring Approach for Functionally Graded Axisymmetric Hollow Bodies Under Plane Elasticity

Abstract One of the main requirements in design structures made functionally graded materials is their best response when used an actual environment. This optimum behaviour may be achieved by searching for optimal variation mechanical and physical properties along which material compositionally grades. In works available literature, solution such optimization problem usually obtained values so called heterogeneity factors (characterizing expression property variations) that objective function minimized. Results, however, do not necessarily guarantee realistic give rise to unfeasible volume fractions if mapped into a micromechanical model. paper motivated confidence more intrinsic should priori consist search constituents’ rather than tuning parameters prefixed classes variations. Obtaining class requires tools borrowed from dynamic theory. More precisely, herein so-called Pontryagin Minimum Principle used, leads unexpected results terms derivative fractions, regardless involved particular, this line investigation, axisymmetric bodies subject internal pressure plane elasticity holds formulated analytically solved. The assumed radial direction goal find gradation minimizes maximum equivalent stress. A numerical example on internally pressurized cylinders also performed. corresponding found perform better fraction profiles commonly employed literature.