Generalized viscoelastic designer functionally graded auxetic materials engineered/tailored for specific task performances

For arbitrary linear Kelvin model viscoelastic constitutive relations, generalized analyses based on collocation, least squares, Lagrangean multipliers, calculus of variation and inverse formulations are presented for determining viscoelastic designer material properties tailored and engineered to be best suited for specific boundary and loading conditions and their time histories. Optimum 3-D anisotropic designer materials, including auxetic viscoelastic functionally graded ones, are studied to minimize thermal stresses, creep buckling, creep rates, deflections, aero- and hydro- dynamic noise and static and dynamic aero-viscoelastic effects while concurrently lowering failure probabilities and extending structural survival times and maximizing or minimizing energy dissipation and its rate. The analyses are formulated for single structural elements as well as the entire structure. Extensions to the entire vehicle that incorporate aerodynamics, stability and control are discussed and the dimensions of computational requirements are estimated.