Answer to Question #180736 in Material Science Engineering for Jessica

Question

When a pressure vessel has to be mobile its weight becomes important. Aircraft bodies, rocket casings and liquid natural gas containers are examples; they must be light, and at the same time, they must be safe. Therefore, the design of these vessels involves multiple constraints with a single objective.Let us assume you are involved in the selection of materials for the construction of such a pressure vessel. For simplicity, assume that the vessel is spherical and that the radius, R, and the pressure difference,P,across the wall are both fixed by design. Note that the volume of a thin-walled sphere is 4π(R^2)t. During operation, the pressure vessel should not yield,i.e.,the stress in the wall should not exceed 𝜎y. Assume the hoop stress in the wall is (PR)/(2t), where t is the thickness.

A) Derive the materials index, M1, for the design criteria. Start this problem by listing the objective, the constraints and the free variables.

Answer 1

Components have functions: to carry loads safely, to transmit heat, to store energy, to insulate, and so forth. Each function has an associated material index. Materials with high values of the appropriate index maximize that aspect of the performance of the component.

Tie, minimum weight, stiffness prescribed ρ/𝜎_y