Question

Give a example for a simple engineering problem which includes, ProblemDescription, Data and Information/Collection, Definition of Design Variables , Optimization Criterions ,Formulation of Constraints with steps

Answer 1

DESIGN OF CAN

STEP 1: PROJECT/PROBLEM DESCRIPTION

The purpose of this project is to design a can, to hold at least 400 ml of liquid, as well as to meet other design requirements. The cans will be produced in the billions, so it is desirable to minimize their manufacturing costs. Since cost can be directly related to the surface area of the sheet metal used, it is reasonable to minimize the amount of sheet metal required. Fabrication, handling, aesthetics, and shipping considerations impose the following restrictions on the size of the can: The diameter should be no more than 8 cm and no less than 3.5 cm, whereas the height should be no more than 18 cm and no less than 8 cm.

STEP 2: DATA AND INFORMATION COLLECTION

Data for the problem are given in the project statement.

STEP 3: DEFINITION OF DESIGN VARIABLES The two design variables are defined as

• D = diameter of the can, cm

• H = height of the can, cm

STEP 4: OPTIMIZATION CRITERION

Minimizing the total surface area S of the sheet metal for the three parts of the cylindrical can:

 the surface area of the cylinder

 the surface area of the two ends

Therefore, the optimization criterion, or cost function (the total area of sheet metal), is given as

STEP 5: FORMULATION OF CONSTRAINTS

The first constraint is that the can must hold at least 400 cm3 of fluid

If it had been stated that “the can must hold 400 ml of fluid,” then the preceding volume constraint would be an equality. The other constraints on the size of the can are