By Y C Fung
Aimed toward complicated undergraduates and graduate scholars, this extraordinary textual content surveys aeroelastic difficulties, their old historical past, uncomplicated actual thoughts, and the rules of study. It has additionally confirmed hugely beneficial to designers and engineers fascinated with flutter, structural dynamics, flight quite a bit, and comparable topics.
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Additional info for An Introduction to the Theory of Aeroelasticity
Example text
For steel with E 5 29,000 ksi and a yield stress of 50 ksi, k is given as 32 (AISC, 2005). 8 MINIMUM-COST CYLINDRICAL TANK DESIGN STEP 1: PROJECT/PROBLEM DESCRIPTION Design a minimum-cost cylindrical tank closed at both ends to contain a fixed volume of fluid V. The cost is found to depend directly on the area of sheet metal used. STEP 2: DATA AND INFORMATION COLLECTION Let c be the dollar cost per unit area of the sheet metal. Other data are given in the project statement. I. 9 DESIGN OF COIL SPRINGS STEP 3: DEFINITION OF DESIGN VARIABLES The design variables for the problem are identified as R 5 radius of the tank H 5 height of the tank STEP 4: OPTIMIZATION CRITERION The cost function for the problem is the dollar cost of the sheet metal for the tank.
Also, performance of the numerical algorithms for a solution to the optimization problem may be affected by these transformations. 6 Feasible Set The term feasible set will be used throughout the text. A feasible set for the design problem is a collection of all feasible designs. The terms constraint set and feasible design space are also used to represent the feasible set of designs. The letter S is used to represent the feasible set. Mathematically, the set S is a collection of design points satisfying all constraints: S 5 fx j hj ðxÞ 5 0; j 5 1 to p; gi ðxÞ # 0; i 5 1 to mg ð2:4Þ The set of feasible designs is sometimes referred to as the feasible region, especially for optimization problems with two design variables.
In addition, the tensile force will be taken as positive. Thus, the bar will be in compression if the force carried by it has negative value. By solving the two equations simultaneously for the unknowns F1 and F2, we obtain ! sinθ 2 cosθ F1 5 20:5Wl 1 h s ! ðbÞ sinθ 2 cosθ 2 F2 5 20:5Wl h s To avoid bar failure due to overstressing, we need to calculate bar stress. If we know the force carried by a bar, then the stress σ can be calculated as the force divided by the bar’s cross-sectional area (stress 5 force/area).