Đó là, bất kỳ giảm hơn nữa trong các chức năng chi phí dẫn đến rời khỏi khu vực khả thi tại điểm tối thiểu ứng cử viên. Điều này có thể được quan sát thấy trong hình. 4-19. khả thi đó là một tối thiểu địa phương cho chủ đề (x) f hi (x) = 0, i = 1 p gj (x) £ 0; j = 1 m. Sau đó có tồn tại số nhân Lagrange | P t 3 RO RoRi RĨ Transcribe the problem into the standard design optimization model also use Ro cm Rt cm . Use the following data P 14kN I 10 m mass density p 7850kg m3 allowable bending stress sb 165MPa allowable shear stress ta 50 MPa. Design a hollow circular beam shown in Fig. E2-24 for two conditions when P 50 kN the axial stress s should be less than sa and when P 0 deflection 8 due to self-weight should satisfy 8 . The limits for dimensions are t to cm R to cm and R t 20. Formulate the minimum weight design problem and transcribe it into the standard form. Use the following data 8 5w74 384EI w self weight force length N m sa 250MPa modulus of elasticity E 210GPa mass density p 7800kg m3 s P A gravitational constant g s2 moment of inertia I pR t m . Beam l 3m FIGURE E2-24 Hollow circular beam. 54 INTRODUCTION TO OPTIMUM DESIGN 3 Graphical Optimization Upon completion of this chapter you will be able to Graphically solve any optimization problem having two design variables Plot constraints and identify their feasible infeasible side Identify the feasible region feasible set for the problem Plot objective function contours through the feasible region Graphically locate the optimum solution for a problem and identify active inactive constraints Identify problems that may have multiple unbounded or infeasible solutions Optimization problems having only two design variables can be solved by observing the way they are graphically represented. All constraint functions are plotted and a set of feasible designs the feasible set for the problem is identified. Objective function contours are then drawn and the optimum design is determined by visual inspection. In this chapter we illustrate the graphical solution process and introduce several concepts related to optimum design problems. In the following section a design optimization problem is formulated and used to describe the solution process. Some concepts related to .
