TAILIEUCHUNG - Applied Structural Mechanics Fundamentals of Elasticity Part 13

Tham khảo tài liệu 'applied structural mechanics fundamentals of elasticity part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 346 15 Fundamentals of structural optimization 16 MP-algorithms For the bar stresses we formulate the following constraints E1 X -8ti x i x - tidm 1 . 13 Ila s2 x -gCj x dm - j x - 0 . lib Finally we demand non-negativity for the cross-sectional areas of the bars XL 0 for all i -- 1 -. - 13 - 12 c The constrained optimization problem is solved using an external penalty function by means of which the task is transformed into an unconstrained problem. With we state 26 f . 2 V x Ri2 max o gj x J i 1 2 3. 13 j l f gj x in the infeasible domain where max 0 gj X c in the feasible domain Here the choice of a suitable initial value for the penalty parameter Rj is crucial for the present task we choose R1 IQ-5 . The unconstrained problem 13 can be solved by means of suitable algorithms in the present case the POWELL -method of conjugate gradients has been used where a quadratic polynomium LAGRANGE-interpolation has proved sufficient for a one-dimensional minimization. In addition it could be shown that different initial designs Aj 100 . - 1000mm2 virtually lead to the same optimal solution. The calculation the scale of which requires the use of a computer yields the result that the force F is mostly carried via bars 4 to 8 into the supports 7 8 9 denoted by bold lines in Fig. D-3 . Consequently the remaining bars need very small cross-sectional areas only. Fig. D-3 Optimized truss structure by changing the cross-sections of the bars Exercise D-15 16-3 347 Exercise D15 16-3 Fig. D-4 shows a section of a circular cylindrical shell c with a ring stiffener s. The considered part of a boiler is subjected to a constant internal pressure p and has a constant inner temperature 0iC. The temperature distribution within boiler and stiffener has been determined by measurements for the cylindrical section c we assume a linear temperature distribution over the thickness with the gradient 10c const in the longitudinal direction ec z - 0C Z 0C with Op _ 0iC Ỡoc Ip 0OC 0iC yc - c