tailieunhanh - Electrical Engineering Mechanical Systems Design Handbook Dorf CRC Press 2002819s_10

Tham khảo tài liệu 'electrical engineering mechanical systems design handbook dorf crc press 2002819s_10', kỹ thuật - công nghệ, điện - điện tử phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | K FIGURE Stiffness-to-mass ratio vs. 8 for l0 30. mi k J where r and L are the cross-section radius and length of bars or strings when the C4T1 structure is under external load F. C4T11 at 8 0 At 8 0 it is known from the previous section that the use of mass is minimum while the stiffness is maximum. Therefore a simple analysis of C4T11 at 8 0 will give an idea of whether it is possible to reduce the mass while preserving stiffness. For the C4T10 structure the stiffness is given by K Enr2. L0 For a C4T11 structure at 8 0 . two pairs of parallel bars in series with each other the length of each bar is L0 2 and its stiffness is kb E 2 T . L1 L0 For this four-bar arrangement the equivalent stiffness is same as the stiffness of each bar . K1 2 . L0 To preserve stiffness it is required that K1 K0 2 Enr2 _ Enr2 . L0 L0 2002 by CRC Press LLC So r0 2r0. Then the mass of C4T11 at Ỗ 0 for stiffness preserving design is r 0 L m1 4pnr0L1 4pn 2 pn0L0 m0 which indicates at Ỗ 0 that the mass of C4T11 is equal to that of C4T10 in a stiffness-preserving design. Therefore the mass reduction of C4T1 structure in a stiffness-preserving design is unlikely to happen. However if the horizontal string th is added in the C4T11 element to make it a C4T0 element then stiffness can be improved as shown in . Summary The concept of self-similar tensegrity structures of Class k has been illustrated. For the example of massless strings and rigid bars replacing a bar with a Class 0 tensegrity structure C4T1 with specially chosen geometry Ỗ 09 the mass of the new system is less than the mass of the bar the strength of the bar is matched and a stiffness bound can be satisfied. Continuing this process for a finite member of iterations yields a system mass that is minimal for these stated constraints. This optimization problem is analytically solved and does not require complex numerical codes. For elastic bars analytical .