Parametric modeling and shape optimization of four typical Schwedler spherical reticulated shells

다국어 초록 (Multilingual Abstract)

Spherical reticulated shells are widely applied in structural engineering due to their good bearing capability and attractive appearance. Parametric modeling of spherical reticulated shells is the basis of internal analysis and optimization design. In the present study, generation methods of nodes and the corresponding connection methods of rod elements are proposed. Modeling programs are compiled by adopting the ANSYS Parametric Design Language (APDL). A shape optimization method based on the two-stage algorithm is presented, and the corresponding optimization program is compiled in FORTRAN environment. Shape optimization is carried out based on the objective function of the minimum total steel consumption and the restriction condition of strength, stiffness, slenderness ratio, stability. The shape optimization of four typical Schwedler spherical reticulated shells is calculated with the span of 30 m~80 m and rise to span ratio of 1/7~1/2. Compared with the shape optimization results, the variation rules of total steel consumption along with the span and rise to span ratio are discussed. The results show that: (1) The left and right rod-Schwedler spherical reticulated shell is the most optimized and should be preferentially adopted in structural engineering. (2) The left diagonal rod-Schwedler spherical reticulated shell is second only to left and right rod regarding the mechanical behavior and optimized results. It can be applied to medium and small-span structures. (3) Double slash rod-Schwedler spherical reticulated shell is advantageous in mechanical behavior but with the largest total weight. Thus, this type can be used in large-span structures as far as possible. (4) The mechanical performance of no latitudinal rod-Schwedler spherical reticulated shell is the worst and with the second largest weight. Thus, this spherical reticulated shell should not be adopted generally in engineering.

참고문헌 (Reference)

1 Yas, M. H., "Two-objective stacking sequence optimization of a cylindrical shell using genetic algorithm" 14 (14): 499-506, 2007

2 Jenkins, W. M., "Towards structural optimization via the genetic algorithm" 40 (40): 1321-1327, 1991

3 Svanberg, K., "The method of moving asymptotes-a new method for structural optimization" 24 (24): 359-373, 1987

4 Vyzantiadou, M. A., "The application of fractal geometry to the design of grid or reticulated shell structures" 39 (39): 51-59, 2007

5 Lu, X. Y., "The Optimization of Reticulated Shell Structures Based On Discrete Variables" Building Industry Press 2013

6 Luo, Z., "Structural shape and topology optimization using a meshless Galerkin level set method" 90 (90): 369-389, 2012

7 Jenkins, W. M., "Structural optimization with the genetic algorithm" 69 (69): 418-422, 1991

8 Durgun, İ., "Structural design optimization of vehicle components using cuckoo search algorithm" 54 (54): 185-188, 2012

9 Sun, H. C., "Structural Optimization with Discrete Variables" Dalian University of Technology Press 2002

10 Rajan, S. D., "Sizing, shape, and topology design optimization of trusses using genetic algorithm" 121 (121): 1480-1487, 1995

11 Rahami, H., "Sizing, geometry and topology optimization of trusses via force method and genetic algorithm" 30 (30): 2360-2369, 2008

12 A. Kaveh, "Sizing, geometry and topology optimization of trusses using force method and supervised charged system search" 국제구조공학회 50 (50): 365-382, 2014

13 Lu, X. Y., "Shape optimizing design of kiewiti spherical reticulated shell" 424 : 324-329, 2012

14 Gholizadeh, S, "Shape optimization of structures for frequency constraints by sequential harmony search algorithm" 45 (45): 627-646, 2013

15 Deng, H., "Shape optimization of spatial reticulated shell structures" 33 (33): 371-375, 1999

16 Chiu, M. C., "Shape optimization of multi-chamber mufflers with plug-inlet tube on a venting process by genetic algorithms" 71 (71): 495-505, 2010

17 J. Wu, "Shape optimization for partial double-layer spherical reticulated shells of pyramidal system" 국제구조공학회 55 (55): 555-581, 2015

18 Sun, H. C., "Shape optimization designs of trusses with discrete variables" 35 (35): 10-16, 1995

19 Wu, J., "Parametric modeling and shape optimization of four typical schwedler reticulated shells" Shandong Jianzhu University 2013

20 Salajegheh, E., "Optimum design of trusses with discrete sizing and shape variables" 6 (6): 79-85, 1993

21 Salajegheh, E., "Optimum design of structures with high-quality approximation of frequency constraints" 31 (31): 381-384, 2000

22 Saka, M.P., "Optimum design of nonlinear elastic framed domes" 29 (29): 519-528, 1998

23 Xu, J., "Optimized design of single - layer reticulated shell" 12 (12): 35-37, 2006

24 Fraternali, F., "On the structural shape optimization through variational methods and evolutionary algorithms" 18 (18): 225-243, 2011

25 Jenkins, W. M., "On the application of natural algorithms to structural design optimization" 19 (19): 302-308, 1997

26 Pedersen, N. L., "Improving bending stress in spur gears using asymmetric gears and shape optimization" 45 (45): 1707-1720, 2010

27 Shen, Z.Y., "Grid and Lattice Shell" Tongji University Press 1996

28 Dong, S.L., "Future and prospects of reticulated shells" 9 (9): 31-34, 2003

29 Qian, X., "Full analytical sensitivities in NURBS based isogeometric shape optimization" 199 (199): 2059-2071, 2010

30 Wu, W., "Finite element shape optimization for biodegradable magnesium alloy stents" 38 (38): 2829-2840, 2010

31 Lipson, S.L., "Discrete sizing of trusses for optimal geometry" 103 (103): 1031-1046, 1977

32 Yildiz, A. R., "Comparison of evolutionary-based optimization algorithms for structural design optimization" 26 (26): 327-333, 2013

33 P. Emmanuel Nicholas, "Buckling optimization of laminated composite plate with elliptical cutout using ANN and GA" 국제구조공학회 52 (52): 815-827, 2014

34 Dietl, J.M., "Beam shape optimization for power harvesting" 2010

35 Chen, Z.H., "APDL Parametric Calculation and Analysis" China Water Power Press 2009

36 Shang, X.J., "ANSYS Structural Finite Element Senior Analysis Method and Sample Applications" China Water Power Press 2005

37 Gong, S.G., "ANSYS Parametric Programming and Command Manual" China Machine Press Beijing 2010

38 Chai, S., "A two-level delimitative and combinatorial algorithm for a kind of (0, 1, 2) programing" 36 (36): 258-263, 1996

39 A. Kaveh, "A new PSRO algorithm for frequency constraint truss shape and size optimization" 국제구조공학회 52 (52): 445-468, 2014

40 Xia, Q., "A level set solution to the stress-based structural shape and topology optimization" 90 : 55-64, 2012