Shape optimization for partial double-layer spherical reticulated shells of pyramidal system

Abstract

Triangular pyramid and Quadrangular pyramid elements for partial double-layer spherical reticulated shells of pyramidal system are investigated in the present study. Macro programs for six typical partial double-layer spherical reticulated shells of pyramidal system are compiled by using the ANSYS Parametric Design Language (APDL). Internal force analysis of six spherical reticulated shells is carried out. Distribution regularity of the stress and displacement are studied. A shape optimization program is proposed by adopting the sequence two-stage algorithm (RDQA) in FORTRAN environment based on the characteristics of partial double-layer spherical reticulated shells of pyramidal system and the ideas of discrete variable optimization design. Shape optimization is achieved by considering the objective function of the minimum total steel consumption, global and locality constraints. The shape optimization of six spherical reticulated shells is calculated with the span of 30m~120m and rise to span ratio of 1/7~1/3. The variations of the total steel consumption along with the span and rise to span ratio are discussed with contrast to the results of shape optimization. The optimal combination of main design parameters for six spherical reticulated shells is investigated, i.e., the number of the optimal grids. The results show that: (1) The Kiewitt and Geodesic partial double-layer spherical reticulated shells of triangular pyramidal system should be preferentially adopted in large and medium-span structures. The range of rise to span ratio is from 1/6 to 1/5. (2) The Ribbed and Schwedler partial double-layer spherical reticulated shells of quadrangular pyramidal system should be preferentially adopted in small-span structures. The rise to span ratio should be 1/4. (3) Grids of the six spherical reticulated shells can be optimized after shape optimization and the total steel consumption is optimized to be the least.