• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.555-581
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• 2015

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.

• Structural Engineering and Mechanics
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• v.56 no.5
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• pp.813-833
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• 2015

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.

• Structural Engineering and Mechanics
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• v.10 no.2
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• pp.111-123
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• 2000

An asymptotic solution for snap-through buckling of single-layer squarely-reticulated shallow spherical shells continuously supported on springs is developed in this paper. Based on the fundamental governing equations and boundary conditions, a nondimensional analytical expression associated with the external load, stiffness of spring and central transverse displacement (deflection) is derived with the aid of asymptotic iteration method. The effects of stiffness of spring and characteristic geometrical parameter on buckling of the structures are given by the analyses of numerical examples. In a special case, for reticulated circular plates, the influence of stiffness of spring on the characteristic relation between load and deflection is also demonstrated.

• Wind and Structures
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• v.8 no.6
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• pp.443-454
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• 2005

Wind loading is very important, even dominant in some cases, to large-span single-layer reticulated shells. At present, usually equivalent static methods based on quasi-steady assumption, as the same as the wind-resistant design of low-rise buildings, are used in the structural design. However, it is not easy to estimate a suitable equivalent static wind load so that the effects of fluctuating component of wind on the structural behaviors, especially on structural stability, can be well considered. In this paper, the effects of fluctuating component of wind load on the stability of a single-layer reticulated spherical shell model are investigated based on wind pressure distribution measured simultaneously in the wind tunnel. Several methods used to estimate the equivalent static wind load distribution for equivalent static wind-resistant design are reviewed. A new simple method from the stability point of view is presented to estimate the most unfavorable wind load distribution considering the effects of fluctuating component on the stability of shells. Finally, with comparisive analyses using different methods, the efficiency of the presented method for wind-resistant analysis of single-layer reticulated shells is established.

• Earthquakes and Structures
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• v.13 no.5
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• pp.455-464
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• 2017

This paper develops a new method for analyzing the structural seismic behavior of single-layer reticulated shells based on exponential strain energy density (ESED). The ESED method reveals a characteristic point from a relationship between ESED sum and peak seismic acceleration. Then, the characteristic point leads to an updated concept of structural failure and an ESED-based criterion for predicting structural failure load. Subsequently, the ESED-based criterion and the characteristic point are verified through numerical analysis of typical single-layer reticulated shells with different configurations and a shaking table test of the scale shell model. Finally, discussions further verify the rationality and application of the ESED-based criterion. The ESED method might open a new way of structural analysis and the ESED-based criterion might indicate a prospect for a unified criterion for predicting seismic failure loads of various structures.