Single-layer Lattice Shell Research Articles

Stability Analysis of the Radiant Cable Suspendome

Radiant cable suspendome based on single-layer lattice shell is proposed in this paper whose cable-strut system is like that of Radiant Beam String Structure, the purpose of this paper is to do stability analysis of the structure.The linear buckling analysis of the hybrid structure and the single-layer lattice shell who has the same geometry parameters is carried out, we can preliminarily understand the stability of the hybrid structure. At the same time, nonlinear buckling analysis is carried out to study the stability of the hybrid structure under different rise-span ratios, different prestress level and half-span load. The results show that the introduction of prestressed cables greatly improve the structure's stability and reduce the structure sensitivity to original geometrical imperfection.

Seismic performance of single-layer lattice shells with VF-FPB

Friction pendulum bearings (FPB) are recognized as a kind of effective isolation device for protecting and retrofitting an existing structure, but they are not adaptive to different seismic inputs due to the constant friction coefficient and constant radius of curvature. A new isolation bearing called variable-friction friction pendulum bearings (VF-FPB) was proposed which could overcome this limitation while retaining all the advantages of an FPB. Unlike a conventional FPB, the sliding surface of a VF-FPB was divided into several parts with different surface materials which allowed the coefficient of friction to change when the slider went across different parts. This means that the stiffness of a VF-FPB changed as the relative displacement between the slider and the sliding surface changes. In the current paper, the isolation mechanism of a typical VF-FPB was analyzed. The numerical model of a single-layer lattice shell was developed and the effect of VF-FPB installation on the structure was studied. The VF-FPBs used in the study had their surfaces divided into two parts, and it was found that an ‘optimal range’ exists for the dimensions of two component parts for the best earthquake isolation effect. It was concluded that VF-FPBs could improve the seismic performance of a single layer lattice shell more effectively than conventional FPBs.

Stability Analysis of Latticed Shells

ANSYS14.0 structural analysis software is used in order to make a ring rib-reticulated shell for the overall stability analysis. Considering the geometric nonlinear analysis and initial geometric imperfections influence , obtain a key node of the load - displacement curve and assess the ultimate strength of the structure. The results showed that: the structure meets the "Space grid rules" for monolayer shells stability requirements. And it is found that load distribution form and initial geometry defect has a great deal whit bearing capacity of single-layer lattice shell stability by comparison.

Vertical and Horizontal Seismic Response Analyses of Long-Span and Single-Layer Spherical Lattice Shell Structure

The dynamic characteristics of 80 m single-layer spherical lattice shell structure are analyzed to control its vibration under seismic load. Through the response spectrum curve of current design specification, the analyses for the vertical and horizontal seismic responses of the single-layer spherical lattice shell structure are made by CQC, and the displacement response of the nodes and internal force of the rods unit are calculated respectively. The calculation results show that the vertical and horizontal seismic responses of the long-span lattice shell structure are in great difference, and should be performed in vibration control at the same time, which could provide certain references for the seismic design and vibration control of single-layer spherical lattice shell structure.

Prediction of Confined Blast Loading in Single-Layer Lattice Shells

Single-layer lattice shells (also known as gridshells) are widely used for architecturally innovative structures. When an explosion occurs inside such a structure, confined blast loading on the structural components will be seriously affected by different factors, such as charge locations and weight, structural types and forms. Moreover, slight changes of blast loading perhaps result in various responses for such a complicated structure. In this paper, blast loads on single-layer lattice shell are calculated by AUTODYN software package. The effect of scaled distance, ratio of rise to span and ratio of height to span are investigated. Simplification of blast loading is studied, and the principles of equivalent loading process are validated with a 40 meters single-layer Kiewitt-8 reticulated dome. In order to predict the blast loading, a precise and simple model is derived from numerical results, which is suitable for a wide scope of single-layer lattice shells. Two applications with different charge weight, structural spans and forms are worked out by using the blast prediction model. Good agreements of comparisons are achieved between prediction model and numerical results.

Dynamic damage criterion and damage mode for single layer lattice shell

When member buckling and joint fractures are considered in the numerical analyses of single layer lattice shells, the relationship curve between peak ground acceleration of the earthquake and the maximum nodal displacement, and the time–history curve of maximum nodal displacement, are erratic and unpredictable. Therefore, with such considerations, the current approach to determine dynamic damage of single layer lattice shells by comparing peak ground acceleration of the earthquake with critical ground acceleration derived from incremental dynamic analysis is inappropriate. An improved structure dynamic damage criterion is proposed for single layer lattice shells in this paper, which reviews the balance status of structure dynamic resistance against the earthquake action, and the structure damage time can be predicted by the occurrence of non-convergent solution to the structural nonlinear dynamic equilibrium equations in the iterative process from the mathematical point of view. Numerical examples are presented to illustrate the simplicity and practicality of the proposed criterion. This criterion serves clear physical meaning and is of considerable potential applicability in analyzing single layer lattice shell structures. Results of parametric analyses of single layer lattice shells under severe earthquake actions indicate that the structure dynamic damage is not determined by material strength failure. For single layer spherical lattice shell, it is determined by structural instability resulted from member buckling; and for single layer cylindrical lattice shell, it is determined by the combined effect of structural instability and the change of structural topology that resulted from member buckling and joint fractures respectively.

Collapse optimization for domes under earthquake using a genetic simulated annealing algorithm

There are two primary collapse scenarios for single-layer latticed shells subjected to severe earthquake action: dynamic instability and strength failure. Of these, dynamic instability is the collapse scenario that must be avoided. First, taking the minimization of the standard deviation of the well-formedness as the optimization objective and the member sections as the optimization variables, an optimization model representing collapse scenarios for single-layer spherical shells is established. This optimization model also accounts for the displacement and stress constraints. Second, a genetic simulated annealing algorithm (GASA) is proposed by combining a genetic algorithm (GA) and a simulated annealing algorithm (SA). Finally, partial and overall optimizations are performed for a single-layer spherical shell that collapses due to instability under earthquake action. The results show that the optimized structure is subject to ideal strength failure under earthquake action with clear warning signs prior to collapse. In addition, the GASA performs better than the GA for optimization. Therefore, it is concluded that the optimization model and method presented in this paper can be used to perform collapse scenario optimization for single-layer spherical shells subjected to earthquake action.

Novel cable-stiffened single-layer latticed shells and their stabilities

The cable-stiffened single-layer latticed shell is a new structural system that aims to enhance the stability of the single-layer latticed shell. This paper compares the stability of a cable-stiffened single-layer latticed shell with that of a single-layer latticed shell using a numerical analysis to investigate the stability behaviour of the new structure. In the analysis, the following influential parameters have been taken into account: (1) layouts of the cables; (2) joint types; (3) pretension in the cables; and (4) cross-sections of the cables. The results indicate that the buckling load of single-layer latticed shells is improved significantly by the introduction of the cables. For the cable-stiffened single-layer latticed shells with different layouts of cables, both the pretension in the cables and the cross-sections of the cables have a considerable effect on their stabilities. Meanwhile, the numerical analysis also indicates that although joint types have a remarkable effect on the stability of a single-layer latticed shell, the effect on the corresponding cable-stiffened single-layer latticed shell is limited.

The Stability Analysis on the Different Types of Single Layer Latticed Shell

This single-layer spherical reticulated shell has the advantages of reasonable stress,beautiful appearance ,fast construction,is widely applied in practical engineering. Through the static stability analysis of three kinds of single-layer spherical lattice shell structure using ansys, we get them in the uniform deformation under static load, the modal, buckling load. The results show that: The Kiewitt latticed shells displacement is small, structure is stable, better than SchwedLer and lianfang.

Design Recommendation for Large Depth-to-Span Ratio and Opening of Single-Layer Spericallattice Shells

The application of perforated shell gradually increased, but the current design method has no explicit provisions. In this paper, based on large depth-to-span ratio and openings of single-layer spherical lattice shells structure for static and dynamic analysis, and the effects of opening and not opening shell difference of internal force under static load and deformation, I put forward the design proposal.

Research on Practical Design Method of Single-Layer Lattice Shell Components

There are some limitations on the calculation about effective length factor of the single-layer lattice shell structure`s component by the current specifications. That`s why Euler formula is commonly used to anti-push the effective length in engineering design. In traditional design, one or few components were used to calculate the effective length factor, and the single biggest value is assigned to all components for design. Owing to the coarse method, values of some components` effective length are too large or too small. This paper improved the traditional design method, and used excel in formula programming to calculate effective length factors of all components. Then all factors are assigned to all components for designing by SAP2000. At the end of the article, it explored the difference in this new design method with the traditional design method.

Stability analysis of single-layer elliptical paraboloid latticed shells with semi-rigid joints

Based on the bending stiffness of socket joints obtained through experiments, the finite element models of single-layer elliptical paraboloid latticed shells with the semi-rigid socket joints are established. Parametric analysis of the latticed shells is carried out using ANSYS. The parameters considered are bending stiffness, ratio of rise to span, rotation-stiffness, ball size, asymmetric load distribution, tube section, support conditions and initial imperfections. The effects of the different parameters on the critical loads of the shells are thereby identified. Both geometric and material nonlinearity are considered during the analysis. Finally, formulae are derived for the calculation of critical loads of the shells under symmetric and asymmetric loading conditions. This will be useful for the design and application of single-layer latticed shells with semi-rigid joints.

Stability of lamella cylinder cable-braced grid shells

A cable-braced grid shell is a new type of single-layer latticed shell suitable for glass roofs. Compared with traditional single-layer latticed shells, this new type of shell has a unique mesh shape, mesh form and surface shape. The lamella cylinder cable-braced grid shell is the single-layer latticed structure, and therefore, stability is a key design factor. These shells are also sensitive to initial imperfections, and thus, the influence of initial imperfections on stability should be considered. Therefore, in this paper, a lamella cylinder cable-braced grid shell with imperfections is used to develop formulas to describe the buckling load based on the continuum analogy. The major contributions of this paper include the formula for the linear buckling load of a lamella cylinder cable-braced grid shell with imperfections, which is deduced based on the continuum analogy. Then, the equivalent rigidity for a lamella mesh is determined. Last, the formula for the linear buckling load is verified by numerical examples, the errors are analyzed, and a corresponding correction factor is provided.

Dynamic Stability and Ultimate Capacity of Suspended Dome under Earthquakes

Suspended dome is a reasonable and novel type of long-span hybrid spatial structures based upon single-layer spherical lattice shell and tensegrity system. Based upon the structural force-bearing characteristics, the combined finite element model of beam elements, truss elements and cable elements is set up. A method taking the maximum displacement on nodes under earthquake acceleration of each level as dynamic response representative parameter is proposed to study the dynamic stable ultimate capacity of suspended dome by application of the incremental dynamic analysis in combination with B-R kinetic criterion. Furthermore, considering suspended dome has the clear advantage over Single-Layer Spherical Lattice Shell for a structure with a long span and a small ratio of rise to span, the influences of factors such as structural parameters, geometric parameters, and different earthquake input are investigated on dynamic stability for a kiewitt-type suspended dome with a long span and a small ratio of rise to span. Finally of suspended dome some conclusions are obtained such as the initial defects can clearly reduce dynamic stable ultimate capacity, and since the rise-span ratio, pre-stressing level and cross section area are not monotonous as variety to the structural dynamic stability, they should be optimized to enhance or improve the structural dynamic stability, which can be rules for engineering design.

Stability Analysis of the Radiant Cable Suspendome

Radiant cable suspendome based on single-layer lattice shell is proposed in this paper whose cable-strut system is like that of Radiant Beam String Structure, the purpose of this paper is to do stability analysis of the structure.The linear buckling analysis of the hybrid structure and the single-layer lattice shell who has the same geometry parameters is carried out, we can preliminarily understand the stability of the hybrid structure. At the same time, nonlinear buckling analysis is carried out to study the stability of the hybrid structure under different rise-span ratios, different prestress level and half-span load. The results show that the introduction of prestressed cables greatly improve the structure's stability and reduce the structure sensitivity to original geometrical imperfection.

NONLINEAR STABILITY OF A SINGLE-LAYER HYBRID GRID SHELL

This paper presents a study of a hybrid grid shell, which is made of quadrangular meshes diagonally stiffened by pre-tensioned thin cables. The construction of the hybrid structure by translating a spatial curve against another spatial curve is firstly described. Then the elasto-plastic buckling analyses of the perfect hybrid structure and the corresponding single-layer lattice shell are carried out, and the influence of the asymmetric load on the failure loads is discussed based on a finite element model. Furthermore, the different shapes and sizes of imperfections are considered in this study. Two schemes of imposing imperfections are chosen: the first several eigenvalue buckling modes and the deformed shape of the loaded structure obtained from a geometrical non-linear analysis are chosen as the imperfection shape. Finally, the effects of different structural parameters, such as the rise-to-span ratio, beam section dimension, area and pre-stress of cables and boundary conditions, on the failure loads are investigated.

Application and development of modern long-span space structures in China

Modern long-span space structures, developed during the 1970s and 1980s, are light and effective structures based on new technologies and light-weight high-strength materials, such as membranes and steel cables. These structures include air-supported membrane structures, cable-membrane structures, cable truss structures, beam string structures, suspen-domes, cable domes, composite structures of cable dome and single-layer lattice shell, Tensairity structures and so forth. For the premodern space structures widely used since the mid-twentieth century (such as thin shells, space trusses, lattice shells and ordinary cable structures), new space structures have been developed by the combination of different structural forms and materials. The application of prestressing technology and the innovation of structural concepts and configurations are also associated with modern space structures, including composite space trusses, open-web grid structures, polyhedron space frame structures, partial double-layer lattice shells, cable-stayed grid structures, tree-type structures, prestressed segmental steel structures and so forth. This paper provides a review of the structural characteristics and practical applications in China of modern rigid space structures, modern flexible space structures and modern rigid-flexible combined space structures.

Evaluation of the Buckling Load of an Elliptic Paraboloid Cable-Braced Grid Shell Using the Continuum Analogy

A cable-braced grid shell is a new type of single-layer latticed shell suitable for glass roofs. Compared with traditional single-layer latticed shells, this new type of shell has a unique mesh shape (planar quadrilateral mesh), mesh form (steel and crossing cables), and surface shape (from the translation surface method). The grid shell is a single-layer latticed structure, and therefore stability is one of the key factors in the structural design. Therefore, in this paper, an elliptic paraboloid cable-braced grid shell with imperfections is used as an example with which to determine the formulas for the buckling load based on the continuum analogy. The main contents of this paper include the formula for the linear buckling load of an elliptic paraboloid cable-braced grid shell with imperfections, which is determined based on the continuum analogy. The equivalent rigidity for the cable-braced grid shell is then determined, and the effect of the cables on the shear rigidity is discussed. Finally, the formula for the linear buckling load is verified with numerical examples, and the errors are analyzed and a corresponding correction factor is given.

Calculation Model on Single Layer Lattice Shell Static and Dynamic Impact Analysis

Take single layer lattice shell hinge support model, elastic supporting model and whole structure model as object of study, systematic study the working performance of the lattice shell roof structure under different calculation model. Comparison and analysis of various calculation model of static and dynamic, aiming at the lower adopt concrete structure upper span space structure of this kind of composite structure, using different material combination structure damping ratio of practical calculation formula, separately calculated hinge support model and the whole structure model of dynamic response, results show that consider composite structure damping ratio and the whole structure modeling of the calculation model more accord with engineering practice.

Research on failure scenarios of domes based on form vulnerability

In this paper, form vulnerability theory was applied to the analysis of the failure mechanisms of single-layer latticed spherical shells subjected to seismic excitations. Three 1/10 scale testing models were designed with characteristics as follows: Model 1 possesses overall uniform stiffness and is expected to collapse in the strength failure mode as some members become plastic; Model 2 possesses six man-made weak parts located on six radial main rib zones and is expected to collapse in the dynamic instability mode with all members still in the elastic stage; Model 3 strengthens the six weak zones of Model 2, and therefore, its stiffness is uniform. Model 3 is proposed to collapse in the strength failure mode when the members are still in the elastic stage. By increasing the peak ground accelerations of seismic waves gradually, the shaking table tests were carried out until all three models collapsed (or locally collapsed). On the basis of form vulnerability theory, topological hierarchy models of the test models were established through a clustering process, and various failure scenarios, including overall collapse scenarios and partial collapse scenarios, were identified by unzipping corresponding hierarchical models. By comparison of the failure scenarios based on theoretical analysis and experiments, it was found that vulnerability theory could effectively reflect the weakness zones in topological relations of the structures from the perspective of internal causes. The internal mechanisms of the distinct failure characteristics of reticulated shells subjected to seismic excitations were also revealed in this process. The well-formedness of structural clusters, Q, is closely related to the collapse modes, i.e., uniform changes of Q indicate a uniform distribution of overall structural stiffness, which indicates that strength failure is likely to happen; conversely, non-uniform changes of Q indicate that weak zones exist in the structure, and dynamic instability is likely to occur.