Optimization for Maximum Nonlinear Buckling Load and Topics on Imperfection of Latticed Shells

The present paper represents comparison of continuum shells and latticed shells with qualitative analysis. For shells, the mechanical characteristics in the two perpendicular directions are continuous and related to each other, and any change in thickness will result in change in stiffness in any direction. In latticed shells, members are discrete and stiffnesses in two mutually perpendicular directions are discontinuous and independent of each other. Therefore, sensitivity of geometrical imperfection for buckling of latticed shells should be different from that of continuum shells. The author proposes a shape optimization method for maximum buckling load of a latticed shell. A single layer latticed dome is taken as a numerical example, and the results show that the buckling load parameter for full area loading case increases 32.75% compared to that of its initial shape. Furthermore, the numerical example demonstrates that an optimum latticed shell with maximum buckling load, unlike an optimum continuum shell, may not be sensitive to its geometrical imperfection.

Dynamic behavior of single-layer latticed cylindrical shells subjected to seismic loading

The single-layer latticed cylindrical shell is one of the most widely adopted space-fl'amed structures.In this paper,free vibration properties and dynamic response to horizontal and vertical seismic waves of single-layer latticed cylindrical shells are analyzed by the finite element method using ANSYS software.In the numerical study,where hundreds of cases were analyzed,the parameters considered included rise-span ratio,length-span ratio,surface load and member section size.Moreover,to better define the actual behavior of single-layer latticed shells,the study is focused on the dynamic stress response to both axial forces and bending moments.Based on the numerical results,the effects of the parameters considered on the stresses are discussed and a modified seismic force coefficient method is suggested.In addition,some advice based on these research results is presented to help in the future design of such structures.

Seismic isolation analysis of FPS bearings in spatial lattice shell structures

A theoretical model of a friction pendulum system （FPS） is introduced to examine its application for the seismic isolation of spatial lattice shell structures. An equation of motion of the lattice shell with FPS bearings is developed. Then, seismic isolation studies are performed for both double-layer and single-layer lattice shell structures under different seismic input and design parameters of the FPS. The influence of frictional coefficients and radius of the FPS on seismic performance are discussed. Based on the study, some suggestions for seismic isolation design of lattice shells with FPS bearings are given and conclusions are made which could be helpful in the application of FPS.

Damage Assessment, Repair and Field Test of Steel Lattice Shell after Fire

A real case of a steel lattice shell suffering a fire was studied. Based on the theory of field modeling, fire dynamic simulator (FDS) was used to identify the temperature field. The damage mechanism of the structure was determined by FEM analysis. After damage assessment, the shell was repaired with the pipe-encasement method. Finally, field test was employed to check the capacity of the structure after repair. The numerical study results indicate that the damage assessment agrees well with field inspection, verifying the accuracy of fire numerical simulation and FEM analysis. The field test results prove that the pipe-encasement method is secure and reasonable, and the repaired shell is safe.

NONLINEAR DYNAMICAL BIFURCATION AND CHAOTIC MOTION OF SHALLOW CONICAL LATTICE SHELL

The nonlinear dynamical equations of axle symmetry are established by the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations are given in geometrical nonlinear range. A nonlinear differential equation containing the second and the third order nonlinear items is derived under the boundary conditions of fixed and clamped edges by the method of Galerkin. The problem of bifurcation is discussed by solving the Floquet exponent. In order to study chaotic motion, the equations of free oscillation of a kind of nonlinear dynamics system are solved. Then an exact solution to nonlinear free oscillation of the shallow conical single-layer lattice shell is found as well. The critical conditions of chaotic motion are obtained by solving Melnikov functions, some phase planes are drawn by using digital simulation proving the existence of chaotic motion.

Buckling Load Evaluation Method for Single Layer Cylindrical Lattice Shells

A rational design evaluation procedure is investigated for the elastic overall buckling load carrying capacity of single layer cylindrical lattice shell roof structures. The nature of the imperfection sensitivity of these structures is for the first time reviewed in this paper. This allows the development of the reduced stiffness buckling analytical concept for the lattice shells based upon the introduction of a simple lower bound estimation equation through the use of the so-called continuum shell analogy theory. The linear and nonlinear buckling loads found from conventional finite element analyses are compared with the present estimations. Finally, the elastic-plastic load carrying capacity estimation method through the use of the present elastic lower bound criteria is also proposed.

Random fractal-based computational design of an ice-ray (IR) lattice shell structure

Chinese ice-ray (IR) lattices, known for their intricate and visually fascinating random patterns as decorative elements in traditional 18th-century Chinese window design, exhibit underlying stiffness as latticed window fences. Such unique patterns represent a new morphology within the family of stochastic lattices. However, the latent structural potential within the random patterns of ice-ray lattices remains largely unexplored, particularly in the context of lattice shell design. This study systematically studies the geometric qualities of ice-ray lattice patterns and develops an algorithm to model these patterns for ice-ray lattice shell design. Subsequently, it assesses the structural feasibility and effectiveness of these lattice shells in comparison to conventional gridshells. The practicality of constructing random lattice shells using digital fabrication tools is also explored. Employing fractal geometry as a foundational framework, this research not only offers insights into the potential of ice-ray lattices for innovative lattice shell design but also introduces a new structural morphology to the field, expanding the possibilities of incorporating stochastic patterns in lattice shell design. Ultimately, it opens up new opportunities for innovative lattice shell designs, emphasizing the potential of stochastic patterns in structural applications.

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 in- stability 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 weak- ness zones in topological relations of the structures from the perspective of internal causes. The intemal 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.