Jianguo Cai

Effects of temperature variations on the in-plane stability of steel arch bridges

The in-plane stability of shallow parabolic arches subjected to a central concentrated load and temperature variations was in- vestigated in this paper. The virtual work principle method was used to establish the non-linear equilibrium and buckling equations. Analytical solutions for the non-linear in-plane symmetric snap-through and antisymmetric bifurcation buckling loads were obtained. Then, the effects of temperature changes on the in-plane stability for arches with supports that stiffen under compression were studied. The results show that the influence of temperature variations on the critical loads for both buckling modes (symmetric snap-through and anti symmetric bifurcation) is significant. The critical loads for the two buckling modes are more than those only under external loads without thermal loading. Moreover, the critical loads increase with an increase of the thermal loadings. It can also be found that the effects of applying a temperature field increase when either initial stiffness coefficient α or the stiffening rate β is raised. Furthermore, the effect of thermal loading on the critical load increases with the span-rise ratio m for arches with any initial stiffness coefficient α and the stiffening rate β. DOI: 10.1061/(ASCE)BE.1943-5592.0000208.

Geometric design and mechanical behavior of a deployable cylinder with Miura origami

The folding and deployment of a cylinder with Miura origami patterns are studied in this paper. First, the geometric formulation of the design problem is discussed. Then the loading case of the axial strains and corresponding external nodal loads applied on the vertices of the top polygon during the motion is investigated analytically. The influence of the angle between the diagonal and horizontal fold lines α and β and the number of Miura origami elements n on the dynamic behavior of the basic segment is also discussed. Then the dynamic behavior is analyzed using numerical simulations. Finally, the deployment process of a cylinder with multi-stories is discussed. The numerical results agree well with the analytical predictions. The results show that the range of motion, i.e. the maximal displacement of top nodes, will also increase with the increase of angles α and β. This cylinder, with a smaller n, may have a bistable behavior. When n is larger, the influence of n on the axial strains and external nodal loads is slight. The numerical results agree well with the analytical predictions. Moreover, the deployment of the cylinder with multi-stories is non-uniform, which deploys from the upper story to the lower story.

NONLINEAR STABILITY ANALYSIS OF HYBRID GRID SHELLS

In this paper, we investigate the buckling capacity of a hybrid grid shell, which is made of quadrangular meshes diagonally stiffened by pre-tensioned thin cables. The eigenvalue buckling, geometrical nonlinear elastic buckling and elasto-plastic buckling analyses of the hybrid structure were carried out. Then the influences of the shape and scale of imperfections on the elasto-plastic buckling loads were discussed. Also, the effects of different structural parameters, such as the rise-to-span ratio, cross-section of beams, area and pre-stress of cables and boundary conditions, on the failure load were investigated. The results show that the buckling capacity is reduced when taking into account the material nonlinearity. Furthermore, the hybrid structure is highly imperfection sensitive and the reduction of the failure load due to imperfections can be considerable. The proper shape and scale of the imperfection are also important. It is also shown that there exists an optimal rise-to-span ratio resulting in a relatively high buckling capacity for a specific span. Moreover, the enlarging of the cross-section of steel beams notably improves the stability performance of the structure. However, the area and pre-stress of cables pose small effect on the structural stability.

The Foldability of Cylindrical Foldable Structures Based on Rigid Origami

Foldable structures, a new kind of space structures developed in recent decades, can be deployed gradually to a working configuration and also can be folded for transportation, thus have potentially broad application prospects in the fields of human life, military, aerospace, building structures, and so on. Combined with the technology of origami folding, foldable structures derive more diversified models, and the foldable structures in cylindrical shape are mainly studied in this paper. Some researchers use the theory of quaternion representing spatial fixed-point rotation and construct the rotating vector model to obtain the quaternion rotation sequence method (QRS method) analyzing origami, but the method is very limited and not suitable for the cylindrical foldable structures. In order to solve the problem, a new method is developed, which combines the QRS method and the dual quaternion method. After analyzing the folding angle via the QRS method for multivertex crease system and calculating the coordinates of all vertices via the dual quaternion, the rigid foldability can be checked. Finally, two examples are carried out to confirm validity and versatility of the method.

Effects of the prestress levels on the stiffness of prismatic and star-shaped tensegrity structures:

On the basis of the introduction of the stiffness matrix of tensegrity structures, the eigenvalue analysis is carried out to study the influence of the prestress level on the stiffness of tensegrity structures. The triangular prismatic tensegrity structure, the star-shaped tensegrity structure and the star-shaped tensegrity structure with a central strut are selected as the numerical examples. The analytical results show that some eigenvalues increase linearly with the prestress level, whereas other eigenvalues firstly increase and then decrease or firstly decrease and then increase with the increase of the prestress level. This is because the stiffness matrix of the tensegrity structures is mainly composed of the material stiffness matrix and geometric stiffness matrix. As the contribution of these two parts of stiffness to eigenvalue models is different, the trends of eigenvalue variations are different with the increase of the prestressed level.

Nonlinear stability of a single-layer hybrid grid shell

Abstract 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 failur...

Motion analysis of a foldable barrel vault based on regular and irregular Yoshimura Origami

This paper investigates the geometry of a foldable barrel vault with Yoshimura Origami patterns during the motion. On the base of the geometry analysis of the origami unit, the radius, span, rise, and longitudinal length of the foldable barrel vault with regular Yoshimura Origami pattern in all configurations throughout the motion are determined. The results show that the radius of curvature and the span increase during deployment. But the rise increases first, followed by a decrease with increasing fold angle. Furthermore, the influence of the apex angle of the origami unit and the numbers of triangular plates in the span direction on the geometric parameters is also investigated. Finally, the method to obtain the rise and span of the barrel vault with irregular origami pattern is also given.

Investigation of the Static and Dynamic Behavior of a Deployable Hybrid Grid Shell

The deployable hybrid grid shell, which can be deformed elastically by bending until the desired form is obtained, is an attractive structural form in the design and construction of long-span transparent glass roof structures. These hybrid structures are very slender and lightweight. Therefore, the structural behavior of the hybrid grid shell needs to be well understood. The mechanical characteristic, static and dynamic behaviors of the grid shell have been investigated in this paper. The effect of the structural parameters, such as rise-to-span ratios, cross-sections of steel beams, areas and pre-stress of cables, on the structural behavior has been studied in detail. Results show that the hybrid grid shell with a good translucence is more efficient than the general single-layer reticulated shell structure. The vertical structural stiffness initially increases with the increase of the rise-to-span ratio and then decreases afterwards. There exists an optimum rise-to-span ratio resulting in an optimum stiffness for the specified span. The optimum value of the ratio is found between 0.15 and 0.20 from the simulation study presented in this paper. Given a specific height-to-span ratio, the increase of the beam section greatly reduces the nodal displacement and member forces and increases the natural frequency. However, it can be found that increasing the areas and pre-stress of cables is not an economical way to improve the structural behavior.

Effects of symmetric imperfections on the behavior of bistable struts

The behavior of a bistable strut for variable geometry structures was investigated in this paper. A three-hinged arch subjected to a central concentrated load was used to study the effect of symmetric imperfections on the behavior of the bistable strut. Based on a nonlinear strain–displacement relationship, the virtual work principle was adopted to establish both the pre-buckling and buckling nonlinear equilibrium equations for the symmetric snap-through buckling mode. Then the critical load for symmetric snap-through buckling was obtained. The results show that the axial force is in compression before the arch is buckled, but it becomes in tension after buckling. Thus, the previous formulas cannot be used for the analysis of post-buckling behavior of three-hinged shallow arches. Then, the principle of virtual work was also used to establish the post-buckling equilibrium equations of the arch in the horizontal and vertical directions as well as the static boundary conditions, which are very important for bistable struts.

Mobility analysis of planar radially foldable bar structures

This paper studies the planar radially foldable bar structures consisting of more generalized angulated elements (GAEs) that contain intermediate parallelograms. Since every general GAE subtends a constant angle in motion, the mobility of every GAE was discussed. Firstly, the kinematic equation of the system was obtained based on the consistency of the intermediate nodal coordinates. Computing the rank of the kinematic matrix of the equation, the mobility of general type I and II GAEs has been studied in detail. Furthermore, the mobility of the general GAEs bounded by an arbitrary triangle (not limited to isosceles or similar triangles) was discussed. The required condition throughout the motion of the system was given.