The Nonlinear Stability Study On K6 Single-layer Spherical Reticulated Shell

As single-layer spherical reticulated shells are widely used in our country, its span is more and more big, while the thickness is smaller and smaller.Under the effect of external load, shell structure is damaged frequently. Therefore, the problem of calculating the net shell structure stability has became a crucial problem in the design work. But the existing research about stability for K6 single-layer spherical reticulated shell structure is less.This article use the K6 single-layer spherical reticulated shell as the research object,and systematically studies the structure of the elastic and elastic-plastic stability problems by studied the stability of a large number of different forms of reticulated shell,The main research contents include the following aspects:(1) Introducting the whole process of analysis of the equilibrium path tracking algorithm, a criterion of critical load and applying method of initial imperfection, which are used in this paper. And the geometry nonlinear tangent stiffness matrix of beam element according to the nonlinear incremental finite element method(fem).(2) Analysing the geometric nonlinear of K6 single-layer spherical reticulated shell structure through APDL parametric design language of ANSYS12.0, and obtaining the load- displacement curve of net shell structure, and studied the influence to elastic stability with the sizes of section, initial flaw size, rise-span ratio, span and load distribution form and boundary support conditions on.(3)Beam element in the elastic-plastic analysis of tangent stiffness matrix is derived by finite segment finite element method. The double nonlinear analysis of geometrical non-linearity and material non-linearity are conducted for K6 single-layerspherical reticulated shell structure. Obtain the load- displacement curve of whole process with different span and different rise-span ratio and section size of different bar of net shell structure. And comparing the results with which only the geometric nonlinear analysis is considered, illustrating the necessity of elastic-plastic stability studies of single-layer spherical reticulated shell. The practical formula of the plastic stability of K6 single-layer spherical reticulated shell is fitted by the regression analysis by Matlab.Through the study found that the net shell of same span, the greater section size it is,the higher bearing capacity of the elastic stability it has, the greater the rise-span ratio it is, the smaller the elastic stability bearing capacity it has;The main factors affecting K6 single-layer spherical reticulated shell elastic stability is Initial defects, when the initial defect ratio is L / 1000, the stability bearing capacity is 47%-63% of the whole net shell; while Asymmetric load distribution and the boundary support conditions has litter effect on the stability of the reticulated shell.When elastic-plastic analysis was carried out on the structure, the stability bearing capacity have fallen significantly, so material non-linearity has a great influence on the stability of the structure bearing capacity, and only geometric nonlinear analysis of reticulated shell structure are considered is not reasonable;For the net shell of same span and rise-span ratio, the greater section size followed and the smaller plastic reduction factor CP are accompanied by the greater influence of elastic-plastic stability of structure;Shell net of the same span and section size, the bigger rise-span ratio has the greater effect of the elastic-plastic; the plastic reduction factor CP of K6 single-layer spherical reticulated shell is 0.416-0.638. Hoping the result of this article has reference value for the actual design engineering.