Stability Performance Optimization Of Single-Layer Reticulated Shell Based On Particle Swarm Algorithm

Single-layer grid shell is widely used in major public buildings and industrial buildings due to its good force performance and beautiful and reasonable shape curve.Since the bearing capacity of single-layer grid shell structure is mainly determined by its stable performance,in recent years,stability performance optimization has gradually become the key research direction in single-layer grid shell structure.Based on the concept of the stiffness parameters of the grid shell member,the variance of the stiffness of the member configuration is constructed to evaluate the difference in the resistance capacity of each node of the structure,and on this basis,the optimization goal is to reduce the variance of the stiffness of the member configuration.Taking the member strength,stability,member length and slenderness ratio,steel consumption and grid shell structure deflection limit as constraints,the section size of the member is optimized by particle swarm algorithm to achieve the uniform distribution of the structural stiffness of the member configuration of each node of the structure,so as to achieve the purpose of cost-effectively improving the ultimate bearing capacity of the structure stability.The main conclusions are as follows:The stiffness of the member configuration introduced based on the stress state of the unstable front member of the grid shell structure can effectively reflect the bearing capacity of the grid shell structure node.The stiffness of the member configuration is clearly defined and easy to calculate.It is convenient and accurate to predict the instability node of the grid shell structure;The analysis shows that the instability node of the grid shell structure occurs at the node with the smallest configuration stiffness.At the same time,the configuration stiffness can be very convenient for the optimization of the stable bearing capacity of the grid shell structure.Using the particle swarm algorithm,the stability performance of cylinder and spherical grid shell is optimized by reducing the variance value of the stiffness of the member configuration as the objective function,so that the grid shell structure is close to equal stability.The optimization results show that the stable bearing capacity of the diamondshaped grid cylindrical grid shell increases by 51.6%when the steel consumption is only increased by 4.90%.The three-way grid cylindrical grid shell increased its stable bearing capacity by 11.53%when the amount of steel used was reduced by 2.14%.For spherical grid shells,the steel used for K6 single-layer grid shells with a sagittal span ratio of 1/3 increased by only 1.2%,and the stable bearing capacity under full-span uniform distribution load and half-span uniform distribution load increased by 19.2%and 10.4%,respectively.The steel used in the K6 single-layer grid shell with a sagittal span ratio of 1/5 only increased by 0.87%,while the stable bearing capacity increased by 5.50%.The Schweidler single-layer grid shell with a sagittal span ratio of 1/5 only increased the amount of steel used by 1.7%,while the stable bearing capacity increased by 23.8%.In the optimization analysis of the stable bearing capacity of the grid shell by using particle swarms,in order to improve the optimization efficiency and the accuracy of the optimization results,it is recommended that the particle population size be 50～1000 in the particle swarm algorithm program,and generally 50 can achieve better results.The number of iterations can be 200～300 for the grid shell within the span of 50m;The learning factor should be 2.0;the maximum inertia coefficient should be 0.9 to better meet the requirements,and the minimum inertia coefficient value can be in the range of 0.4～0.5.Through the analysis of member changes before and after grid shell optimization,it is shown that the main rib member section is appropriately strengthened when optimizing the member,and the stable bearing capacity of the spherical grid shell is more significant and more economical and reasonable.The greater the difference in the variance value of the stiffness of the member configuration before and after the optimization of the grid shell structure,the more the stable bearing capacity will be improved after optimization.Conversely,the smaller the difference in the variance value of member configuration stiffness before and after optimization,the more uniform the configuration stiffness and the smaller the optimization potential.