Research On Shape And Section Optimization Of Single-layer Reticulated Shell Structure With Free-form Surface Based On Genetic Algorithm

The free-form surface structure is widely used in various large public buildings due to its efficient structure,flexible and free space layout,and beautiful and rich appearance.However,the internal forces of this type of structure are complex,and how to determine the architectural form of this type of building while ensuring its safety is an urgent problem to be solved.In this paper,an optimization algorithm is used to study the shape creation of free-form surface space reticulated shells.The main contents are as follows:(1)In order to obtain the free-form and reasonable mechanical properties of the free-form single-layer reticulated shell structure,the displacement response under the action of unit force was taken as the measurement parameter of the structural connection performance,and NURBS technology was introduced to ensure the smoothness of the structural surface.Based on the evaluation index of the nodal well-formedness under load,the corresponding optimization method of free-form surface structure is proposed.Taking the coordinates of structural control points as the optimization variables and the maximization of the minimum nodal well-formedness as the optimization objective,a genetic algorithm was used to optimize the surface shape of the structure by considering the constraint conditions such as total steel quantity,maximum node displacement and slenderness ratio.The results show that the nodal well-formedness can accurately reflect the joint connection performance,and the genetic optimization algorithm is adopted to optimize the surface shape of the structure,which can obtain the structural shape of the rod mainly subjected to axial compression.The stress mode is effectively improved,the stress is reasonable,and the structure’s ultimate bearing capacity and safety are guaranteed.(2)In order to meet different engineering design requirements at the same time,the shape optimization design of the single-layer reticulated shell structure with free-form surface is carried out from the aspects of structural safety performance,geometry and economic benefits.In the optimization process,the combination of mechanical index and geometric index,or mechanical index and economic index,or different mechanical performance index is selected as the optimization objective function,and the height of the control point of the NURBS surface is used as the optimization variable,and the shape of the free-form surface structure is analyzed based on NSGA-Ⅱ Multi-objective optimization.The following conclusions are drawn: firstly,this optimization method has little change in structure shape before and after optimization,and is suitable for fine-tuning the shape of a given structure.Secondly,the strain energy and node configuration degree are used as the optimization objectives,which belong to the combination of different mechanical indexes,and the structural stiffness and stable bearing capacity of the optimized structure are significantly enhanced;A free-form surface structure with good grid regularity and high structural rigidity can be obtained;with the combination of strain energy and structural steel consumption,a space reticulated shell structure with high structural rigidity and small steel consumption can be obtained,which has high engineering practical value.(3)The cross-sectional size of the free-form surface single-layer reticulated shell structure is also an important factor affecting its mechanical properties.In order to maximize the utilization of structural materials and the ultimate bearing capacity of the structure,a layered optimization method is used to optimize the form and section of the free-form surface single-layer reticulated shell structure.The optimization process is carried out in two layers.Firstly,the total strain energy of the structure is used as the optimization target,and the height of the control points on the NURBS surface is used as the optimization variable.The shape is optimized based on the standard genetic algorithm to obtain the current best structural shape;and then the structural shape is obtained.On the basis of,taking the section size of the bar as the optimization design variable,the section size of the structural bar is adjusted based on the improved genetic algorithm,and the collaborative optimization of the structural shape and the section size of the bar is realized.The results show that,compared with the shape or section optimization alone,this method can obtain the best structural shape and the corresponding bar section size,and maximize the mechanical properties of the structure.