Study On Form Finding And Optimization Of Complex Surface Elastic Gridshell Based On Motion Constraint Simulation

Under the influence of complexity science,the research on the design of complex curved surface architecture has shown a growing trend in recent years.However,due to the inherent complexity in the design of its structural system,there is still a scarcity of constructed buildings in this category.The generation process of complex curved surface architecture under specific rules is referred to as form-finding,and one viable method to address the rationality of structural systems in complex curved surface architecture is the method of mechanical form-finding.In the last century,German engineer Frei Otto devoted himself to the mechanical form-finding research of complex lightweight structures and proposed the concept prototype of elastic gridshell in 1962.Elastic gridshell belong to a type of actively bent structures that actively bend planar members to closely approximate a predetermined target reference surface,resulting in complex curved architectural forms.Elastic gridshell possess numerous advantages,including high material efficiency,lightweight self-weight,and high spatial utilization.Additionally,they are also characterized by convenient transportation,fast construction,reusability,and ease of assembly and disassembly.In 1975,Frei Otto designed and constructed a large-scale wooden elastic gridshell structure,the Mannheim Multihalle,which validated the feasibility of upscaling elastic gridshell structures.However,the design and construction of elastic gridshells are still relatively limited.The main reason is that the construction of elastic gridshells first requires the pre-assembly of planar member grids,which poses a construction challenge and limits the form-finding methods for elastic gridshells.This paper takes the simulation of motion constraints in elastic behavior of members as the starting point and conducts in-depth research on the transformation process of geometric forms of members during the bending forming process of elastic gridshells.Based on this,a method for form-finding of complex curved surface elastic gridshells using discrete differential geometry is proposed.This method combines motion constraint simulation to evaluate and optimize the curvature of elastic gridshell members and analyze their structural performance based on the grid of members.The research in this paper is divided into the following three parts: Firstly,the relevant theories of elastic gridshells are reviewed,and the principles of form-finding for elastic gridshells are established.In the first part of the study,a motion constraint simulation method for elastic members is proposed using the Kangaroo dynamic simulation platform,and the equilibrium forms of elastic members under gravity are studied.The feasibility of using a catenary mesh as a reference surface for complex curved surface elastic gridshells is analyzed.The form-finding results of catenary meshes under a given planar grid are explored using a pseudo-chain model,and the form-finding method for catenary meshes based on boundary constraints and height constraints is further improved through the Rhino VAULT thrust network analysis.This serves as a reference surface for the division of elastic gridshells.In the second part,based on the catenary mesh,a reference surface with a specified structure is obtained using mesh reverse engineering.On this reference surface,a spatial equilateral mesh is obtained based on surface UV structures using relevant methods of discrete differential geometry.The equilateral mesh division ensures the deploy ability of the mesh and facilitates the acquisition of planar orthogonal grids during the construction phase.The feasibility of the equilateral mesh division method is validated through mesh unfolding simulation.On the basis of the equilateral mesh division,an iterative optimization program is designed using the motion constraint simulation of elastic members.The minimum strain energy is set as the optimization objective,and the mesh curvature is used as a measure of member form.This effectively reduces the mesh curvature and provides more freedom for the design of elastic gridshells.The third part is the feasibility analysis of the mesh division method,i.e.,the structural performance analysis of elastic gridshells.The Karamba3 D structural finite element analysis platform is used to analyze the structural stiffness and buckling performance of elastic gridshells.The structural analysis shows that when all nodes are hinged and the elastic modulus of members is low,the buckling performance of elastic gridshells is poor.To address this issue,the Kagome member grid is optimized to improve the buckling performance of elastic gridshells,and suitable member dimensions are obtained through cross-sectional dimension analysis to establish a member offset model.This completes a comprehensive design process,providing an accurate digital model for construction.The study shows that the form-finding and optimization methods proposed in this paper have good applicability in the design of complex curved surface architecture.The equilateral mesh division method and mesh curvature optimization method can rationalize the grid of complex curved surface elastic gridshells.The proposed form-finding method is based on the Rhino & Grasshopper platform,which eliminates the design complexity caused by platform conversion in the overall form-finding process.