Research On Shape Optimization And Grid Generation Of Free-form Single-layer Grid Structure

With the rapid development of computer-aided design technology,especially the computer graphics and building construction technology,free-form grid structures have become the main trend of today’s spatial structure development.However,due to the freedom and variety of freeform grid structure,how to reasonably determine its architectural form and the surface grid is still one of the hotspots and difficulties in the field of current spatial structure research.To address these issues,this paper takes the free-form single-layer grid structure as the research object,and launches a systematic research on it.Firstly,for the surface morphology,some shape optimization methods considering the influence of the structural imperfection sensitivity and the joints stiffness are proposed.Then,for the issues about grid generation for free-form surface,considering the uniformity,regularity,fluency,grid orientation,and the structural performance,a series of grid generation and control methods that suitable for free-form surface are studied and proposed.The details are as follows:(1)In view of the fact that the single-layer spatial grid structure is very sensitive to initial imperfection,a new shape optimization method for free-form single-layer grid structure considering the imperfection sensitivity is proposed which takes the bending strain energy ratio as a constraint.The relationship between the bending strain energy and the total strain energy is adjusted and the proportion of the bending strain energy is controlled.And then the sensitivity of the optimized structure to the initial geometric imperfections is reduced.Finally,an efficient structure with higher buckling load capacity and low imperfection sensitivity is obtained.Furthermore,the redundancy characteristics of the optimized structure is also evaluated based on the damage model.(2)The semi-rigid feature of the joints is introduced into the shape optimization of freeform single-layer grid structure,and the influence of different joint stiffness on shape optimization of grid structure is discussed.And then the mechanical properties of the optimized structure with rigid joints and with the semi-rigid joint were compared and analyzed,and then the structural imperfect sensitivity was evaluated.(3)In order to obtain a uniform sized triangular grid,the rod adaptive method is proposed,which takes the rod in the grid structure as the basic mobile unit.This method is not restricted by the form of the curved surface,and can overcome the mapping distortion error and obtain a highly uniform triangular grid.Based on the rod adaptive method,considering the influence of fixed points,fixed edges,the grid size,curvature of the surface,and the number and position of singular points in the process of grid generation,the multi-objective control of grid generation is realized,and the grid topology is enriched.Therefore,the method can provide more choices for architects.(4)To better adapt to complex surfaces,a novel method for automatic triangular grid generation on a free-form surface based on Coulomb’s law is proposed,which refers to as the particle self-organizing system(PSOS).The nodes of grid structure are compared to the charged particles in electric field,and the self-organizing of particles is realized by the interaction between charged particles,which brings about an even layout of particles.After connecting the optimized particles,a uniform triangular grid will be generated.The PSOS can effectively avoid the mapping distortion and is suitable for grid generation of arbitrary free-form surface.(5)In order to better express the architectural implication,a progressive mesh generation method based on initial points and lines for free-form surface is proposed,which considers the line fluency,the grid regularity and the grid orientation.Then the grid layout with high grid quality and smooth lines can be obtained,and the direction and size of the grid can be controlled.(6)In order to obtain the grid topology with better mechanical properties under the given constraint of free-form curved surface,three solutions are proposed.Firstly,based on the sensitivity of the overall strain energy to the change of the nodal coordinates,the grid topology with maximum stiffness can be obtained by taking the total strain energy as the objective function,and then the smoothness optimization is carried out to improve the line smoothness.Secondly,the particle self-organizing system(PSOS)is improved.According to the axial force of the rod,the value of charged particles is changed,and then the grid density is adjusted,so as to obtain the grid layout with uniform grid density and reasonable stress.Finally,based on the structural principal stress trajectory,a mesh generation method for free-form surface is proposed by combining the surface mapping principle and the particle-spring method.Compared with the traditional grid with uniform layout,the grid generated based on structural principal stress trajectory has better structural performance,higher structural efficiency and more flexible design.(7)In addition,in order to determine the reasonable strong axis direction of rectangular members in single-layer grid structure,the geometric torsion is optimized.Then the program interface for converting the structural geometric model into the finite element model is compiled,which can provide some technical supports for the parametric design of free-form grid structures.