Rib-Shell Based Structure Optimization

Optimal structure design is a very important problem in architecture geometry,mechanical engineering,computer graphics and many other fields.Usually,it means designing and optimizing a structure to satisfy certain goals like minimal weight or cost,maximal stiffness and so on,under some practical constraints,like volume,weight,geometry constraints,etc..A common goal of optimal structure design is to design and optimize a structure to save more material while meeting certain strength requirement.This paper proposes to achieve this goal by optimizing rib structure.Rib has an excellent capability to resist bending and doesn't occupy too much space.And it's usually used to reinforce a shell.Although ribs are widely used in architecture engineering,it still remains a challenge to generate a reasonable rib layout on an arbitrary surface while achieving good strengthen-ing performance.To address this problem,this paper proposes a computational method to generate such a rib layout.The essential of our method is to place ribs along the principal stress lines,which indicate the trajectories of internal force and naturally encode the optimal topology for any structure under a given set of boundary conditions.Given a surface,we assign it a thickness and regard it as a shell.After imposing the external loads,we perform a Finite Element Analysis and compute the principal stress field.With this cross field we calcu-late a field-aligned global parametrization and further extract a quad-mesh whose edges align with the principal stress directions.By tracing consecutive quad-mesh edges we obtain an initial rib network.Then a topology and geometry optimizations are applied to this rib network.Considering the differences of contribution from each rib,we simplify the rib network by dropping ribs with little contribution.And a further position opti-mization is applied to the remaining ribs.When the topology is determined,geometry optimization is carried out to optimize the cross-sectional shape of ribs,to further reduce the material usage while striving to achieve better reinforcement effect.Stress analysis and physical experiment validate the effectiveness and performance of our method.The final chapter makes a conclusion of this paper and prospects a further research on optimal structure design in the near future.