Parameterized Level-set Based Topology Optimization Method Considering Symmetry And Pattern Repetition Constraints

Symmetry and repetitive patterns are very common in both natural and artificial structures.Design with symmetry and pattern repetition(SPR)can be very useful in practical engineering.In this paper,a new optimal structure design method based on parameterized level-set considering SPR constraints is discussed and some practical engineering applications based on this method are explored.Firstly,this paper combines a parameterized level-set method together with radial basis functions(RBFs)interpolation strategy,which allows for decoupling the design variables from the finite element(FE)analysis mesh.The merits of the decoupling are that the RBFs knots can be mapped independently on regular or irregular design domain,and SPR constraints can be imposed by simply building a bijective relationship between RBF knots regardless of analysis mesh.Furthermore,due to the parameterization of the level-set function,there are fewer numerical manipulations that need to be implemented than the conventional level set method during the optimization process.Secondly,this paper proposes a multi-discretization scheme based on parameterized level set.In this approach,due to the decoupled property,a coarse discretization is applied to conduct the structural analysis whereas another dense discretization is employed to represent the structure topology.As a result,both efficient analysis and smoother and more precise topology are available.Thirdly,this paper borrows the concept of Lego from the toy industry to define Lego engineering structures(LES).In practical engineering applications,macrostructures can be disassembled into small scale components with the same or similar pattern,to satisfy mould manufacturing,installation,transportation,recycling,maintenance or other practical constraints.The components can be prefabricated and then assembled using high-strength bolts or buckles,to form the so-called LES since this process is like building structures with Lego elements.Based on this,this paper proposes to implement optimal design of LES considering symmetry and pattern repetition constraints.Finally,this paper combines radial basis function together with spatial distribution function and go further a step to discuss the mechanical and aesthetic integrated optimal design of structures considering symmetry and pattern repetition constraint.Richer change of the rhythm and topology of the structures pattern are available,which can further satisfy the designer’s aesthetic demand for structures.