| Digital design and analysis technologies,like Computer-Aided Design(CAD)Computer-Aided Engineering(CAE)and Topology Optimization(TO)have been developed rapidly in recent years,which can create the possibility for seamless connection from the initial conceptual design stage to the manufacturing phase.However,the key problem between CAD,CAE and TO is that they can not be developed in an integrated model,it’s hard to realize the digital,intelligent and integration of the modern product structure.To solve this problem,this paper proposes an isogeometric analysis topology optimization method which can unify CAD geometry model,CAE analysis model and TO model based on isogeometric analysis and topology optimization.Furthermore,we applied this method to several problems,including the multi-material,compliant mechanisms and lattice materials,and we give a comprehensive discussion on these problems.The main work are as follows:Firstly,an isogeometric topology optimization method is proposed based on density distribution function(DDF).Three parts are included in the construction of DDF:(1)Smooth the control point: Shepard function is utilized to define smooth mechanism;(2)NURBS function is used to construct initial DDF: using NURBS-based function and the smoothed density to construct DDF which possesses higher order smoothness and continuity;(3)Threshold projection of DDF,it greatly reduces the existence domain of intermediate density.The DDF ensures unity between CAD geometry model and topology optimization model,and IGA ensures uniform CAD geometry model and CAE analytic model.The isogeometric topology optimization can unify the CAD,CAE and TO.The effectiveness of the proposed method is verified by some 2D and 3D examples.Secondly,the isogeometric topology optimization formulation for the multimaterial design is proposed.A multi-material interpolation model is established by using the DDF in Chapter 2.Three key aspects are involved in the model:(1)Fields of Design Variables are featured with high continuity and smooth,which can eliminate the discrete distribution of traditional multi-materials in the design domain;(2)Nonoverlap area can be realized by defining design variables and topology variables respectively,so that the density point in the design domain corresponding to the specific material or void;(3)The decouple expression and serial mechanism of design variables and topology variables can reduce the nonlinear degree of the traditional coupled parallel mechanism,which reduces the complexity of numerical calculation.Later,2D and 3D numerical examples are both discussed,which can present the validity of the proposed method.Then,an isogeometric topology optimization formulation for compliant mechanisms is established.An enough smooth and continuous DDF is constructed to describe the spatial distribution of materials in the optimization iteration,which can effectively avoid the problem of topological discontinuity caused by hinge structures in compliant mechanisms.The proposed method can ensure the high demand for numerical accuracy in compliant mechanisms,and solve various numerical problems existing in previous work,such as instability in iterations,non-convergence and so on.Several 2D and 3D numerical examples are presented,which can present the validity of the proposed method.Later,an isogeometric topology optimization formulation for ultra-lightweight lattice materials is proposed.The DDF is utilized to describe the material distribution in the design domain,which can effectively ensure the continuity and smoothness of the structural boundary and avoid the topological fracture problem caused by the small volume fraction of the material in the optimization of the lattice structure.The NURBS based homogenization with a periodic boundary formulation to predict effective macroscopic properties based on the topology of lattice structures,then define the objective function of the isogeometric topology optimization formulation.The main objective is to find the lattice structure with ultra-lightweight.Several 2D and 3D numerical examples are implemented,and a series of new ultra-lightweight lattice materials can be excavated,the numerical results of the elastic tensor matrix show the validity of the proposed methodSubsequently,the proposed method is applied to optimize the main load-bearing structure of the satellite propulsion module,and the optimized structure is verified,which can present the validity of the structure.Then,the structure model is printed in3 D.Finally,the main research achievements and innovations are outlined,and we also provide some prospects for the future work. |
