Research On Explicit Topology Optimization Considering Nonlinearity-Related Problems

As an effective design method,structural topology optimization method has been widely used in aerospace,automobile,ship and other fields,and brought great economic benefits.With the fast development of topology optimization in the past 30 years,related research frontier has been gradually shifted from problems under linear elastic and small deformation assumption to topology optimization considering nonlinear effects.Actually,the linear and elasticity assumption is only an ideal simplification of real practice.In order to obtain a more reasonable and meaningful design,it is very necessary to consider the non-linearity(geometrical and material nonlinearity)during structural design.It has been shown that,when nonlinear effects is taken into consideration with using of fixed finite element grids,traditional implicit topology optimization method(e.g.,SIMP method,BESO/BESO method)will encounter the following difficulties:(1)serious distortion of low density elements brings serious trouble of the convergence of the intermediate design,and hence affects the entire optimization process;(2)as the increase of structural deformation,the computational effects of finite element analysis increase dramatically,and the efficiency of solution process of topology optimization decreases remarkably;(3)since the structural geometry is implicitly described by the finite elements,difficulties such as obtaining geometry information,seamlessly connecting by CAD/CAE softwares of optimized result and solving nonlinear programming with huge numbers of design variables will appear in optimization process;(4)when optimization problem about the buckling mode is solved,local instability and pseudo eigenmodes caused by the low density element region,as a result,the design maybe far from reality.In order to solve the above problems encountered associated with traditional topology optimization approaches,it is devoted to investigate on nonlinear structural topology optimization problems via a newly explicit topology optimization framework.The specific research contents are summarized as follows:An explicit topological optimization method describing the structural boundary using B-spline curves is developed to design structures under finite deformation.Related sensitivity analysis with respect to the initial configuration and current configuration is derived.The non-convergence issue is overcome by using of the proposed removal degrees of freedom technique during finite element analysis process.During numerical investigation,the effects of different initial design,different number of control points of B-splines,different treatments of boundary cutting elements and different amplitudes of external forces on the optimization results are discussed.In addition,comparison and discussion on the present designs and optimized design of SIMP method are presented.An explixit topology optimization method for the design of hyperelastic structures under large deformation is developed.The Mooney-Rivlin constitutive model is adopted to the hyperelastic response.After presenting the mathematical formulation and the corresponding sensitivity results.During numerical investigation,the effects of different initial design,different number of finte element on the optimization results are discussed.It is verified that,by using of fewer design variables,through a robust and stable optimization process,optimized hyperelastic structures with B-spline described boundaries,which can be transferred to the CAD/CAE system directly,can be obtained by the proposed approach.A design method for the film-substrate flexible electronic device is developed,and presenting the mathematical formulation.The commercial finite element software ABAQUS and the genetic algorithm are used to analyze and optimize the related designs.The design of flexible electronic devices involves highly nonlinear effects such as large deformation,post-buckling and bifurcations.Since the cut-patterns of film-substrate structure can be described by only a few design variables and cut-patterns of the mechanical guided three-dimensional self-assembly structures are designed.The current design strategy mostly is based on experience and trial-and-error process.This method supplies a systematic optimization design approach for advanced devices as flexible electronics.