Research On Buckling Topology Optimization Methods For Stiffened Structures

Stiffened structures are main load carrying components in aerospace equipment such as launching vehicles.Stiffeners can elevate bending stiffness of thin shells and panels significantly.In this way,buckling deformation is avoided improving these structures'capability to bearing axial compression load.With the ever-increasing weight of payload,size of aerospace equipment also enlarges fast leading to stiffened structures with high radiusthickness ratio.Designing of these structures with stability constraint is becoming more challenging.Meanwhile the need of light design of these structures servicing in harsher environment is more imperative than any time before.It is of great significance to obtain innovative stiffener layout through topology optimization which would elevate stiffened structures' buckling load while reducing or not adding structures' weight.To obtain structural configuration of stiffened-structure form in continuum topology optimization,geometric constraint which will generate stiffeners is needed in the formulation.Also,a highly efficient and robust solution method for optimization problems involving buckling eigenvalues is also needed to overcome convergence issues.Moreover,since unknown imperfections induced from manufacturing and servicing will compromise the load carrying capability of stiffened structures,a topology optimization method which could ensure that optimized stiffened structures' load carrying ability is robust in actual service environment,is also needed.Focus on stiffened thin-walled structures,this dissertation firstly proposed an extrusion constraint based on anisotropic Helmholtz filtering,which is used to generate stiffener in continuum topology optimization.Secondly,a globally convergent solution method for optimization problems involving eigenvalues are proposed.Its high efficiency and robustness make it an appropriate solution technique for topology optimization problems with stability concern.Thirdly,an optimization framework for cell design of grid-stiffened cylindrical shell structure is constructed considering stability constraint.Finally,topology optimization method which is capable of generating diverse competitive designs is proposed and applied in cell design.This method could provide several stiffener layout patterns with similar load-carrying capability in a single optimization process.To achieve these objectives,following research work has been conducted:Based on anisotropic Helmholtz density filter,a novel implementation of extrusion constraint is proposed,with which efficient continuum topology optimization of stiffened structure is achieved.In this implementation,local coordinate systems used for anisotropic filtering are constructed according to the extrusion direction.Filter radius in extrusion direction is far larger than other directions.With this new implementation,background mesh is not needed.Model pre-reprocessing is simplified greatly,reducing human intervention and processing time.These advantages make the new implementation more appropriate for the stiffener layout design of complex curved surface.Optimization method for problems involving both single and multiple eigenvalues is studied.Eigenvalue-related problem is often solved in an iterative manner.It is approximated by linear perturbation to get separable,linear programming sub-problem which is used for solving the primal optimization problem.However,solving sub-problem directly would result in large increments of design variables.The new design point obtained will be located at somewhere sub-problem fails to approximating the original problem.This renders globally stable convergence of the primal eigenvalue optimization problem impossible.To address this issue,two kinds of new sub-problems are advised including trust region based sub-problem and MMA based sub-problem,which could adaptively control the increments of design variables.Their efficacy and convergence property are demonstrated by examples.Topology optimization method for cell design of large-scale grid-stiffened cylindrical shells considering stability constraint is proposed.Equivalent shell stiffness is computed by asymptotic homogenization(AH)method.Linear buckling analysis is then conducted to calculate critical buckling load.Based on this analysis scheme and the derived sensitivity of buckling load,a topology optimization framework of grid-stiffened shells considering stability constraint is built.In the illustrative example of a large-scale grid-stiffened cylindrical shell,the framework could effectively obtain periodical cell with new topology configuration which achieves an increase of 21%in the magnitude of axial compression load compared with traditional cell configuration.With the proposed framework,the potential of grid-stiffened structure is fully exploited.Novel grid pattern obtained displays great improvement of load carrying capability.A continuum topology optimization method which is capable of generating diverse competitive designs is proposed.Three different optimization strategies were discussed including minimax strategy,weighted summation strategy and greedy strategy.Three graphicsbased diversity measurement are put forward.These measurements can intuitively and quantitively tell the differences between topology configurations,thus can be directly added to the optimization formulation which is then solved by gradient based mathematical programming method.Range and impact of different diversity measurement are discussed in order to make reasonable choice.This method is later applied in the cell design of grid-stiffened structures.Grid cells with obviously different topology configurations are obtained.After introducing modal and concentrated dip imperfection with varying amplitude to grid-stiffened cylindrical shells composed of these cells,their ability to resist unknown imperfections is investigated by nonlinear post-buckling analysis.The results indicate that although critical linear buckling load of new designs obtained by optimization is elevated,their imperfectionresisting capability is not necessarily improved.However,utilizing our optimization method could generate multiple diverse competitive designs in a single optimization process,from which a design with better imperfection-resisting ability can always be chosen.