| Vibration phenomena are common in the engineering field.With the complication of modern industrial equipment,the problem of structural vibration damage is becoming more and more serious.It is urgent to develop dynamic optimization design methods.In the process of dynamic optimization,the finite element analysis takes a long time and the optimization efficiency is low.It is necessary to develop a reduced-order model to increase the speed of the finite element analysis.Applying damping material is a very simple and practical method of damping vibration.However,after applying damping material,the system becomes a non-proportional damping system,which further aggravates the length of dynamic analysis.In view of the above problems,a structural dynamic topology optimization method based on an adaptive reduced-order model is established,which can be applied to non-proportional damping systems;an adaptive distributed topology optimization method for damping materials based on pseudo-density gradients is established,and the simultaneous optimization of the damping material and the matrix is realized;a topology optimization method of adaptive distribution of not all coated damping materials is proposed,which can save the amount of damping materials.The main research contents include:(1)A dynamic topology optimization method based on adaptive reduced-order model is established.First,an adaptive dynamic order reduction method based on Krylov subspace is established,which can effectively improve the efficiency of structural dynamic analysis,and a comparison between the full-order model and the reduced-order model is given to prove the effectiveness of this reduced-order algorithm.Secondly,with dynamic flexibility as the target and volume as the constraint,the dynamic topology optimization method under simple harmonic load is established based on the adaptive reduced-order model,and the sensitivity analysis is performed based on the adjoint method,and the dynamic topology optimization based on the reduced-order model is established.The process uses the modified SIMP interpolation model to improve the local displacement phenomenon.The dynamic topology optimization examples of the full-order model and the reduced-order model are compared.The numerical examples show that the results of the dynamic optimization based on the reduced-order model and the dynamic optimization of the full-order model are almost the same.On the premise of ensuring the analysis accuracy,the reduced-order model can greatly improve the optimization speed.(2)The topology optimization method of damping coating material for non-proportional damping system is studied.Considering that the structure of the damping material is a non-proportional damping system,the traditional modal superposition method cannot be used for analysis.The reduced-order model based on the Krylov subspace does not need to solve the eigenvalues,and directly solves the equation system,which can perform the dynamics of the non-proportional damping system Analysis.With dynamic flexibility as the target and volume as the constraint,based on the adaptive reduced-order model,the dynamic topology optimization method of non-proportional damping system considering damping materials is studied,and the effectiveness of the method is demonstrated through numerical calculation.Numerical examples show that the adaptive reduced-order model has very high analysis accuracy under non-proportional damping systems.The topology optimization of the damping material can effectively reduce the dynamic displacement response amplitude of the structure.(3)An adaptive distributed topology optimization method for damping materials based on density gradient is established.First,based on the dual density filtering technology,the topological boundary of the matrix structure is obtained by solving the spatial gradient of the element pseudo-density,and the effect of adaptive coating of the damping material on the topological characteristic boundary of the matrix can be achieved.A material interpolation model of coating structural properties is established.Secondly,combined with the adaptive reduced-order model,an adaptive distributed topology optimization method for damping materials was established,and comparison and verification of optimization examples considering damping coatings and not considering damping coatings were carried out.The numerical examples show that,compared with uncoated Topological results,considering the optimization results of coating materials can effectively reduce the dynamic displacement response amplitude of the structure.(4)The introduction of new design variables in the coating structure interpolation model controls the presence or absence of damping coating materials.While adaptively distributing the features,the amount of damping coating material is restricted,the effect of not all coatings is achieved,and the amount of damping material can be reduced.An adaptive distributed dynamic topology optimization method for not all coated damping materials is proposed.Numerical examples show that the optimization results of not all coatings can effectively reduce the dynamic displacement response amplitude of the structure when the amount of damping material is reduced. |
PDF Full Text Request