Structural Dynamic Topology Optimization Based On Nodal Design Variables

Currently,topology optimization is an important tool that widely used in machinery,aerospace and other design field of engineering structure,has made significant achievements in terms of method-research and theory-application.And structural dynamic topology optimization is one of the present most challenging topics.Variable density method has become the most popular topology optimization method due to its advantages of high optimizing efficiency and simple program.In order to improve the ability of the optimization model to describe the material density field,achieving the goal of ascension to optimization performance,the present paper researches topological optimization method based on node-density as design variables,and addresses several important dynamic problems.Research work and achievements are as follows:(1)Based on variable density method,topology optimization method based on node design variables is investigated in order to avoid numerical instability phenomenon of checkerboard patterns that occured during the topology optimization with element density as the design variables.Mapping function method is used to construct the consecutive field of density distribution,numerical problems of element-density penalty method have been solved from the origin.The introduction of variable-parameter nonlinear mapping function ensures that nearly 0/1 distribution optimization result is obtained.And the static stiffness optimization model is set up on the basis,iteration expression of design variables is derived using the algorithm of Optimization Criteria,sensitivity formula respect to node variables is deduced.The numerical example of classic cantilever beam structure verifies the validity of the proposed method.In addition,the influence of different optimization parameters on the topology optimization results is discussed.(2)Topology optimization model of structure under the harmonic force excitation based on node variables is established.According to common structural vibration problems under harmonic load,a model with minimum displacement response amplitude objective and material volume constraint is established for structural dynamic topology optimization.The SIMP material interpolation model is improved to solve problem of localized modes.Structural displacement responseexpression is deduced on the basis of frequency response method and modal superposition method,as well as the sensitivity formula of displacement response amplitude corresponding to node variables.The optimization model is solve by using the OC algorithm.Examples of structural topology optimization under different excitation frequencies and harmonic load directions are presented,simultaneously the structural topology under high frequency excitation is given.The designed numerical example shows that the proposed method is feasible to optimize the model of multi-excitation source.(3)Establishment of structural dynamic topology optimization based on node variables method under the constraint of mode shapes.Considering the optimal design of structural dynamic characteristics,the method proposed in the second chapter is applied to implement the issue of eigenfrequency optimizing.Furthermore,the frequency optimization problem with the consideration of the mode shapes and volume constraints is discussed,the introduction of MAC mode tracking method eliminates the problem of modal exchange in optimization process.The presented numerical examples obtain optimization results which are close to the references;On the basis of above research,the optimization model is established under the condition of the fixed order mode shapes for the objective of minimizing the displacement response amplitude at the specified point,the model is solved by using Method of Moving Asymptote algorithm.Numerical example shows the effectiveness of the proposed method,finally it is applied to the instance of constructing stator of linear ultrasonic motor.