Structural Dynamic Characteristics Topology Optimization With Level Set Based Method And Optimal Design For AFM Probe

Structural topology optimization is a systematic method for structure design.Through structural analysis and optimization algorithm,it searches the material distribution under specific constraints to make one or more performance of structure optimal.And it is widely used in aerospace,automobile industry,material engineering,civil engineering and other fields.It shrotens the period for trials and errors and reduces the reliance on designer's experience,also provides tools for innovative design of many complex structures.Dynamic performance design is an important aspect in today's structure design.By designing the dynamic characteristics,it can not only avoid the damage caused by vibration,but also optimize the performance of a structure worked on the vibration principle.In this paper,we study the theory of structural topology optimization for dynamic characteristics in detail,and apply topology optimization to the design of atomic force microscope microprobe.The main contributions are as follows:1)Solved the localized mode problem in maximization of structural eigenfrquency with level set based topology optimization.We describe the problem of eigenfrequency optimization,and the“artificial localized mode” problem arised in traditional SIMP based topology optimization is discussed.To avoid the localized mode caused by weak material,we propse a finite element analysis in strict 0-1 topology description combined with level set framework.Also,we propse mode recognition criteria based on vibration-free ratio to pick out localized mode result from drastic topological changes.2)Study with a robust topology optimization for structural eigenfrequency problem by considering inward boundary perturbation.Erosion the boundary of traditional deterministic optimized structure may result in non-trivial loss of performance.Sometimes it even causes fail of the structure.Therefore,we examine a generic deterministic structural optimization problem defined in the level set framework.Relying on the analysis of the first-order shape derivative and the optimality conditions,the robust optimization problem by intentionally creating uniform erosion in every iteration is introduced.The optimization objective is the eigenfrequency defined on inward perturbed structure,while the design variable is the boundary of unperturbed structure.Also,we give the method to map sensitivity analysis on inward perturbed boundary to the unperturbed boundary.3)Apply topology optimization to the design of tapping-mode atomic force microscope microprobe.In tapping-mode measurement for surface topography,the measurement performance depends highly on dynamic characteristics of the probe.In order to improve the scanning velocity and detection sensitivity,it requires the probe to have higher resonance frequency and large reflection slope at its free end in corresponding resonance mode shape.Therefore,we set a multi-objective optimization problem,and give the geometry model and mechanical model of a probe.We derive sensitivity of eigenvalue/eigenvector with respect to deign variables and the optimization problem is solved by gradient based method.On this basis we study the working principle of multi-frequency atomic force microscopy.When multi-frequency atomic force microscope is at work,its probe taps with sample surface and results in a periodic nonlinear interaction force.The force acts on the probe and produces harmonic responses.Detection of higher harmonic components provides a tool for material discrimination.To enhance the higher harmonic signals,we propose to optimize structure of the probe to tune frequency of a desired harmonic to match well with one of the probe's resonance frequency.Combined with probe's first-roder mode design requirements,we propose a multi-objective optimization scheme.