Research On Topology Optimization Of Compliant Mechanisms Using The Ground Structural Approach

Compliant mechanisms achieve force and motion transmission through elastic deformation of relative flexibility of its members. Compared with rigid-body mechanisms, compliant mechanisms have many advantages such as a simple structure, simplified manufacturing processes, reduced friction, reduced assembly time, reduced weight, increased precision, reduced weight and miniaturization. Thus, it has been applied widely in the micro-electro-mechanical systems device design, biological engineering micro-manipulation, fiber alignment and aerospace. Topology optimization of compliant mechanisms has drawn more and more attentions because it only needs to designate a design domain and the positions of the inputs and outputs. In this paper, dynamic topology optimization of compliant mechanisms, reliability-based topology optimization of compliant mechanisms and topology optimization of compliant mechanisms with geometrical nonlinearity using the structure approach are investigated deeply. The main contributions of this thesis are listed as follows:A methodology for multi-objective topology optimization of multiple inputs and multiple outputs compliant mechanisms using the ground structure approach is presented. The multi-objective is developed by the minimum strain energy and the maximum mutual potential energy to design a mechanism, which meets both stiffness and flexibility requirements, respectively. Based on this, the multi-objective function of topology optimization of multiple inputs multiple outputs compliant mechanism is also developed by the strain energy and the mutual potential energy. The suppression strategy of output coupling terms is studied,and the expression of the output coupling terms is further developed. Numerical simulations are presented to show that the proposed optimization model is valid.A methodology for dynamic topology optimization of compliant mechanisms using the ground structure approach is presented. The function is developed by the maximum dynamic magnification factor and the minimum strain energy to design a mechanism which meets both stiffness and flexibility requirements under harmonic excitation, respectively. The objective function is normalized to eliminate magnitude difference of the objectives. Some numerical examples with different driving frequencies, different structural damping factors and different output spring stiffness are presented to illustrate the effect of driving frequency, damping factor and output spring stiffness.A methodology for reliability-based topology optimization of compliant mechanisms using the ground structure approach is presented. The applied load and the structural geometry size are considered as the uncertain variables. That the strain energy and mutual potential energy have upon system reliability are evaluated by regarding as a series systems. The first-order reliability method is adopted to solve the failure probability of the series system. The numerical example is simulated to show that the proposed method is correct and effective because it helps to obtain mechanisms with higher performance than those obtained by the deterministic topology optimization. Based on the topology mechanisms and the restriction of fabrication technology, the prototypes of the compliant inverters are determined. The prototypes are manufactured by means of wire cutting technology. The displacements of the compliant inverters are measured by using the measurement system. The experimental results approximately agree with the numerical results. It shows that properties of compliant inverters can meet the designing demands.A topology optimization method of compliant mechanisms with geometrical nonlinearity under displacement loading is presented in this paper. Geometrically nonlinear plane frame structural response is solved using the co-rotational Total Lagrange finite element formulation and the equilibrium is solved using the incremental scheme combined with Newton-Raphson iteration. The multi-objective function is developed by the minimum strain energy and maximum geometric advantage to design a mechanism which meets both stiffness and flexibility requirements. Compared with the result using linear formulation, the benefits of the optimal mechanisms obtained by nonlinear formulation are illustrated by the numerical example.