This paper proposes a new topology optimization method, which can adjust the geometrical complexity of optimal configurations, using the level set method and incorporating a fictitious interface energy derived from the phase field method. First, a topology optimization problem is formulated based on the level set method, and the method of regularizing the optimization problem by introducing fictitious interface energy is explained. Next, the reaction-diffusion equation that updates the level set function is derived and an optimization algorithm is then constructed, which uses the Finite Element Method to solve the equilibrium equations and the reaction-diffusion equation when updating the level set function. Finally, several optimum design examples are shown to confirm the validity and utility of the proposed topology optimization method.

Compliant mechanisms are mechanical devices that achieve motion via elastic deformation. A new method for topological synthesis of single-piece compliant mechanisms is presented, using a ' 'design for required deflection'' approach. A simple beam example is used to illustrate this concept and to provide the motivation for a new multi-criteria approach for compliant mechanism design. This new approach handles motion and loading requirements simultaneously for a given set of input force and output deflection specifications. Both a truss ground structure and a two-dimensional continuum are used in the implementation which is illustrated with design examples.^ 238

a b s t r a c tThis paper discusses a structural optimization method that optimizes shape and topology based on the phase field method. The proposed method has the same functional capabilities as a structural optimization method based on the level set method incorporating perimeter control functions. The advantage of the method is the simplicity of computation, since extra operations such as re-initialization of functions are not required. Structural shapes are represented by the phase field function defined in the design domain, and optimization of this function is performed by solving a time-dependent reaction diffusion equation. The artificial double well potential function used in the equation is derived from sensitivity analysis. The proposed method is applied to two-dimensional linear elastic and vibration optimization problems such as the minimum compliance problem, a compliant mechanism design problem and the eigenfrequency maximization problem. The numerical examples provided illustrate the convergence of the various objective functions and the effect that perimeter control has on the optimal configurations.

Flextensional actuators can be defined as a piezoceramic (or a stack of piezoceramics) connected to a flexible mechanical structure that converts and amplifies the output displacement of the piezoceramic. Essentially, the actuator performance depends on the distribution of stiffness and flexibility in the coupling structure and, therefore, on the coupling structure topology. In this work, we propose a general method for designing flextensional actuators with large output displacement (or generative force) by applying the topology optimization method. The goal is to design a flexible structure coupled to the piezoceramic that maximizes the output displacement (or force) in some specified direction. Static and low frequency applications are considered. To illustrate the implementation of the method, 2-D topologies of flextensional actuators are presented because of the lower computational cost; however, the method can be extended to 3-D topologies. By designing other types of coupling structures connected to the piezoceramic, new designs of flextensional actuators that produce output displacements or forces in different directions can be obtained, as shown. This method can be extended for designing flextensional hydrophones and sonars.

This paper introduces the Guide-Weight method into solving the topology optimization problems of compliant mechanisms. Guide-Weight method is a kind of Optimality Criteria methods, and it possesses the characteristics of clear physical meaning, high computational efficiency and great generality, which is definitely suitable for solving this class of problems. First, all theoretical derivations of GW are carried out. Furthermore, the relative spring stiffness ratio is proposed to update the input and output port element's stiffness value, and this approach exhibits high efficiency and strong robustness. Lastly, some typical benchmarks in this field are tested using GW method, with which the results obtained by other algorithms are compared.