A structural optimization method based on the level set method using a new geometry-based re-initialization scheme

Compliant mechanisms are designed to be flexible to achieve a specified motion as a mechanism. Such mechanisms can function as compliant thermal actuators in micro-electromechanical systems by intentionally designing configurations that exploit thermal expansion effects in elastic material when appropriate portions of the mechanism structure are heated or are subjected to an electric potential. This paper presents a new structural optimization method for the design of compliant thermal actuators based on the level set method and the finite element method (FEM). First, an optimization problem is formulated that addresses the design of compliant thermal actuators considering the magnitude of the displacement at the output location. Next, the topological derivatives that are used when introducing holes during the optimization process are derived. Based on the optimization formulation, a new structural optimization algorithm is constructed that employs the FEM when solving the equilibrium equations and updating the level set function. The re-initialization of the level set function is performed using a newly developed geometry-based re-initialization scheme. Finally, several design examples are provided to confirm the usefulness of the proposed structural optimization method.

Download Full-text

Design of Compliant Thermal Actuators Using Structural Optimization Based on the Level Set Method

Volume 1: 34th Design Automation Conference, Parts A and B ◽

10.1115/detc2008-49618 ◽

2008 ◽

Cited By ~ 1

Author(s):

Takayuki Yamada ◽

Shintaro Yamasaki ◽

Shinji Nishiwaki ◽

Kazuhiro Izui ◽

Masataka Yoshimura

Keyword(s):

Structural Optimization ◽

Level Set Method ◽

Level Set ◽

Compliant Mechanisms ◽

Optimization Method ◽

Equilibrium Equations ◽

Micro Electro Mechanical Systems ◽

Thermal Actuators ◽

Level Set Function ◽

Set Function

Compliant mechanisms are a new type of mechanism, designed to be flexible to achieve a specified motion as a mechanism. Such mechanisms can function as compliant thermal actuators in Micro-Electro Mechanical Systems (MEMS) by intentionally designing configurations that exploit thermal expansion effects in elastic material when appropriate portions of the mechanism structure are heated. This paper presents a new structural optimization method for the design of compliant thermal actuators based on the level set method and the Finite Element Method (FEM). First, an optimization problem is formulated that addresses the design of compliant thermal actuators considering the magnitude of the displacement at the output location. Next, the topological derivatives that are used when introducing holes during the optimization process are derived. Based on the optimization formulation and the level set method, a new structural optimization algorithm is constructed that employs the FEM when solving the equilibrium equations and updating the level set function. The re-initialization of the level set function is performed using a newly developed geometry-based re-initialization scheme. Finally, several design examples are provided to confirm the usefulness of the proposed structural optimization method.

Download Full-text

Structural Optimization Using Adaptive Level Set Method

ASME/ISCIE 2012 International Symposium on Flexible Automation ◽

10.1115/isfa2012-7110 ◽

2012 ◽

Cited By ~ 1

Author(s):

Mingdong Zhou ◽

Michael Yu Wang ◽

Li Li

Keyword(s):

Structural Optimization ◽

Level Set Method ◽

Level Set ◽

Three Dimensional ◽

Optimization Method ◽

Mesh Simplification ◽

Surface Model ◽

Triangle Mesh ◽

Mesh Model ◽

Representation Scheme

A novel structural optimization method that utilizes both explicit and implicit geometric representations is presented. In this method, an octree grid is adopted to accommodate the free structural interface of an implicit level set model and a corresponding 2-manifold triangle mesh model. Within each iteration of optimization, the interface is evolved implicitly by using a semi-Lagrange level set method, during which the signed distance field is evaluated directly and accurately from the current surface model other than interpolation. After that, another mesh model is extracted from the updated field and serves as the input of subsequent design process. This hybrid and adaptive representation scheme not only achieves “narrow band computation”, but also facilitates the structural analysis by using a geometry-aware mesh-free approach. Moreover, a feature preserving and topological errorless mesh simplification algorithm can also be leveraged to enhance the computational efficiency. A three dimensional benchmark example is provided to demonstrate the capability and potential of this method.

Download Full-text