Topological design of compliant smart structures with embedded movable actuators

Abstract

In the optimal configuration design of piezoelectric smart structures, it is favorable to use actuation elements with certain predefined geometries from the viewpoint of manufacturability of fragile piezoelectric ceramics in practical applications. However, preserving the exact shape of these embedded actuators and tracking their dynamic motions presents a more challenging research task than merely allowing them to take arbitrary shapes. This paper proposes an integrated topology optimization method for the systematic design of compliant smart structures with embedded movable PZT (lead zirconate titanate) actuators. Compared with most existing studies, which either optimize positions/sizes of the actuators in a given host structure or design the host structure with pre-determined actuator locations, the proposed method simultaneously optimizes the positions of the movable PZT actuators and the topology of the host structure, typically a compliant mechanism for amplifying the small strain stroke. A combined topological description model is employed in the optimization, where the level set model is used to track the movements of the PZT actuators and the independent point-wise density interpolation (iPDI) approach is utilized to search for the optimal topology of the host structure. Furthermore, we define an integral-type constraint function to prevent overlaps between the PZT actuators and between the actuators and the external boundaries of the design domain. Such a constraint provides a unified and explicit mathematical statement of the non-overlap condition for any number of arbitrarily shaped embedded actuators. Several numerical examples are used to demonstrate the effectiveness of the proposed optimization method.

A velocity field level set method for shape and topology optimization

“…In this study, we use the ersatz material model based on a fixed finite element mesh. If the extend finite element method is used instead of the ersatz material method, special treatments should be taken (see the works of Wang et al and Wei et al).…”

“…Kang and Wang and Wang et al first introduced design variables (orientation and position variables) defining the layout of embedded components into the level set‐based geometrical representation in topology optimization problems . Recently, several other explicit geometry‐based parameterization schemes have also been studied –.…”

Survey on Recent Designs of Compliant Micro-/Nano-Positioning Stages

“…Huang et al [127] proposed bi-directional evolutionary structural optimization (bi-directional ESO (BESO)) to implement the structure optimization with desired stiffness. Wang et al [128] used the level set method to track the motion of the actuator and the independent point-wise density interpolation (iPDI) method to optimize the structure, so as to realize the optimization of both actuating position and structure. De Leon et al [129] added the stress constraint in the optimization to avoid the one-node-connected hinge problem.…”

Structural shape and topology optimization of cast parts using level set method

“…Inspired by our previous work of treating non‐overlap conditions (a typical type of geometrical constraints in multi‐component layout design) of embedded components with an integral constraint , we propose a new casting constraint in the form of domain integration to reduce the complexity in derivation and computation of the shape derivatives. This constraint is expressed as where R (·) is the ramp function (i.e., , as shown in Figure ; b is a specified positive parameter denoting the width of a narrowband, and H (·) is the Heaviside function; the function equals 1 when and 0 when or Φ > α 2 , and Figure shows the case for α 1 = −1 and α 2 = 1.…”

“…Inspired by our previous work of treating non-overlap conditions (a typical type of geometrical constraints in multi-component layout design) of embedded components with an integral constraint [17,19], we propose a new casting constraint in the form of domain integration to reduce the complexity in derivation and computation of the shape derivatives. This constraint is expressed as…”