Topological design of electromechanical actuators with robustness toward over- and under-etching
Abstract In this paper, we combine the recent findings in robust topology optimization formulations and Helmholtz partial differential equation based density filtering to improve the topological design of electromechanical actuators. For the electromechanical analysis, we adopt a monolithic formulation to model the coupled electrostatic and mechanical equations. For filtering, we extend the Helmholtz-based projection filter with Dirichlet boundary conditions to ensure appropriate design boundary conditions. For the optimization, we use the method of moving asymptotes, where the sensitivity is obtained from the adjoint approach. Our study shows that the robust filter approach produces topology optimized actuators with minimal length control and crisp structural boundaries. In particular, the minimal length control of both structural features and gap widths avoids common modeling artifacts in topology optimization, i.e. one-element wide structural parts or gaps. It thus leads to physically realizable designs that are robust against manufacturing imprecision such as over- and under-etching.
Topology optimization of electrostatically actuated microsystems
This study addresses the design of electrostatically actuated microelectromechanical systems by topology optimization. The layout of the structure and the electrode are simultaneously optimized. A novel, continuous, material-based description of the interface between the structural and electrostatic domains is presented that allows the optimization of the interface topology. The resulting topology optimization problem is solved by a gradient-based algorithm. The electromechanical system response is determined by a coupled high-fidelity finite element model and a staggered solution procedure. An adjoint formulation of the coupled electromechanical design sensitivity analysis is introduced, and the global sensitivity equations are solved by a staggered method. The proposed topology optimization method is applied to the design of mechanisms. The optimization results show the significant advantages of varying the interface topology and the layout of the electrode versus conventional approaches optimizing the structural layout only.
Object Oriented Design of Parallel and Sequential Finite Element Codes
The Finite Element (FE) Method is a widely accepted general purpose numerical modelling tool. Typical FE programs consist of several hundred thousand lines of procedural code and many complex data structures. Alternative approaches, based on object oriented programming (OOP) concepts, are becoming popular as evidenced by the exhaustive bibliography of the use of OOP techniques in FEM [3]. OOP is based on the idea of “objects” that encapsulate both the data and the operations on the data. The implementation details are hidden and every object defines itself clear interfaces for communication. This makes code very simple to maintain and modify, and hence attractive for use on research FE codes. In this paper we describe aspects of the design and implementation of an OOP based FE code primarily for use in large geomechanics simulations. The code allows various types of FE analysis, in both sequential and parallel computing environments, as well as the modelling of multi-field physical phenomena. A novel feature of this work is that, instead of using direct generalisation of the data structures used in a procedural code (i.e. representing a domain as an object and performing the calculations on the domain) each of the finite elements in this code is defined as a separate object. In addition, material constitutive behaviour and geometric primitives are also represented as objects. This gives great flexibility for adding new elements, materials or modelling new physical phenomena. Combination of different element types, for instance mixing structural (i.e. bending) elements with continuum elements, is also made simpler. Since the mathematical operations performed by an element are very similar to the operations performed by constraints or external loads, no distinction is made between them. Extending this idea further, every operation on elements, for example removing or adding elements to the model, is also represented as an element object. The performance of a sequential FE code depends on the performance of the individual processor, the latency for access to data in the local memory and its bandwidth. In a parallel implementation performance additionally depends on the message activity, the load balancing and the bandwidth of message passing interface between the separate processes. The modular structure in the object oriented (OO) code clarifies the communication patterns and makes data decomposition and load balancing easier. This significantly improves scalability of the code.