skip to main content

Title: Generative Design of Bionic Structures Via Concurrent Multiscale Topology Optimization and Conformal Geometry Method
Abstract Topology optimization has been proved to be an efficient tool for structural design. In recent years, the focus of structural topology optimization has been shifting from single material continuum structures to multimaterial and multiscale structures. This paper aims at devising a numerical scheme for designing bionic structures by combining a two-stage parametric level set topology optimization with the conformal mapping method. At the first stage, the macro-structural topology and the effective material properties are optimized simultaneously. At the second stage, another structural topology optimization is carried out to identify the exact layout of the metamaterial at the mesoscale. The achieved structure and metamaterial designs are further synthesized to form a multiscale structure using conformal mapping, which mimics the bionic structures with “orderly chaos” features. In this research, a multi-control-point conformal mapping (MCM) based on Ricci flow is proposed. Compared with conventional conformal mapping with only four control points, the proposed MCM scheme can provide more flexibility and adaptivity in handling complex geometries. To make the effective mechanical properties of the metamaterials invariant after conformal mapping, a variable-thickness structure method is proposed. Three 2D numerical examples using MCM schemes are presented, and their results and performances are compared. The achieved more » multimaterial multiscale structure models are characterized by the “orderly chaos” features of bionic structures while possessing the desired performance. « less
; ;
Award ID(s):
Publication Date:
Journal Name:
Journal of Mechanical Design
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Topology optimization has been proved to be an automatic, efficient and powerful tool for structural designs. In recent years, the focus of structural topology optimization has evolved from mono-scale, single material structural designs to hierarchical multimaterial structural designs. In this research, the multi-material structural design is carried out in a concurrent parametric level set framework so that the structural topologies in the macroscale and the corresponding material properties in mesoscale can be optimized simultaneously. The constructed cardinal basis function (CBF) is utilized to parameterize the level set function. With CBF, the upper and lower bounds of the design variables can be identified explicitly, compared with the trial and error approach when the radial basis function (RBF) is used. In the macroscale, the ‘color’ level set is employed to model the multiple material phases, where different materials are represented using combined level set functions like mixing colors from primary colors. At the end of this optimization, the optimal material properties for different constructing materials will be identified. By using those optimal values as targets, a second structural topology optimization is carried out to determine the exact mesoscale metamaterial structural layout. In both the macroscale and the mesoscale structural topology optimization,more »an energy functional is utilized to regularize the level set function to be a distance-regularized level set function, where the level set function is maintained as a signed distance function along the design boundary and kept flat elsewhere. The signed distance slopes can ensure a steady and accurate material property interpolation from the level set model to the physical model. The flat surfaces can make it easier for the level set function to penetrate its zero level to create new holes. After obtaining both the macroscale structural layouts and the mesoscale metamaterial layouts, the hierarchical multimaterial structure is finalized via a local-shape-preserving conformal mapping to preserve the designed material properties. Unlike the conventional conformal mapping using the Ricci flow method where only four control points are utilized, in this research, a multi-control-point conformal mapping is utilized to be more flexible and adaptive in handling complex geometries. The conformally mapped multi-material hierarchical structure models can be directly used for additive manufacturing, concluding the entire process of designing, mapping, and manufacturing.

    « less
  2. The wear of materials continues to be a limiting factor in the lifetime and performance of mechanical systems with sliding surfaces. As the demand for low wear materials grows so does the need for models and methods to systematically optimize tribological systems. Elastic foundation models offer a simplified framework to study the wear of multimaterial composites subject to abrasive sliding. Previously, the evolving wear profile has been shown to converge to a steady-state that is characterized by a time-independent elliptic equation. In this article, the steady-state formulation is generalized and integrated with shape optimization to improve the wear performance of bi-material composites. Both macroscopic structures and periodic material microstructures are considered. Several common tribological objectives for systems undergoing wear are identified and mathematically formalized with shape derivatives. These include (i) achieving a planar wear surface from multimaterial composites and (ii) minimizing the run-in volume of material lost before steady-state wear is achieved. A level-set based topology optimization algorithm that incorporates a novel constraint on the level-set function is presented. In particular, a new scheme is developed to update material interfaces; the scheme (i) conveniently enforces volume constraints at each iteration, (ii) controls the complexity of design features using perimeter penalization,more »and (iii) nucleates holes or inclusions with the topological gradient. The broad applicability of the proposed formulation for problems beyond wear is discussed, especially for problems where convenient control of the complexity of geometric features is desired.« less
  3. Ferromagnetic soft materials can generate flexible mobility and changeable configurations under an external magnetic field. They are used in a wide variety of applications, such as soft robots, compliant actuators, flexible electronics, and bionic medical devices. The magnetic field enables fast and biologically safe remote control of the ferromagnetic soft material. The shape changes of ferromagnetic soft elastomers are driven by the ferromagnetic particles embedded in the matrix of a soft elastomer. The external magnetic field induces a magnetic torque on the magnetized soft material, causing it to deform. To achieve the desired motion, the soft active structure can be designed by tailoring the layouts of the ferromagnetic soft elastomers. This paper aims to optimize multi-material ferromagnetic actuators. Multi-material ferromagnetic flexible actuators are optimized for the desired kinematic performance using the reconciled level set method. This type of magnetically driven actuator can carry out more complex shape transformations by introducing ferromagnetic soft materials with more than one magnetization direction. Whereas many soft active actuators exist in the form of thin shells, the newly proposed extended level set method (X-LSM) is employed to perform conformal topology optimization of ferromagnetic soft actuators on the manifolds. The objective function comprises two sub-objective functions,more »one for the kinematic requirement and the other for minimal compliance. Shape sensitivity analysis is derived using the material time derivative and the adjoint variable method. Three examples are provided to demonstrate the effectiveness of the proposed framework.« less
  4. Soft active materials can generate flexible locomotion and change configurations through large deformations when subjected to an external environmental stimulus. They can be engineered to design 'soft machines' such as soft robots, compliant actuators, flexible electronics, or bionic medical devices. By embedding ferromagnetic particles into soft elastomer matrix, the ferromagnetic soft matter can generate flexible movement and shift morphology in response to the external magnetic field. By taking advantage of this physical property, soft active structures undergoing desired motions can be generated by tailoring the layouts of the ferromagnetic soft elastomers. Structural topology optimization has emerged as an attractive tool to achieve innovative structures by optimizing the material layout within a design domain, and it can be utilized to architect ferromagnetic soft active structures. In this paper, the level-set-based topology optimization method is employed to design ferromagnetic soft robots (FerroSoRo). The objective function comprises a sub-objective function for the kinematics requirement and a sub-objective function for minimum compliance. Shape sensitivity analysis is derived using the material time derivative and adjoint variable method. Three examples, including a gripper, an actuator, and a flytrap structure, are studied to demonstrate the effectiveness of the proposed framework.
  5. We present a virtual element method (VEM)-based topology optimization framework using polyhedral elements, which allows for convenient handling of non-Cartesian design domains in three dimensions. We take full advantage of the VEM properties by creating a unified approach in which the VEM is employed in both the structural and the optimization phases. In the structural problem, the VEM is adopted to solve the three-dimensional elasticity equation. Compared to the finite element method, the VEM does not require numerical integration (when linear elements are used) and is less sensitive to degenerated elements (e.g., ones with skinny faces or small edges). In the optimization problem, we introduce a continuous approximation of material densities using the VEM basis functions. When compared to the standard element-wise constant approximation, the continuous approximation enriches the geometrical representation of structural topologies. Through two numerical examples with exact solutions, we verify the convergence and accuracy of both the VEM approximations of the displacement and material density fields. We also present several design examples involving non-Cartesian domains, demonstrating the main features of the proposed VEM-based topology optimization framework. The source code for a MATLAB implementation of the proposed work, named PolyTop3D, is available in the (electronic) Supplementary Material accompanyingmore »this publication.« less