A Heaviside function‐based density representation algorithm for truss‐like buckling‐induced mechanism design

Abstract

Summary Motivated by key advances in manufacturing techniques, the tailoring of materials to achieve novel properties such as energy dissipation properties has been the focus of active research in engineering and materials science over the past decade. The goal of material design is to determine the optimal spatial layout to achieve a desired macroscopic constitutive response. However, the manufacturing abilities are the key factors to constrain the feasible design space, eg, minimum length and geometry complexity. Traditional density‐based method, where each element works as a variable, always results in complicated geometry with large number of small intricate features. To address the aforementioned challenges, a new density field representation technique, named, Heaviside function‐based geometric representation algorithm, is proposed in this paper, where density field is represented by truss‐like components. Truss‐like components have less control parameters and easier to handle for sensitivities derivation, especially for distance sensitivities. Using bar components to explicitly represent density field can explore design space effectively and generate simple structures without any intricate small features at borders. Furthermore, this density representation method is mesh independent and design variables are reduced significantly so that optimization problem can be solved efficiently using small‐scale optimization algorithm, eg, sequential quadratic programming. However, finding a reasonable initial component distribution is critical to avoid optimization failure. To overcome this difficulty, a jump‐start method is proposed by solving inverse subproblem. The overall optimization progress is divided into three stages, ie, the first stage is obtaining coarse snap‐through material configuration based on traditional density‐based method; the second stage is an inverse optimization problem to fit the geometry component to the solution obtained in stage I; and the stage III is maximizing the energy dissipation capacity. To demonstrate the powerful ability in design buckling‐induced mechanism of the proposed density representation algorithm, buckling‐induced energy dissipation mechanism with snap‐through behavior to achieve the desired energy dissipation capacity considering failure constraint is demonstrated through four numerical examples.

Fail-Safe Topology Optimization Using Damage Scenario Filtering

“…Subsequently, the effectiveness of this approach has been validated through corresponding numerical examples. By employing the independent continuous mapping method and incorporating discrete conditions involving topological variables and fundamental frequency constraints, a fail-safe topology optimization model is formulated and solved [27][28][29]. The numerical results indicate that, compared to traditional frequency-based topology optimization designs, the optimized fail-safe structures exhibit more intricate configurations and comprehensive material distribution, resulting in increased redundancy and mitigating the sensitivity of structural frequencies to localized damage.…”

Linear and nonlinear topology optimization design with projection‐based ground structure method (P‐GSM)

“…Guo and Zhang et al proposed a homogenization framework with the use of asymptotic analysis to achieve the fast design of devices filled with quasiperiodic microstructure, where a mapping function is implemented to transform an infill graded microstructure to a spatially periodic configuration. Some other advanced multiscale design methods for simultaneous achieving macro‐ and microscale topology optimization or nonlinear metamaterial design can be found in References .…”

A density‐based boundary evolving method for buckling‐induced design under large deformation

“…[16][17][18][19][20][21][22][23] Meanwhile, several other advanced TO methods are proposed in recent years. [24][25][26][27][28][29][30][31][32] In recent years, designing the flexible electronics, soft robots and wearable electronic devices draw great attention from academia and industry due to their extraordinary mechanical response. [33][34][35] Such devices and structures usually experience large deformations under external loading conditions, which is different from the traditional stiff structure design.…”

“…Furthermore, the projection‐based geometry description method has been extended to solve stress constraint problem, inverse design of lattice, three‐dimensional compliance problem, and multimaterial designs, etc 16‐23 . Meanwhile, several other advanced TO methods are proposed in recent years 24‐32 …”