Dispersive Elastodynamics of 1D Banded Materials and Structures: Design

Within periodic materials and structures, wave scattering and dispersion occur across constituent material interfaces leading to a banded frequency response. In an earlier paper, the elastodynamics of one-dimensional periodic materials and finite structures comprising these materials were examined with an emphasis on their frequency-dependent characteristics. In this work, a novel design paradigm is presented whereby periodic unit cells are designed for desired frequency band properties, and with appropriate scaling, these cells are used as building blocks for forming fully periodic or partially periodic structures with related dynamical characteristics. Through this multiscale dispersive design methodology, which is hierarchical and integrated, structures can be devised for effective vibration or shock isolation without needing to employ dissipative damping mechanisms. The speed of energy propagation in a designed structure can also be dictated through synthesis of the unit cells. Case studies are presented to demonstrate the effectiveness of the methodology for several applications. Results are given from sensitivity analyses that indicate a high level of robustness to geometric variation.Comment: 33 text pages, 27 figure

On the Virtual Element Method for Topology Optimization on polygonal meshes: a numerical study

It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the accuracy of the method employed to discretize the underlying differential problem, which may not be able to correctly capture the physics of the problem. In light of the above remarks, in this paper we consider polygonal meshes and employ the virtual element method (VEM) to solve two classes of paradigmatic topology optimization problems, one governed by nearly-incompressible and compressible linear elasticity and the other by Stokes equations. Several numerical results show the virtues of our polygonal VEM based approach with respect to more standard methods

A novel explicit design method for complex thin-walled structures based on embedded solid moving morphable components

In this article, a novel explicit approach for designing complex thin-walled structures based on the Moving Morphable Component (MMC) method is proposed, which provides a unified framework to systematically address various design issues, including topology optimization, reinforced-rib layout optimization, and sandwich structure design problems. The complexity of thin-walled structures mainly comes from flexible geometries and the variation of thickness. On the one hand, the geometric complexity of thin-walled structures leads to the difficulty in automatically describing material distribution (e.g., reinforced ribs). On the other hand, thin-walled structures with different thicknesses require various hypotheses (e.g., Kirchhoff-Love shell theory and Reissner-Mindlin shell theory) to ensure the precision of structural responses. Whereas for cases that do not fit the shell hypothesis, the precision loss of response solutions is nonnegligible in the optimization process since the accumulation of errors will cause entirely different designs. Hence, the current article proposes a novel embedded solid component to tackle these challenges. The geometric constraints that make the components fit to the curved thin-walled structure are whereby satisfied. Compared with traditional strategies, the proposed method is free from the limit of shell assumptions of structural analysis and can achieve optimized designs with clear load transmission paths at the cost of few design variables and degrees of freedom for finite element analysis (FEA). Finally, we apply the proposed method to several representative examples to demonstrate its effectiveness, efficiency, versatility, and potential to handle complex industrial structures

Computational Based Investigation of Lattice Cell Optimization under Uniaxial Compression Load

Structural optimization is a methodology used to generate novel structures within a design space by finding a maximum or minimum point within a set of constraints. Topology optimization, as a subset of structural optimization, is often used as a means for light-weighting a structure while maintaining mechanical performance. This article presents the mathematical basis for topology optimization, focused primarily on the Bi-directional Evolutionary Structural Optimization (BESO) and Solid Isotropic Material with Penalization (SIMP) methodologies, then applying the SIMP methodology to a case study of additively manufactured lattice cells. Three lattice designs were used: the Diamond, I-WP, and Primitive cells. These designs are all based on Triply Periodic Minimal Surfaces (TPMS). Individual lattice cells were subjected to a uniaxial compression load, then optimized for these load conditions. The optimized cells were then compared to the base cell designs, noting changes in the stress field response, and the maximum and minimum stress values. Overall, topology optimization proved its utility under this loading condition, with each cell seeing a net gain in performance when considering the volume reduction. The I-WP lattice saw a significant stress reduction in conjunction with the mass and volume reduction, marking a notable increase in cell performance

Passive Aeroelastic Tailoring

The Passive Aeroelastic Tailoring (PAT) project was tasked with investigating novel methods to achieve passive aeroelastic tailoring on high aspect ratio wings. The goal of the project was to identify structural designs or topologies that can improve performance and/or reduce structural weight for high-aspect ratio wings. This project considered two unique approaches, which were pursued in parallel: through-thickness topology optimization and composite tow-steering

A stable and accurate control-volume technique based on integrated radial basis function networks for fluid-flow problems

Radial basis function networks (RBFNs) have been widely used in solving partial differential equations as they are able to provide fast convergence. Integrated RBFNs have the ability to avoid the problem of reduced convergence-rate caused by differentiation. This paper is concerned with the use of integrated RBFNs in the context of control-volume discretisations for the simulation of fluid-flow problems. Special attention is given to (i) the development of a stable high-order upwind scheme for the convection term and (ii) the development of a local high-order approximation scheme for the diffusion term. Benchmark problems including the lid-driven triangular-cavity flow are employed to validate the present technique. Accurate results at high values of the Reynolds number are obtained using relatively-coarse grids

Deep Reinforcement Learning for the Design of Structural Topologies

Advances in machine learning algorithms and increased computational efficiencies have given engineers new capabilities and tools for engineering design. The presented work investigates using deep reinforcement learning (DRL), a subset of deep machine learning that teaches an agent to complete a task through accumulating experiences in an interactive environment, to design 2D structural topologies. Three unique structural topology design problems are investigated to validate DRL as a practical design automation tool to produce high-performing designs in structural topology domains. The first design problem attempts to find a gradient-free alternative to solving the compliance minimization topology optimization problem. In the proposed DRL environment, a DRL agent can sequentially remove elements from a starting solid material domain to form a topology that minimizes compliance. After each action, the agent receives feedback on its performance by evaluating how well the current topology satisfies the design objectives. The agent learned a generalized design strategy that produced topology designs with similar or better compliance minimization performance than traditional gradient-based topology optimization methods given various boundary conditions. The second design problem reformulates mechanical metamaterial unit cell design as a DRL task. The local unit cells of mechanical metamaterials are built by sequentially adding material elements according to a cubic Bezier curve methodology. The unit cells are built such that, when tessellated, they exhibit a targeted nonlinear deformation response under uniaxial compressive or tensile loading. Using a variational autoencoder for domain dimension reduction and a surrogate model for rapid deformation response prediction, the DRL environment was built to allow the agent to rapidly build mechanical metamaterials that exhibit a diverse array of deformation responses with variable degrees of nonlinearity. Finally, the third design problem expands on the second to train a DRL agent to design mechanical metamaterials with tailorable deformation and energy manipulation characteristics. The agent’s design performance was validated by creating metamaterials with a thermoplastic polyurethane (TPU) constitutive material that increased or decreased hysteresis while exhibiting the compressive deformation response of expanded thermoplastic polyurethane (E-TPU). These optimized designs were additively manufactured and underwent experimental cyclic compressive testing. The results showed the E-TPU and metamaterial with E-TPU target properties were well aligned, underscoring the feasibility of designing mechanical metamaterials with customizable deformation and energy manipulation responses. Finally, the agent\u27s generalized design capabilities were tested by designing multiple metamaterials with diverse desired loading deformation responses and specific hysteresis objectives. The combined success of these three design problems is critical in proving that a DRL agent can serve as a co-designer working with a human designer to achieve high-performing solutions in the domain of 2D structural topologies and is worthy of incorporation into a wide array of engineering design domains