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Topology optimization problems typically consider a single load case or a small, discrete number of load cases; however, practical structures are often subjected to infinitely many load cases that may vary in intensity, location and/or direction (e.g. moving/rotating loads or uncertain fixed loads). The variability of these loads significantly influences the stress distribution in a structure and should be considered during the design. We propose a locally stress-constrained topology optimization formulation that considers loads with continuously varying direction to ensure structural integrity under more realistic loading conditions. The problem is solved using an Augmented Lagrangian method, and the continuous range of load directions is incorporated through a series of analytic expressions that enables the computation of the worst-case maximum stress over all possible load directions. Variable load intensity is also handled by controlling the magnitude of load basis vectors used to derive the worst-case load. Several two- and three-dimensional examples demonstrate that topology-optimized designs are extremely sensitive to loads that vary in direction. The designs generated by this formulation are safer, more reliable, and more suitable for real applications, because they consider realistic loading conditions. 

A bioinspired, untethered, and small-scale origami crawler achieves effective locomotion and steering in severely confined spaces. 

Inspired by the embodied intelligence observed in octopus arms, we introduce magnetically controlled origami robotic arms based on Kresling patterns for multimodal deformations, including stretching, folding, omnidirectional bending, and twisting. The highly integrated motion of the robotic arms is attributed to inherent features of the reconfigurable Kresling unit, whose controllable bistable deploying/folding and omnidirectional bending are achieved through precise magnetic actuation. We investigate single- and multiple-unit robotic systems, the latter exhibiting higher biomimetic resemblance to octopus’ arms. We start from the single Kresling unit to delineate the working mechanism of the magnetic actuation for deploying/folding and bending. The two-unit Kresling assembly demonstrates the basic integrated motion that combines omnidirectional bending with deploying. The four-unit Kresling assembly constitutes a robotic arm with a larger omnidirectional bending angle and stretchability. With the foundation of the basic integrated motion, scalability of Kresling assemblies is demonstrated through distributed magnetic actuation of double-digit number of units, which enables robotic arms with sophisticated motions, such as continuous stretching and contracting, reconfigurable bending, and multiaxis twisting. Such complex motions allow for functions mimicking octopus arms that grasp and manipulate objects. The Kresling robotic arm with noncontact actuation provides a distinctive mechanism for applications that require synergistic robotic motions for navigation, sensing, and interaction with objects in environments with limited or constrained access. Based on small-scale Kresling robotic arms, miniaturized medical devices, such as tubes and catheters, can be developed in conjunction with endoscopy, intubation, and catheterization procedures using functionalities of object manipulation and motion under remote control. 

Structures containing tension-only members, i.e., cables, are widely used in engineered structures (e.g., suspension and cable-stayed bridges, tents, and bicycle wheels) and are also found in nature (e.g., spider webs). We seek to use the ground structure method to obtain optimal cable network configurations. The structures are modeled using principles of nonlinear elasticity that allow for large displacements, i.e., global configuration changes, and large deformations. The material is characterized by a hyperelastic constitutive relation in which the strain energy is nonzero only when the axial stretch of a member is greater than or equal to one (i.e., tension-only behavior). We maximize the stationary potential energy of the equilibrated system, which avoids the need for an additional adjoint equation in computing the derivatives needed for the solution of the optimization problem. Several examples demonstrate the capabilities of the proposed formulation for topology optimization of cable networks. Motivated by nature, a spider web–inspired cable net is designed. 

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 accompanying this publication.