Direct laser lithography (DLL) is a key enabling technology for 3D constructs at the microscale and its potential is rapidly growing toward the development of active microstructures. The rationale of this work is based on the different involved methodology, which is referred as indirect, when passive microstructures become active through postprocessing steps, and direct, when active structures are directly obtained by fabricating microstructures with active materials or by introducing heterogeneous mechanical properties and specific design. An in‐depth analysis of both indirect and direct methods is provided. In particular, the wide range of materials and strategies involved in each method is reported, including advantages and disadvantages, as well as examples of fabricated structures and their applications. Finally, the different techniques are briefly summarized, and critically discussed by highlighting how the new synergies between DLL and active materials are opening completely new scenarios, in particular for sensing (e.g., mechanical) and actuation at the microscale.
We consider a saddle-point formulation for a sixth-order partial differential equation and its finite element approximation, for two sets of boundary conditions. We follow the Ciarlet-Raviart formulation for the biharmonic problem to formulate our saddle-point problem and the finite element method. The new formulation allows us to use the H 1 -conforming Lagrange finite element spaces to approximate the solution. We prove A priori error estimates for our approach. Numerical results are presented for linear and quadratic finite element methods.Key words. sixth-order problem, higher order partial differential equations, biharmonic problem, mixed finite elements, error estimates.
Sensors detecting angles created by deformable structures play an increasing role in soft robotics and wearable systems. However, the typical sensing method based on strain measurement strongly depends on the viscoelastic behaviors of soft substrates and on the location of sensors that affect the sensing reliability. In this work, the changes in magnetic field coupling produced in space by planar coil deformation are investigated, for implementing a new direct transduction strategy, the soft inductive angle sensing (SIAS). A numerical analysis tool is developed for rigorously studying the inductance variations resulting from planar coils’ bending, folding, and folding with a small arc. Copper or liquid metal coils, having different shapes, pitches, and sizes are built and characterized. Results show that the SIAS is hysteresis‐free, velocity‐independent, highly sensitive, ultrastable, and with fast response, guaranteeing highly precise (0.1° incremental folding angle change) and reliable measurements. It is insensitive to coil materials and to behavior of embedding soft materials, and scalable (across 10 times scale). The SIAS is adopted in three case studies (a self‐sensing origami, a sensorized soft pneumatic actuator, and a wearable sensor) to highlight its low implementation complexity, high‐performance, and versatility, providing some insights on the enormous potential of this mechanism.
We modify a three-field formulation of the Poisson problem with Nitsche approach for approximating Dirichlet boundary conditions. Nitsche approach allows us to weakly impose Dirichlet boundary condition but still preserves the optimal convergence. We use the biorthogonal system for efficient numerical computation and introduce a stabilisation term so that the problem is coercive on the whole space. Numerical examples are presented to verify the algebraic formulation of the problem.2 A Three-field Formulation for Poisson Problem 2 A Three-field Formulation for Poisson Problem
Sobolev SpacesLet V = H 1 (Ω) and L = L 2 (Ω) 2 . The Sobolev spaces H k (S) for S ⊂ Ω or S ⊂ Γ, and k ≥ 0 are defined in the standard way [5]. We introduce the space H −1/2 (Γ), the dual space of H 1/2 (Ω), with the norm µ −1/2,Γ = sup z∈H 1/2 (Γ) µ, z z 1/2,Γ
The gradient recovery method is a technique to improve the approximation of the gradient of a solution by using post-processing methods. We use an L 2 -projection based on an oblique projection, where the trial and test spaces differ, for efficient numerical computation. We modify our oblique projection by applying the boundary modification method to obtain higher order approximation on the boundary patch. Numerical examples are presented to demonstrate the efficiency and optimality of the approach.
A solution method is developed for a linear model of ice shelf flexural vibrations in response to ocean waves, in which the ice shelf thickness and seabed beneath the ice shelf vary over distance, and the ice shelf/sub–ice-shelf cavity are connected to the open ocean. The method combines a decomposition of the ice shelf displacement profile at a prescribed frequency of motion into mode shapes of free vibrations, a finite-element method for the cavity water motion and a non-local operator to connect to the open ocean. An investigation is conducted into the effects of ice shelf thickening, seabed shoaling and the grounding-line conditions on time-harmonic ice shelf vibrations, induced by regular incident waves in the swell regime. Furthermore, results are given for ice shelf vibrations in response to irregular incident waves by superposing time-harmonic responses, and ocean-to-ice-shelf transfer functions are derived. The findings add to evidence that ice shelves experience appreciable flexural vibrations in response to swell, and that ice shelf thickening and seabed shoaling can have a considerable influence on predictions of how ice shelves respond to ocean waves.
We present a mixed finite element method for a three-field formulation of the Poisson problem and apply a biorthogonal system leading to an efficient numerical computation. The three-field formulation is similar to the Hu-Washizu formulation for the linear elasticity problem. A parameterised approach is given to stabilise the problem so that its associated bilinear form is coercive on the whole space. Analysis of optimal choices of parameter approximation and numerical examples are provided to evaluate our stabilised form.
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