Buckling Electrothermal NEMS Actuators: Analytic Design for Very Slender Beams

Analytic approximations are presented for the response of buckling-mode electrothermal actuators with very slender beams with a width-to-length ratio of W/L≤0.001 of the type found in nanoelectromechanical systems (NEMS). The results are found as closed-form solutions to the Euler beam bending theory rather than by an iterative numerical solution or a time-consuming finite element analysis. Expressions for transverse deflections and stiffness are presented for actuators with the common raised cosine and chevron pre-buckled shapes. The approximations are valid when the effects of bending dominate over those of axial compression. A few higher-order approximations are also presented for less slender beams with 0.001≤W/L≤0.01.

Design of tension structures and shells using the Airy stress function

Discontinuities in the Airy stress function for in-plane stress analysis represent forces and moments in connected one-dimensional elements. We expand this representation to curved membrane-action structures, such as shells and cable nets, and graphically visualise the internal stresses and section forces at the boundary necessary for equilibrium. The approach enhances understanding of the interplay between form and forces and can support design decisions related to form-finding and force efficiency. As illustrative examples, the prestressing needed for three existing cable nets is determined, and its influence on the edge-beam bending moment is explored.

A comparative assessment and unification of bond models in DEM simulations

Bonded contact models have been increasingly used in the discrete element method (DEM) to study cemented and sintered particulate materials in recent years. Several popular DEM bond models have been proposed in the literature; thus it is beneficial to assess the similarities and differences between the different bond models before they are used in simulations. This paper identifies and discusses two fundamental types of bond models: the Spring Bond Model where two bonded particles are joined by a set of uniform elastic springs on the bond’s cross-section, and the Beam Bond Model in which a beam is used to connect the centres of two particles. A series of cantilever beam bending simulation cases were carried out to verify the findings and assess the strength and weakness of the bond models. Despite the numerous bond models described in the literature, they can all be considered as a variation of these two fundamental model types. The comparative evaluation in this paper also shows that all the bond models investigated can be unified to a general form given at a predefined contact point location.

On a Novel Approximate Solution to the Inhomogeneous Euler–Bernoulli Equation with an Application to Aeroelastics

This paper focuses on the development of an explicit finite difference numerical method for approximating the solution of the inhomogeneous fourth-order Euler–Bernoulli beam bending equation with velocity-dependent damping and second moment of area, mass and elastic modulus distribution varying with distance along the beam. We verify the method by comparing its predictions with an exact analytical solution of the homogeneous equation, we use the generalised Richardson extrapolation to show that the method is grid convergent and we extend the application of the Lax–Richtmyer stability criteria to higher-order schemes to ensure that it is numerically stable. Finally, we present three sets of computational experiments. The first set simulates the behaviour of the un-loaded beam and is validated against the analytic solution. The second set simulates the time-dependent dynamic behaviour of a damped beam of varying stiffness and mass distributions under arbitrary externally applied loading in an aeroelastic analysis setting by approximating the inhomogeneous equation using the finite difference method derived here. We compare the third set of simulations of the steady-state deflection with the results of static beam bending experiments conducted at Cranfield University. Overall, we developed an accurate, stable and convergent numerical framework for solving the inhomogeneous Euler–Bernoulli equation over a wide range of boundary conditions. Aircraft manufacturers are starting to consider configurations with increased wing aspect ratios and reduced structural weight which lead to more slender and flexible designs. Aeroelastic analysis now plays a central role in the design process. Efficient computational tools for the prediction of the deformation of wings under external loads are in demand and this has motivated the work carried out in this paper.

Analysis of Beam Bending with an Elliptical Cross-Section

This paper calculates the stress function constants to determine and analyse the stress field of a beam with an elliptical cross-section under transverse loading. This was performed using linear elasticity principles. The Beltrami-Michell compatibility equations were used to derive the formulas used to calculate these parameters in the beam with the elliptical cross-section. This paper uses dimensionless analysis to comprehend the effect of each variable in the problem. The loading was applied at the centre of the right-end face of the elliptical beam. This loading configuration is the same as an existing linear elasticity problem; however, that problem models a cylindrical beam instead of an elliptical one. Thus, the existing parameters from the cylindrical model were used to verify the formulas, calculated in this paper, for the elliptical beam.

Physics Doesn't Bite - A Simple Experiment for Introducing Biomechanical Operational Principles of the Temporomandibular Joint

Biophysics is rarely mentioned as one of the most useful parts of dental and medical students' curricula. However, with growing complexity of tools and methods used in diagnostics and therapy, the knowledge of their physical foundations becomes important and helps with choosing the optimal solutions for both, a patient and a doctor. The aim of the proposed activity is to develop students' intuition about simple physical models that help with understanding fundamental properties of temporomandibular joint (TMJ). A simple device, which allows for bite force measurement, is proposed. It is based on beam bending and a strain gauge Wheatstone bridge circuit, mounted on two connected arms: the stiff one and the more elastic one. Linear regression is the only mathematical concept needed for understanding the physical background of the proposed activity. During the proposed activity - measuring of bite force for incisors, premolars and molars - students are confronted with basic concepts, such as lever, torque, electrical circuit, calibration curve. By utilizing a simple idea, instead of a commercially available device, students can understand where the data come from. Proposed system delivers physiologically reasonable results.

Comprehensive Study on Shape Shifting Behaviors of Thermally Activated Hinges in FDM-based 4D Printing

4D printing of shape shifting structures, aka “hinges”, has raised a new standard in many fields. By using these hinges in certain parts of a 3D printed structures, a pre designed complex 3D shape with potential multifunctional application can be achieved from flat structure. This paper proposes a comprehensive semi-empirical model to predict the final shape shifting behavior and magnitude of the hinges printed by FDM process. First, all FDM main parameters are selected and reduced by design of experiment to printing speed, lamina thickness, nozzle temperature as well as printing pattern. In order to develop the model, a time-dependent constitutive model with these four process parameters were extracted for strain of an SMP homogeneous single layer structure using a fractional Zener model accompanied with Multiple Linear Regression (MLR) technique. Thereafter, the mathematical relations for shape shifting behavior of bilayer 4D printed structures were developed for beam bending and twisting by modifying Timoshenko’s constitutive equations. A comprehensive shape-shifting model was established including 3D printing parameters, angles, thickness ratios, activation time and temperature which was compared to the experimental data and results predicted both shape shifting behavior and magnitude of the hinges with good agreement. In addition, a novel flowchart was suggested to design and achieve the desired shape shifting behaviors. The proposed model and flowchart are novel tools to design 4D structures through desired shape-shifting of the hinges.

Methods for Shape Fitting in Morphing Compliant Mechanisms

While compact folding is desirable for applications such as deployable mechanisms, achieving this with compliant mechanisms can be challenging. One reason for this is that the relaxed and stressed states of the mechanism are known and the loads producing the transition are unknown. The relaxed state is determined by the desired, deployed state and the stressed geometry is determined by the storage space. Approaches for solving this problem often require significant software development or cannot address problems in three dimensions. To address this problem, this work describes a method for designing 3D compliant mechanisms that can fold compactly. If the stressed and relaxed geometry are specified, an algebraic method can be used to find loads which best approximate the desired geometry. A least-squares approach is used to minimize error. A simplification of this method in two dimensions is also described. To further enhance the accuracy of the shape approximation, a method for varying the beam bending stiffness is described. For comparison, an inverse finite-element solver was implemented and paired with an optimizer and used to solve the same problem. Both methods were used to design a compliant, compactly folding beam. These results were compared with results from a commercial, finite-element software package.

Pyroelectric-controlled bending of a self-trapped optical beam in a photorefractive iron doped lithium niobate crystal

We present the experimental demonstration of a self-trapped optical beam bending in a photorefractive Fe-doped lithium niobate (LN:Fe) crystal controlled by the pyroelectric effect. Formation of self-trapped beams with typical [Formula: see text]50[Formula: see text][Formula: see text]m diameter and large bending of [Formula: see text]140[Formula: see text][Formula: see text]m are depicted in a 1[Formula: see text]cm length LN:Fe crystal for a laser beam at 632.8[Formula: see text]nm wavelength and 0.5[Formula: see text]mW power with a 30∘C crystal temperature change. The self-trapped beam bending is opposite to the crystal [Formula: see text]-axis. The underlying physics is elaborated and numerical simulations are performed. The long-living waveguiding channels with controlled curvilinear trajectories are promising for optical information routing.