Elastic Constraints Research Articles

Local buckling of composite beams with edge-stiffened flanges subjected to axial load

Local buckling analysis of thin walled composite beams is presented, where the flanges are stiffened at their free edges. The web and the flanges are modelled by rotationally restrained long orthotropic plates. Explicit expressions are developed for the calculation of the lowest buckling load. For the stability of the flange distortional buckling, plate buckling (or local buckling) and their interaction are considered, while the stabilizing effect of the web is taken into account by elastic constraint. Web buckling is modelled with a long plate, whose edges are constrained by stiffeners with warping stiffness. The accuracy of the method is demonstrated through numerical examples.

Temperature and Substrate Dependence of Piezoelectric Sensitivity for PVDF Films

The piezoelectric sensitivity, via both the direct and converse effects, for commercial polyvinylidene fluoride (PVDF) films is measured as a function of temperature and frequency, for two substrates, nylon and aluminum. The average effective sensitivity for the PVDF on nylon was 29 pm/V for both direct and converse effect, independent of frequency over 0.5 to 200 Hz. Direct effect sensitivity on aluminum substrate was about a factor of five greater. Analysis of effects of substrate's thermal and elastic constraint disclosed insufficient effect to account for the observed increase of sensitivity. Flexoelectric effects were considered as the cause. The direct and converse sensitivity increased at approximately 2% per degree Celsius over the frequency range 0.5 to 200 Hz.

Transport user benefits calculation with the “Rule of a Half” for travel demand models with constraints

The importance of user benefits in transport projects assessments is well-known by transport planners and economists. Generally they have the greatest impact on the result of cost-benefit analysis. It is common practice to adopt the consumer surplus measure for calculating transport user benefits. Normally the well-known “Rule of a Half”, as a practical approximation for the integral of the demand curve, is used to determine the change of consumer surplus. Changes in travel demand and consumer surplus are influenced by all modeled changing variables, which primarily comprise the generalized costs. However, travel demand models with multiple constraints additionally contain variable “shadow prices”, added to the generalized costs. Such models are often used for travel demand modeling of large-scale areas. The most discussed and well-known model in the field of transport modeling is the doubly constrained gravity model. Beside this model with inelastic constraints, there are also more flexible models with elastic constraints. In this paper we enter into the question of whether applying the Rule of a Half with regard only to the generalized costs and neglecting the shadow prices is valid in the case of travel demand models with multiple constraints. For this purpose, a theoretical analysis in this paper provides a mathematical proof.

Electromechanical Complex of Test Loading Stand of Multistage Transmissions with Automatic Control

We investigated the modes of operation of the drive and loading electromechanical systems of the test loading stand, which provides necessary motion trajectories and changes loads of steps in transmission with command and automatic control. We revealed the factors that determine accuracy and dynamic properties of the controlled dynamical system with elastic mechanical constraints. We proposed system structures of energy-saving power consumption in the node connecting the stand to the electrical network.

A 3D Neurovascular Bundles Segmentation Method based on MR-TRUS Deformable Registration.

In this paper, we propose a 3D neurovascular bundles (NVB) segmentation method for ultrasound (US) image by integrating MR and transrectal ultrasound (TRUS) images through MR-TRUS deformable registration. First, 3D NVB was contoured by a physician in MR images, and the 3D MR-defined NVB was then transformed into US images using a MR-TRUS registration method, which models the prostate tissue as an elastic material, and jointly estimates the boundary deformation and the volumetric deformations under the elastic constraint. This technique was validated with a clinical study of 6 patients undergoing radiation therapy (RT) treatment for prostate cancer. The accuracy of our approach was assessed through the locations of landmarks, as well as previous ultrasound Doppler images of patients. MR-TRUS registration was successfully performed for all patients. The mean displacement of the landmarks between the post-registration MR and TRUS images was less than 2 mm, and the average NVB volume Dice Overlap Coefficient was over 89%. This NVB segmentation technique could be a useful tool as we try to spare the NVB in prostate RT, monitor NVB response to RT, and potentially improve post-RT potency outcomes.

Vibroisolation of Vibratory Conveyors

Vibratory conveyors are used especially within serial productions for the transport of diverse materials and parts for assembling. The desired oscillating movement is accomplished by electromagnetic exciting forces. The exciting force of this dynamic system actuates between the carrying element and the inertial mass. The inertial mass is fixed to the ground by an elastic constraint using a relatively stiff rubber spring. This elastic constraint ensures the conveyor’s stability and defines its position towards the assembly line, but does not meet relevant effective vibration isolation demands. One possible solution would be a vibratory conveyor air suspension as is being introduced below.

Cycle response characteristics research on a class of piecewise nonlinear elastic and damping double constraint system

Piecewise nonlinear constraint exists in various fields and it always affects the stability of a system. In order to realize the dynamic characteristic of the system constrained by these nonlinearity, we consider two kinds of typical piecewise nonlinear constraints under the dynamic conditions, and establish a dynamic model with double piecewise nonlinear constraint of elasticity and damping, according to the generalized dissipation Lagrange principle. An average method is used to solve the amplitude and frequency response of the system under a periodic external incentive. By a numerical simulation, we compare the time domain responses under different piecewise nonlinear elastic constraints. The results show that the stronger the piecewise nonlinear elastic constraint, the more obvious the piecewise nonlinear damping constraint is. We also compare the bifurcation responses under different piecewise nonlinear damping constraints, the results show that the chaos state will emerge in an enlarged scope with the increase of the piecewise nonlinear damping coefficient, and threaten the stability of the system. The dynamic evolution process of the system is shown by the phase diagrams and Poincaré sections under the corresponding constraint conditions. By comparing the amplitude-frequency characteristics of the system under different constraint conditions, we obtain the response characteristic of the system and its change rule with the piecewise nonlinear constraints. By comparing and analyzing the amplitude-frequency characteristics under the piecewise nonlinear elastic and piecewise nonlinear damping constraint, we obtain the law of system stability influenced by different nonlinear factors, and the interaction relationship between the two piecewise nonlinear constraints.

Study on the Performance of Pneumatic Planar Bending Flexible Joint with Different Boundary Conditions

In this paper, we develop a new type planar bending flexible joint adopting rubber tube and elastic constraint components. When supplied the air pressure, the joint can elongate in axial direction or bend arbitrarily in the planar. Experiments study on contrast of mechanical character of planar bending flexible joint in different restrained conditions are done on the static experimental device, and the influence of the structure of constraints ring on the elongation and the bending angle of the joint. The experiments show that the deformation of the joint with arc-shaped restraints ring significantly larger than the joint with cylindrical-shaped restraints ring.

Moving Force-Induced Vibration of a Rotating Beam with Elastic Boundary Conditions

In this paper, an analytical technique, the so-called Fourier Spectral method (FSM), is extended to the vibration analysis of a rotating Rayleigh beam considering the gyroscopic effect. The model presented can have arbitrary boundary conditions specified in terms of elastic constraints in the translations and rotations or even in terms of attached lumped masses and inertias. Each displacement function is universally expressed as a linear combination of a standard Fourier cosine series and several supplementary functions introduced to ensure and accelerate the convergence of the series expansion. Lagrange's equation is established for all the unknown Fourier coefficients viewed as a set of independent generalized coordinates. A numerical model is constructed for the rotating beam. First, a numerical example considering simply supported boundary conditions at both ends is calculated and the results are compared with those of a published paper to show the accuracy and convergence of the proposed model. Then, the method is applied to one real work piece structure with elastically supported boundary conditions updated from the modal experiment results including both the frequencies and mode shapes using the method of least squares. Several numerical examples of the updated model are studied to show the effects of some parameters on the dynamic characteristics of the work piece subjected to moving loads at different constant velocities.

Combined EoS and elastic constraints models to predict thermodynamic properties for systems involving semi-crystalline polyolefins

In the present study, an equation of state model (i.e., Sanchez–Lacombe equation of state-SL EoS) and an Activity coefficient model (i.e., UNIFAC-FV) are combined with elastic constraints models to assess the effect of polymer crystallinity on solubility of penetrants (e.g., α-olefins, diluents, light gases, etc.) in polyolefins (i.e., binary and ternary mixtures). It is shown that the predictive capabilities of the employed solubility models can be significantly improved when combined with corresponding models accounting for the elastic constraints effects on polymer chains (i.e., Michaels–Hausslein, Banaszak modification of Michaels–Hausslein). More specifically, it is illustrated that for the SL EoS, the fraction of elastically effective chains (f) is the only adjustable parameter which has to be considered to accurately predict the solubility of penetrants in semi-crystalline polyolefins at conditions of industrial importance. In addition, such a combined model results in reduction of the adjustable parameters (i.e., binary interaction parameters, kij), particularly in multi-component mixtures. It is also depicted that the parameter f is a function of polymer crystallinity and temperature in a way that f increases with increasing crystallinity and decreasing temperature. Moreover, it is demonstrated that the incorporation of elastic constraints models in UNIFAC-FV improves its predictive capabilities by about 25%. Finally, a comprehensive sensitivity analysis is carried out to investigate the effect of parameter f on the predictive capabilities of the SL-EoS combined with elastic constraints models.

A trial-and-error congestion pricing scheme for networks with elastic demand and link capacity constraints

This paper proposes a combination of trial-and-error congestion pricing schemes that have been studied in the literature. It not only considers the minimization of the total system cost but also addresses the capacity constraints. A two-level iteration method is proposed for solving the hybrid problem, in which the approximate subgradient projection method is used for the outer level iteration phase, and the partial linearization method is used for the inner level iteration phase. We prove the convergence of the two-level iteration method, under the condition that the subproblem for the inner level iteration is only solved approximately, which makes the method efficient and practical. A numerical example is presented to illustrate the application of the two-level iteration method to the trial-and-error congestion pricing scheme.

Cross-Layer Resource Allocation in Multi-interface Multi-channel Wireless Multi-hop Networks

In this paper, an analytical framework is proposed for the optimization of network performance through joint congestion control, channel allocation, rate allocation, power control, scheduling, and routing with the consideration of fairness in multi-channel wireless multihop networks. More specifically, the framework models the network by a generalized network utility maximization (NUM) problem under an elastic link data rate and power constraints. Using the dual decomposition technique, the NUM problem is decomposed into four subproblems - flow control; next-hop routing; rate allocation and scheduling; power control; and channel allocation - and finally solved by a low-complexity distributed method. Simulation results show that the proposed distributed algorithm significantly improves the network throughput and energy efficiency compared with previous algorithms.

Tightening elastic (n, 2)-torus knots

We present a theory for equilibria of elastic torus knots made of a single thin, uniform, homogeneous, isotropic, inextensible, unshearable rod of circular cross-section. The theory is formulated as a special case of an elastic theory of geometrically exact braids consisting of two rods winding around each other while remaining at constant distance. We introduce braid strains in terms of which we formulate a second-order variational problem for an action functional that is the sum of the rod elastic energies and constraint terms related to the inextensibility of the rods. The Euler-Lagrange equations for this problem, partly in Euler-Poincare form, yield a compact system of ODEs suitable for numerical solution. By solving an appropriate boundary- value problem for these equations we study knot equilibria as the dimensionless ropelength parameter is varied. We are particularly interested in the approach of the purely geometrical ideal (tightest) limit. For the trefoil knot the tightest shape we could get has a ropelength of 32.85560666, which is remarkably close to the best current estimate. For the pentafoil we find a symmetry-breaking bifurcation.

Designing electronic properties of two-dimensional crystals through optimization of deformations

One of the enticing features common to most of the two-dimensional (2D) electronic systems that, in the wake of (and in parallel with) graphene, are currently at the forefront of materials science research is the ability to easily introduce a combination of planar deformations and bending in the system. Since the electronic properties are ultimately determined by the details of atomic orbital overlap, such mechanical manipulations translate into modified (or, at least, perturbed) electronic properties. Here, we present a general-purpose optimization framework for tailoring physical properties of 2D electronic systems by manipulating the state of local strain, allowing a one-step route from their design to experimental implementation. A definite example, chosen for its relevance in light of current experiments in graphene nanostructures, is the optimization of the experimental parameters that generate a prescribed spatial profile of pseudomagnetic fields (PMFs) in graphene. But the method is general enough to accommodate a multitude of possible experimental parameters and conditions whereby deformations can be imparted to the graphene lattice, and complies, by design, with grapheneʼs elastic equilibrium and elastic compatibility constraints. As a result, it efficiently answers the inverse problem of determining the optimal values of a set of external or control parameters (such as substrate topography, sample shape, load distribution, etc) that result in a graphene deformation whose associated PMF profile best matches a prescribed target. The ability to address this inverse problem in an expedited way is one key step for practical implementations of the concept of 2D systems with electronic properties strain-engineered to order. The general-purpose nature of this calculation strategy means that it can be easily applied to the optimization of other relevant physical quantities which directly depend on the local strain field, not just in graphene but in other 2D electronic membranes.

Linear buckling predictions of unstiffened laminated composite cylinders and cones under various loading and boundary conditions using semi-analytical models

Semi-analytical models for the linear buckling analysis of unstiffened laminated composite cylinders and cones with flexible boundary conditions are presented. The Classical Laminated Plate Theory and the First-order Shear Deformation Theory are used in conjunction with the Donnell’s non-linear equations to derive the buckling equations. Axial, torsion and pressure loads can be applied individually or combined in the proposed models. The stiffness matrices are integrated analytically and for the conical shells an approximation is proposed to overcome non-integrable expressions. Comparisons with the literature show that the classical base functions available for axial compression cannot capture the buckling modes for non-orthotropic laminates. For torsion loads these classical shape functions do not catch the buckling modes even when applying the assumption of pure orthotropy, and it is shown how the proposed models correlate well with experimental data from the literature and finite element results. The use of elastic constraints at the boundaries allows the simulation of different boundary conditions in a versatile way and it is shown how those constants can be adjusted in order to change from one type of boundary condition to another.

Periodic-Doubling and Hopf Bifurcations of a Two-Degree-of-Freedom System with Elastic Constraints and Clearances

Based on the study of a dual component system with elastic constraints, the stability and local bifurcations of the soft-impacts system, such as piecewise property and singularity, was analyzed by using the Poincaré map and Runge-Kutta numerical simulation method. The routes from periodic motions to chaos, via Hopf bifurcation and period-doubling bifurcation, were investigated exactly. In the large constraint stiffness case, the period-doubling and Hopf bifurcation exist in the two-degree-of-freedom system with elastic constraints and clearances. The clearances of the system, stiffness and damping coefficient of the elastic constraints is the main reasons for influencing the chaotic motion. The steady 1-1-1 period orbits or 2-1-1 period orbits will exist within a wideband frequency range and the value of velocity will be higher when appropriate system parameters are chosen.

A series solution for the in-plane vibration analysis of orthotropic rectangular plates with non-uniform elastic boundary constraints and internal line supports

In this investigation, the free in-plane vibration analysis of orthotropic rectangular plates with non-uniform boundary conditions and internal line supports is performed with a modified Fourier solution. The exact solution for the problem is obtained using improved Fourier series method, in which both two in-plane displacements of the orthotropic rectangular plates are represented by a double Fourier cosine series and four supplementary functions, in the form of the product of a polynomial function and a single cosine series expansion, introduced to remove the potential discontinuities associated with the original displacement functions along the edges when they are viewed as periodic functions defined over the entire x–y plane. The unknown expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh–Ritz procedure. The change of the boundary conditions can be easily achieved by only varying the stiffness of the two sets of the boundary springs at the all boundary of the orthotropic rectangular plates without the need of making any change to the solutions. The excellent accuracy of the current result is validated by comparison with those obtained from other analytical approach as well as the finite element method (FEM). Numerical results are presented to illustrate the current method that is applied not only to the homogeneous boundary conditions but also to other interesting and practically important boundary restraints on free in-plane vibrations of the orthotropic rectangular plates, including varying stiffness of boundary springs, point supported, partially supported boundary conditions and internal line supports. In addition to this, the effects of locations of line supports are also investigated and reported. New results for free vibration of moderately orthotropic rectangular plates with various edge conditions and internal line supports are presented, which may be used for benchmarking of researchers in the field.

The elastic and plastic constraint parameters for three-dimensional problems

Fracture toughness and the in-plane and out-of-plane constraint effects are studied through experiments and computations for high-strength carbon steel 34ХН3МА. The subjects for the studies are single-edge-notched bend specimens under three-point bending and compact specimens under tension. Both types of specimens are of non-standard configuration because the specimen thickness-to-width ratio was varied in the range of 0.1–1.0, and the relative crack length was changed in the range of 0.24–0.64. Characterization of the constraint effects was performed using the non-singular T-stresses, the local triaxiality parameter h, and the TZ and TZZ, factors of the stress-state in a 3D cracked body. For the particular geometries of the specimens considered, the numerical constant of the plastic stress field In and the plastic stress intensity factor distributions along the crack front are obtained as a function of the dimensionless crack length and the specimen thickness. It is further demonstrated that the plastic stress intensity factor accounting for the in-plane and out-of-plane constraint effects can be used to characterize the fracture resistance characteristics as a unified single parameter for a variety of specimen geometries.

Stretchable and transparent hydrogels as soft conductors for dielectric elastomer actuators

ABSTRACTA soft ionic conductor can serve as an artificial nerve in an artificial muscle. A polyacrylamide hydrogel is synthesized containing a hygroscopic salt, lithium chloride. Two layers of the hydrogel are used as ionic conductors to sandwich a dielectric elastomer and fabricate a highly stretchable and transparent actuator. When the two layers of the hydrogels are subject to a voltage, the actuator reduces its thickness and expands. An areal strain of 134% is demonstrated. The voltage‐strain curves are calculated by using a model that accounts for the elastic constraint of the hydrogel and the inhomogeneous deformation of the actuator. For actuators fabricated with the hydrogel of various thicknesses and with the dielectric elastomer of various prestretches, excellent agreements are found between experimental data and theoretical predictions. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014, 52, 1055–1060

SU‐D‐9A‐06: 3D Localization of Neurovascular Bundles Through MR‐TRUS Registration in Prostate Radiotherapy

Purpose:Erectile dysfunction (ED) is the most common complication of prostate‐cancer radiotherapy (RT) and the major mechanism is radiation‐induced neurovascular bundle (NVB) damage. However, the localization of the NVB remains challenging. This study's purpose is to accurately localize 3D NVB by integrating MR and transrectal ultrasound (TRUS) images through MR‐TRUS fusion.Methods:T1 and T2‐weighted MR prostate images were acquired using a Philips 1.5T MR scanner and a pelvic phase‐array coil. The 3D TRUS images were captured with a clinical scanner and a 7.5 MHz biplane probe. The TRUS probe was attached to a stepper; the B‐mode images were captured from the prostate base to apex at a 1‐mm step and the Doppler images were acquired in a 5‐mm step. The registration method modeled the prostate tissue as an elastic material, and jointly estimated the boundary condition (surface deformation) and the volumetric deformations under elastic constraint. This technique was validated with a clinical study of 7 patients undergoing RT treatment for prostate cancer. The accuracy of our approach was assessed through the locations of landmarks, as well as previous ultrasound Doppler images of patients.Results:MR‐TRUS registration was successfully performed for all patients. The mean displacement of the landmarks between the post‐registration MR and TRUS images was 1.37±0.42 mm, which demonstrated the precision of the registration based on the biomechanical model; and the NVB volume Dice Overlap Coefficient was 92.1±3.2%, which demonstrated the accuracy of the NVB localization.Conclusion:We have developed a novel approach to improve 3D NVB localization through MR‐TRUS fusion for prostate RT, demonstrated its clinical feasibility, and validated its accuracy with ultrasound Doppler data. This technique could be a useful tool as we try to spare the NVB in prostate RT, monitor NBV response to RT, and potentially improve post‐RT potency outcomes.