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This device is characterized by an elongated body having predetermined elastic properties. An applied tensile force of any magnitude, within a given range, imparts to the body an elongation of a predetermined length. The magnitude of applied tensile force is indicated as a function of the angular motion afforded the threaded sleeve mounted on the body.
The effect of force field type on the predicted elastic properties of a polyimide is examined using a multiscale modeling technique. Molecular Dynamics simulations are used to predict the atomic structure and elastic properties of the polymer by subjecting a representative volume element of the material to bulk and shear finite deformations. The elastic properties of the polyimide are determined using three force fields: AMBER, OPLS-AA, and MM3. The predicted values of Young s modulus and shear modulus of the polyimide are compared with experimental values. The results indicate that the mechanical properties of the polyimide predicted with the OPLS-AA force field most closely matched those from experiment. The results also indicate that while the complexity of the force field does not have a significant effect on the accuracy of predicted properties, small differences in the force constants and the functional form of individual terms in the force fields determine the accuracy of the force field in predicting the elastic properties of the polyimide.
Control-configured vehicle technology has increased the demand for detailed analysis of dynamic stability and control, handling and ride qualities, and control system dynamics at the early stages of preliminary design and development. For these early analyses an approximate, but reasonably accurate, set of equations of motion for elastic airplanes is needed. Such a formulation is developed for the lateral dynamics of elastic airplanes. It makes use of rigid-body aerodynamic stability derivatives and the antisymmetric elastic mode shapes and frequencies in formulating the forces and moments due to elastic motion. Verification of accuracy was made by comparison with B-1 airplane dynamics obtained by other methods. Frequencies and damping ratios of the coupled modes agree acceptably well with four antisymmetric elastic modes included.
We modify the traditional linear-elastic field of an edge dislocation. The modifications stem from symmetry and energy requirements imposed in terms of embedded (deformed) coordinates. These requirements are satisfied if a line force is added to the dislocation field. The modification to the stress field is expressed by coefficients that are a function only of Poisson’s ratio. Qualitatively, the field of the dislocation is increased in the glide direction and decreased in the climb direction. There are small changes to the field of a screw dislocation that do not entail the addition of a line force. Effects of nonlinearity, anisotropic elasticity, and image forces are briefly considered.
The aim of this project is to investigate the closure and reopening of lung airways due to surface tension forces, coupled with airway elasticity. Airways are liquid-lined, flexible tubes and closure of airways can occur by a Rayleigh instability of the liquid lining, or an instability of the elastic support for the airway as the surface tension of the air-liquid interface pulls the tube shut, or both. Regardless of the mechanism, the airway is closed because the liquid lining has created a plug that prevents axial gas exchange. In the microgravity environment, surface tension forces dominate lung mechanics and would lead to more prevalent, and more uniformly distributed air-way closure, thereby creating a potential for respiratory problems for astronauts. Once closed the primary option for reopening an airway is by deep inspiration. This maneuver will pull the flexible airways open and force the liquid plug to flow distally by the incoming air stream. Airway reopening depends to a large extent on this plug flow and how it may lead to plug rupture to regain the continuity of gas between the environment and the alveoli. In addition to mathematical modeling of plug flows in liquid-lined, flexible tubes, this work has involved benchtop studies of propagating liquid plugs down tube networks that mimic the human airway tree. We have extended the work to involve animal models of liquid plug propagation in rat lungs. The liquid is radio-opaque and x-ray video imaging is used to ascertain the movement and distribution of the liquid plugs so that comparisons to theory may be made. This research has other uses, such as the delivery of liquids or drugs into the lung that may be used for surfactant replacement therapy or for liquid ventilation.
Understanding stress distributions in solid materials is complicated by the fact that most materials are polycrystalline in nature, with each crystal having an elastically anisotropic reaction to force. This study is to gain a better understanding on how external forces placed on a polycrystal are related to internal reactions within and between the grains. The hypothesis is that the stress distribution in porous to fully dense materials are self-organized based on strong contacts between and within the individual grains created by force chains. Force chains, commonly known in loaded granular materials, and could be the phenomenon that connect micro to macro deformation. Scale bridging measurements conducted through Raman spectroscopy, Atomic Force Microscopy, and Digital Image Correlation will be used to create stress maps, modulus maps, and elastic strain maps across a variety of geological and pharmaceutical polycrystals. When possible, the resulting maps will be compared to current homogenization schemes and a full field models. Finite element modeling will be used to assess whether the patterning seen in the experimental map is a reasonable approximation based on the orientation data of the samples used. A minimum of three publications is projected to be accomplished focusing each on a different method to experimentally test and analyze stress distributions.
Analytic model resembling thick walled ellipsoid of revolution incorporating three dimensional shape of human left ventricle and ventricular wall thickness effects
The effect of differentiation on the transverse mechanical properties of mammalian myocytes was determined by using atomic force microscopy. The apparent elastic modulus increased from 11.5 +/- 1.3 kPa for undifferentiated myoblasts to 45.3 +/- 4.0 kPa after 8 days of differentiation (P < 0.05). The relative contribution of viscosity, as determined from the normalized hysteresis area, ranged from 0.13 +/- 0.02 to 0.21 +/- 0.03 and did not change throughout differentiation. Myosin expression correlated with the apparent elastic modulus, but neither myosin nor beta-tubulin were associated with hysteresis. Microtubules did not affect mechanical properties because treatment with colchicine did not alter the apparent elastic modulus or hysteresis. Treatment with cytochalasin D or 2,3-butanedione 2-monoxime led to a significant reduction in the apparent elastic modulus but no change in hysteresis. In summary, skeletal muscle cells exhibited viscoelastic behavior that changed during differentiation, yielding an increase in the transverse elastic modulus. Major contributors to changes in the transverse elastic modulus during differentiation were actin and myosin.
The propagation of vibrational energy in bulk, torsional, and flexural modes, in electrically conducting media can undergo strong attenuation if subjected to high magnetic fields in certain spatial arrangements. The reasons for this are induced Eddy currents which are generated by the volume elements in the media moving transversally to the magnetic field at acoustic velocities. In magnetic fields achievable with superconductors, the non-conservative (dissipative) forces are compared to the elastic and inertial forces for most metals. Strong dissipation of vibrational energy in the form of heat takes place as a result. A simplified theory is presented based on engineering representations of electrodynamics, attenuation values for representative metals are calculated, and problems encountered in formulating a generalized theory based on electrodynamics of moving media are discussed. General applications as well as applications specific to maglev are discussed.
In elasticity, the method of forces, wherein stress parameters are considered as the primary unknowns, is known as the Beltrami-Michell formulation (BMF). The existing BMF can only solve stress boundary value problems; it cannot handle the more prevalent displacement of mixed boundary value problems of elasticity. Therefore, this formulation, which has restricted application, could not become a true alternative to the Navier's displacement method, which can solve all three types of boundary value problems. The restrictions in the BMF have been alleviated by augmenting the classical formulation with a novel set of conditions identified as the boundary compatibility conditions. This new method, which completes the classical force formulation, has been termed the completed Beltrami-Michell formulation (CBMF). The CBMF can solve general elasticity problems with stress, displacement, and mixed boundary conditions in terms of stresses as the primary unknowns. The CBMF is derived from the stationary condition of the variational functional of the integrated force method. In the CBMF, stresses for kinematically stable structures can be obtained without any reference to the displacements either in the field or on the boundary. This paper presents the CBMF and its derivation from the variational functional of the integrated force method. Several examples are presented to demonstrate the applicability of the completed formulation for analyzing mixed boundary value problems under thermomechanical loads. Selected example problems include a cylindrical shell wherein membrane and bending responses are coupled, and a composite circular plate.
Airborne observations using lightweight camera systems are desirable for a variety of applications. This system was contemplated as a method to provide a simple remote sensing aerial platform. Kites have been successfully employed for aerial observations, but have historically required natural wind or towing to become airborne. This new method negates this requirement, and widens the applicability of kites for carrying instrumentation. Applicability is primarily limited by the space available on the ground for launching. The innovation is a method for launching kites in low-wind or no-wind conditions. This method will enable instrumentation to be carried aloft using simple (or complex) kite-based systems, to obtain observations from an aerial perspective. This technique will provide access to altitudes of 100 meters or more over any area normally suited for kite flying. The duration of any observation is dependent on wind strength; however, the initial altitude is relatively independent. The system does not require any electrical or combustion-based elements. This technology was developed to augment local-scale airborne measurement capabilities suitable for Earth science research, agricultural productivity, and environmental observations. The method represents an extension of techniques often used in aeronautical applications for launching fixed-wing aircraft, such as sailplanes, using mechanical means not incorporated in the aircraft itself. The innovation consists of an elastic cord (for propulsive force), a tether extension (optional, for additional height), and the kite (instrumentation optional). Operation of the system is accomplished by fixing the elastic cord to ground (or equivalent), attaching the cord with/or without a tether extension to the kite, tensioning the system to store energy, and releasing the kite. The kite will climb until energy is dissipated.
An integrated, consistent analytical framework is developed for modeling the dynamics of elastic hypersonic flight vehicles. A Lagrangian approach is used in order to capture the dynamics of rigid-body motion, elastic deformation, fluid flow, rotating machinery, wind, and a spherical rotating earth model, and to account for their interactions with each other. A vector form of the force, moment and elastic-deformation equations is developed from Lagrange's equation; a useable scalar form of these equations is also presented. The appropriate kinematic equations are developed, and are presented in a useable form. A preliminary study of the significance of selected terms in the equations of motion is conducted. Using generic data for a single-stage-to-orbit vehicle, it was found that the Coriolis force can reach values of up to 6 percent of the vehicle weight, and that the forces and moments attributable to fluid-flow terms can be significant.
Forced vibration of circular cylindrical elastic shell partially filled with incompressible liquid and initially at rest in uniform gravitational field
An initially stressed rectangular plate is subjected to a transverse, time dependent load. The initial stress field is constant and parallel to two of the plate edges. The transverse load is uniformly distributed over a rectangular area, the sides of which are parallel to the sides of the plate. The problem is formulated within the framework of classical, three-dimensional elasticity theory, and an exact solution is obtained in series form. The case of static stability under pre-stress is also considered.
Many small animals use springs and latches to overcome the mechanical power output limitations of their muscles. Click beetles use springs and latches to bend their bodies at the thoracic hinge and then unbend extremely quickly, resulting in a clicking motion. When unconstrained, this quick clicking motion results in a jump. While the jumping motion has been studied in depth, the physical mechanisms enabling fast unbending have not. Here, we first identify and quantify the phases of the clicking motion: latching, loading, and energy release. We detail the motion kinematics and investigate the governing dynamics (forces) of the energy release. We use high-speed synchrotron X-ray imaging to observe and analyze the motion of the hinge’s internal structures of four Elater abruptus specimens. We show evidence that soft cuticle in the hinge contributes to the spring mechanism through rapid recoil. Using spectral analysis and nonlinear system identification, we determine the equation of motion and model the beetle as a nonlinear single-degree-of-freedom oscillator. Quadratic damping and snap-through buckling are identified to be the dominant damping and elastic forces, respectively, driving the angular position during the energy release phase. The methods used in this study provide experimental and analytical guidelines for the analysis of extreme motion, starting from motion observation to identifying the forces causing the movement. Here, the tools demonstrated here can be applied to other organisms to enhance our understanding of the energy storage and release strategies small animals use to achieve extreme accelerations repeatedly.
The purpose of this study was to examine the time course of change in soleus muscle fiber peak force (N), tension (P(sub 0), kN/sq m), elastic modulus (E(sub 0)), and force-pCa and stiffness - pCa relationships. After 1, 2, or 3 wk of Hindlimb Unloading (HU), single fibers were isolated and placed between a motor arm and a transducer, and fiber diameter, peak absolute force, P(sub 0), E(sub 0), and force-pCa and stiffness-pca relationships were characterized. One week of HU resulted in a significant reduction in fiber diameter (68 +/- 2 vs. 57 +/- 1 micrometer), force (3.59 +/- 0.15 vs. 2.19 +/- 0.12 x 10(exp -4) N), P(sub 0) (102 +/- 4 vs. 85 +/- 2 kN/sq m), and E(sub 0) (1.96 +/- 0.12 vs. 1.37 +/- 0.13 X 10(exp 7) N/sq m) and 2 wk of HU caused a further decline in fiber diameter (45 +/- 1 micrometer), force (1.31 +/- 0.06 x 10(exp -4) N), and E(sub 0)(0.96 +/- 0.09 x 10(exp 7) N/sq m). Although the mean fiber diameter and absolute force continued to decline through 3 wk of HU, P(sub 0) recovered to values not significantly different from control. The P(sub 0)/E(sub 0) ratio was significantly increased after 1 (5.5 +/- 0.3 to 7.1 +/- 0.6), 2, and 3 wk of HU, and the 2-wk (9.5 +/- 0.4) and 3-wk (9.4 +/- 0.8) values were significantly greater than the 1-wk values. The force-pCa and stiffness-pCa curves were shifted right- ward after 1, 2, and 3 wk of HU. At 1 wk of HU, the Ca(2+) sensitivity of isometric force, assessed by Ca(2+) concentration required for half-maximal force, was increased from the control value of 1.83 +/- 0.12 to 2.30 +/- 0.10 micrometers. In conclusion, after HU, the decrease in soleus fiber P(sub 0) can be explained by a reduction in the number of myofibrillar cross bridges per cross-sectional area. Our working hypothesis is that the loss of contractile protein reduces the number of cross bridges per cross-sectional area and increases the filament lattice spacing. The increased spacing reduces cross-bridge force and stiffness, but P(sub 0)/E(sub 0) increases because of a quantitatively greater effect on stiffness.
When layers of van der Waals materials are deposited via exfoliation or viscoelastic stamping, nanobubbles are sometimes created from aggregated trapped fluids. Though they can be considered a nuisance, nanobubbles have attracted scientific interest in their own right owing to their ability to generate large in-plane strain gradients that lead to rich optoelectronic phenomena, especially in the semiconducting transition metal dichalcogenides. Determination of the strain within the nanobubbles, which is crucial to understanding these effects, can be approximated using elasticity theory. However, the Föppl–von Kármán equations that describe strain in a distorted thin plate are highly nonlinear and often necessitate assuming circular symmetry to achieve an analytical solution. Here, we present an easily implemented numerical method to solve for strain tensors of nanobubbles with arbitrary symmetry in 2D crystals. The method only requires topographic information from atomic force microscopy and the Poisson ratio of the 2D material. We verify that this method reproduces the strain for circularly symmetric nanobubbles that have known analytical solutions. Finally, we use the method to reproduce the Grüneisen parameter of the E' mode for 1L-WS2 nanobubbles on template-stripped Au by comparing the derived strain with measured Raman shifts from tip-enhanced Raman spectroscopy, demonstrating the utility of our method for estimating localized strain in 2D crystals.
The plane-stress equations of linear elasticity are used in conjunction with those of the boundary element method to develop a novel curved, quadratic boundary element applicable to structures composed of anisotropic materials in a state of plane stress or plane strain. The curved boundary element is developed to solve two-dimensional, elastostatic problems of arbitrary shape, connectivity, and material type. As a result of the anisotropy, complex variables are employed in the fundamental solution derivations for a concentrated unit-magnitude force in an infinite elastic anisotropic medium. Once known, the fundamental solutions are evaluated numerically by using the known displacement and traction boundary values in an integral formulation with Gaussian quadrature. All the integral equations of the boundary element method are evaluated using one of two methods: either regular Gaussian quadrature or a combination of regular and logarithmic Gaussian quadrature. The regular Gaussian quadrature is used to evaluate most of the integrals along the boundary, and the combined scheme is employed for integrals that are singular. Individual element contributions are assembled into the global matrices of the standard boundary element method, manipulated to form a system of linear equations, and the resulting system is solved. The interior displacements and stresses are found through a separate set of auxiliary equations that are derived using an Airy-type stress function in terms of complex variables. The capabilities and accuracy of this method are demonstrated for a laminated-composite plate with a central, elliptical cutout that is subjected to uniform tension along one of the straight edges of the plate. Comparison of the boundary element results for this problem with corresponding results from an analytical model show a difference of less than 1%.