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At least 1,063 records · Page 59

In Situ Characterization of the Effect of Twin-Microstructure Interactions on {$1 0 \bar{1} 2$} Tension and {$1 0\bar {1} 1$} Contraction Twin Nucleation, Growth and Damage in Magnesium

Through in situ electron backscatter diffraction (EBSD) experiments, this paper uncovers dominant damage mechanisms in traditional magnesium alloys exhibiting deformation twinning. The findings emphasize the level of deleterious strain incompatibility induced by twin interaction with other deformation modes and microstructural defects. A double fiber obtained by plane-strain extrusion as a starting texture of AM30 magnesium alloy offered the opportunity to track deformation by EBSD in neighboring grains where some undergo profuse {$1 0\bar {1} 2$} twinning and others do not. For a tensile loading applied along extrusion transverse (ET) direction, those experiencing profuse twinning reveal a major effect of grain boundaries on non-Schmid behavior affecting twin variant selection and growth. Similarly, a neighboring grain, with its $\langle$c$\rangle$-axis oriented nearly perpendicular to tensile loading, showed an abnormally early nucleation of {$1 0\bar {1} 1$} contraction twins (2% strain) while the same {$1 0\bar {1} 1$} twin mode triggering under $\langle$c$\rangle$-axis uniaxial compression have higher value of critical resolved shear stress exceeding the values for pyramidal $\langle$c + a$\rangle$ dislocations. The difference in nucleation behavior of contraction vs. compression {$1 0\bar {1} 1$} twins is attributed to the hydrostatic stresses that promote the required atomic shuffles at the core of twinning disconnections.

36 MATERIALS SCIENCE↗

The effect of topography on the evolution of unstable disturbances in a baroclinic atmosphere

A two layer spectral quasi-geostrophic model is used to simulate the effects of topography on the equilibria, their stability, and the long term evolution of incipient unstable waves. The flow is forced by latitudinally dependent radiative heating. Dissipation is in the form of Rayleigh friction. An analytical solution is found for the propagating finite amplitude waves which result from baroclinic instability of the zonal winds when topography is absent. The appearance of this solution for wavelengths just longer than the Rossby radius of deformation and disappearance of ultra-long wavelengths is interpreted in terms of the Hopf bifurcation theory. Simple dynamic and thermodynamic criteria for the existence of periodic Rossby solutions are presented. A Floquet stability analysis shows that the waves are neutral. The nature of the form drag instability of high index equilibria is investigated. The proximity of the equilibrium shear to a resonant value is essential for the instability, provided the equilibrium occurs at a slightly stronger shear than resonance.

Clark, J. H. E.↗

Transient Creep of a Composite Lower Crust: Constitutive Theory - 1

A composite model is proposed to describe the time-dependent response of the Earth's lower crust. The motivation for such it model is twofold: First, new observations of widespread postseismic deformation indicate that the deep continental crust responds viscoelastically, having both long-and short-term decay times. Second, by any number of observationally based rationales, the lower crust is compositionally and structurally heterogeneous over many length scales. For heterogeneities that have much smaller characteristic lengths than the minimum deformation wavelength of interest, the aggregate rheology can be described by composite media theory. For wavelengths of the order of the thickness of the lower crust (approx. = 25-40 km) and larger, composite theory may be applied to heterogeneities that are smaller than about several hundred meters, or equivalent to the vertical extent of a thick lower crustal mylonitic shear zone. The composite media theory developed here is constructed using both Eshelhy-Mori-Tanaka theory for aligned generalized spheroidal inclusions and a generalized self-consistent method. The inclusions and matrix are considered to be Maxwellian viscoelastic: a rheology that is consistent with past homogeneous models of postseismic stress relaxation. The composite theory presented here introduces a transient response to a suddenly imposed stress field which does not appear in homogeneous Maxwell models. Analytic expressions for the amplitude and duration of the transient and for the effective long-and short-term viscosities of the composite are given which describe the sensitivity to inclusion concentration (phi), to shape, and to ratio of inclusion-to-matrix viscosity (R).

Ivins, Erik R.↗

Method for Estimating Thread Strength Reduction of Damaged Parent Holes with Inserts

During normal assembly and disassembly of bolted-joint components, thread damage and/or deformation may occur. If threads are overloaded, thread damage/deformation can also be anticipated. Typical inspection techniques (e.g. using GO-NO GO gages) may not provide adequate visibility of the extent of thread damage. More detailed inspection techniques have provided actual pitch-diameter profiles of damaged-hardware holes. A method to predict the reduction in thread shear-out capacity of damaged threaded holes has been developed. This method was based on testing and analytical modeling. Test samples were machined to simulate damaged holes in the hardware of interest. Test samples containing pristine parent-holes were also manufactured from the same bar-stock material to provide baseline results for comparison purposes. After the particular parent-hole thread profile was machined into each sample a helical insert was installed into the threaded hole. These samples were tested in a specially designed fixture to determine the maximum load required to shear out the parent threads. It was determined from the pristine-hole samples that, for the specific material tested, each individual thread could resist an average load of 3980 pounds. The shear-out loads of the holes having modified pitch diameters were compared to the ultimate loads of the specimens with pristine holes. An equivalent number of missing helical coil threads was then determined based on the ratio of shear-out loads for each thread configuration. These data were compared with the results from a finite element model (FEM). The model gave insights into the ability of the thread loads to redistribute for both pristine and simulated damage configurations. In this case, it was determined that the overall potential reduction in thread load-carrying capability in the hardware of interest was equal to having up to three fewer threads in the hole that bolt threads could engage. One- half of this potential reduction was due to local pitch-diameter variations and the other half was due to overall pitch-diameter enlargement beyond Class 2 fit. This result was important in that the thread shear capacity for this particular hardware design was the limiting structural capability. The details of the method development, including the supporting testing, data reduction and analytical model results comparison will be discussed hereafter.

Johnson, David L.↗

Transverse cracking and stiffness reduction in composite laminates

A study of transverse cracking mechanism in composite laminates is presented using a singular hybrid finite element model. The model provides the global structural response as well as the precise local crack-tip stress fields. An elasticity basis for the problem is established by employing Lekhnitskii's complex variable potentials and method of eigenfunction expansion. Stress singularities associated with the transverse crack are obtained by decomposing the deformation into the symmetric and antisymmetric modes and proper boundary conditions. A singular hybrid element is thereby formulated based on the variational principle of a modified hybrid functional to incorporate local crack singularities. Axial stiffness reduction due to transverse cracking is studied. The results are shown to be in very good agreement with the existing experimental data. Comparison with simple shear lag analysis is also given. The effects of stress intensity factors and strain energy density on the increase of crack density are analyzed. The results reveal that the parameters approach definite limits when crack densities are saturated, an evidence of the existence of characteristic damage state.

Yuan, F. G.↗

Fluorescence-coupled micropipette aspiration assay to examine calcium mobilization caused by red blood cell mechanosensing

Abstract Mechanical stimuli such as tension, compression, and shear stress play critical roles in the physiological functions of red blood cells (RBCs) and their homeostasis, ATP release, and rheological properties. Intracellular calcium (Ca 2+ ) mobilization reflects RBC mechanosensing as they transverse the complex vasculature. Emerging studies have demonstrated the presence of mechanosensitive Ca 2+ permeable ion channels and their function has been implicated in the regulation of RBC volume and deformability. However, how these mechanoreceptors trigger Ca 2+ influx and subsequent cellular responses are still unclear. Here, we introduce a fluorescence-coupled micropipette aspiration assay to examine RBC mechanosensing at the single-cell level. To achieve a wide range of cell aspirations, we implemented and compared two negative pressure adjusting apparatuses: a homemade water manometer (− 2.94 to 0 mmH 2 O) and a pneumatic high-speed pressure clamp (− 25 to 0 mmHg). To visualize Ca 2+ influx, RBCs were pre-loaded with an intensiometric probe Cal-520 AM, then imaged under a confocal microscope with concurrent bright-field and fluorescent imaging at acquisition rates of 10 frames per second. Remarkably, we observed the related changes in intracellular Ca 2+ levels immediately after aspirating individual RBCs in a pressure-dependent manner. The RBC aspirated by the water manometer only displayed 1.1-fold increase in fluorescence intensity, whereas the RBC aspirated by the pneumatic clamp showed up to threefold increase. These results demonstrated the water manometer as a gentle tool for cell manipulation with minimal pre-activation, while the high-speed pneumatic clamp as a much stronger pressure actuator to examine cell mechanosensing directly. Together, this multimodal platform enables us to precisely control aspiration and membrane tension, and subsequently correlate this with intracellular calcium concentration dynamics in a robust and reproducible manner.

Wang, Haoqing↗

Combining New Satellite Tools and Models to Examine Role of Mesoscale Interactions in Formation and Intensification of Tropical Cyclones

The objective of this research is to start filling the mesoscale gap to improve understanding and probability forecasts of formation and intensity variations of tropical cyclones. Sampling by aircraft equipped to measure mesoscale processes is expensive, thus confined in place and time. Hence we turn to satellite products. This paper reports preliminary results of a tropical cyclone genesis and early intensification study. We explore the role of mesoscale processes using a combination of products from TRMM, QuikSCAT, AMSU, also SSM/I, geosynchronous and model output. Major emphasis is on the role of merging mesoscale vortices. These initially form in midlevel stratiform cloud. When they form in regions of lowered Rossby radius of deformation (strong background vorticity) the mesoscale vortices can last long enough to interact and merge, with the weaker vortex losing vorticity to the stronger, which can then extend down to the surface. In an earlier cyclongenesis case (Oliver 1993) off Australia, intense deep convection occurred when the stronger vortex reached the surface; this vortex became the storm center while the weaker vortex was sheared out as the major rainband. In our study of Atlantic tropical cyclones originating from African waves, we use QuikSCAT to examine surface winds in the African monsoon trough and in the vortices which move westward off the coast, which may or may not undergo genesis (defined by NHC as reaching TD, or tropical depression, with a west wind to the south of the surface low). We use AMSU mainly to examine development of warm cores. TRMM passive microwave TMI is used with SSM/I to look at the rain structure, which often indicates eye formation, and to look at the ice scattering signatures of deep convection. The TRMM precipitation radar, PR, when available, gives precipitation cross sections. So far we have detailed studies of two African-origin cyclones, one which became severe hurricane Floyd 1999, and the other reached TD2 in June 2000 and then died out. The atmosphere off West African is dry and stable. It becomes less so between June and September, as the SST and convection heat up. QuikSCAT shows the African monsoon trough and shear zone extend westward over the ocean to nearly 30 degrees West. The evidence is strong that the two cyclones had in common multiple midlevel mergers, which extended to the surface keeping the surface vortex strong. These continued until both systems were designated TD's by NHC. In the June 2000 case, the main reason for failure was the lower SST and dry, stable atmosphere. This is shown by the comparison of the equivalent potential temperature maps and profiles with those from pre-Floyd. In the vortex which became Floyd, QuikSCAT shows continuous importation of high theta e (warm, moist) air from the south. From September 2-8, this air flowed around the vortex center, building up a high theta-e pool to the north. Then late on September 9, a 100-km wide jet of high theta-e air penetrated the vortex core, a major convective burst' was observed, and an intensifying, more elevated warm core was seen on AMSU. Rapid pressure fall and wind intensification were underway by 0000 UTC on September 10. Floyd became a Hurricane at 1200 UTC on Sept 10, 1999, with successive convective bursts running the hurricane thermodynamic engine by intensifying the warm core. TD2 was a strong African vortex, sustained by moderate convection (up to about 12.5 km) offshore of Africa. It peaked on June 23, showing an apparent "eye" on passive microwave composites. However, it could not assemble the ingredients for a convective burst. Thus it failed to get the thermodynamic hurricane engine going before it moved too far west of the region of lowered Rossby radius. By June 26, cloud systems were dying out. On June 25, a surface vortex was no longer seen on QuikSCAT, although one continued above the surface on model profiles until June 27. One of our main findings so far is showing the role of the mesoscale vortex interactions in sustaining some African vortices far out in to the mid Atlantic, where under adequate thermal/moisture conditions the hurricane heat engine can sometimes be started. We are working on similar studies of Cindy and Irene 1999. Cindy illustrates a case of wind shear working against an early-stage hurricane heat engine, while Irene formed from a Caribbean wave. An enormous value of combinations of satellite tools is that tropical cyclones can be studied in all parts of the global oceans where they occur. Detailed studies like ours are labor intensive but many statistical studies can be based on physical postulates developed. There are other new tools such as MODIS on TERRA of the Earth Observing System (EOS) which can be used to study the microphysics of tropical cyclones world wide, in particular to investigate the presence of mixed phase and the impact of atmospheric aerosols on the hydrometeor structure and rainfall from tropical cyclones.

Simpson, Joanne↗

Contrasts in Sea Ice Formation and Production in the Arctic Seasonal and Perennial Ice Zones

Four years (1997-2000) of RADARSAT Geophysical Processor System (RGPS) data are used to contrast the sea ice deformation and production regionally, and in the seasonal (SIZ) and perennial (PIZ) ice zones. Ice production is of seasonal ice in openings during the winter. 3-day estimates of these quantities are provided within Lagrangian elements initially 10 km on a side. A distinct seasonal cycle is seen in both zones with these estimates highest in the late fall and with seasonal minimums in the mid-winter. Regional divergence over the winter could be up to 30%. Spatially, the highest deformation is in the SIZ north of coastal Alaska. Both ice deformation and production are higher in the SIZ: deformation-related ice production in the SIZ (approx.0.5 m) is 1.5-2.3 times that of the PIZ (approx.0.3 m) - this is connected to ice strength and thickness. Atmospheric forcing and boundary layer structure contribute to only the seasonal and interannual variability. Seasonal ice growth in ice fractures accounts for approx.25-40% of the total ice production of the Arctic Ocean. By itself, this deformation-ice production relationship could be considered a negative feedback when thickness is perturbed. However, the overall effect on ice production in the face of increasing seasonal and thinner/weaker ice coverage could be modified by: local destabilization of the water column promoting overturning of warmer water due to increased brine rejection; and, the upwelling of the pynocline associated with increased occurrence of large shear motion in sea ice.

Kwok, R.↗

The structure and migration of twin boundaries in tetragonal β -Sn: An application of machine learning based interatomic potentials

Although atomistic simulations have contributed significantly to our understanding of twin boundary structure and migration in metals and alloys with hexagonal close packed (HCP) crystal structures, few direct atomistic studies of twinning have been conducted for other types of low symmetry materials, in large part due to a lack of reliable interatomic potentials. In this work, we examine twin boundary structure and migration in a tetragonal material, β-Sn, comparing high resolution Transmission Electron Microscopy (TEM) images of deformation twins in β-Sn to the results of direct atomistic simulations using multiple interatomic potentials. ML-based potentials developed in this work are found to give results consistent with our experimental data, revealing faceted twin boundary structures formed by the nucleation and motion of twinning disconnections. We use bicrystallographic methods in combination with atomistic simulations to analyze the structure, energy and shear coupled migration of observed twin facets in β-Sn. In analogy to Prismatic-Basal (PB/BP) interfaces in HCP metals, we discover low energy asymmetric Prismatic-A-plane (PA/AP) interfaces important to twin growth in β-Sn. Finally, a Moment Tensor Potential (MTP) and Rapid Artificial Neural Network (RANN) interatomic potential suitable for studying twinning and phase transformations in Sn are made publicly available as part of this work.

36 MATERIALS SCIENCE↗

Modelling yield cap evolution in sandstone based on brittle creep experiments

The Zenifim Formation is being considered as a potential disposal formation for a deep borehole nuclear repository concept in Israel. Site selection and repository construction are intended to ensure that waste is separated from circulating groundwater, but long-term deformation of the wellbore could potentially create fluid flow pathways. To understand how time-dependent rock strength could affect wellbore stability, here we conducted creep tests under low to moderate confining pressures on retrieved core from the Zenifim formation. During creep, samples strain slowly as gradual damage accumulation progressively weakens the samples. Failure eventually occurred through the near-instantaneous formation of a shear fracture. Experimental results were used to calibrate a continuum damage poro-elastic model for sandstones. The calibrated damage-poro-elastic model successfully simulates different types of loading experiments including quasi-static and creep. The state of strain in experiments is close to yield during loading as the yield cap continuously evolves with damage accumulation. For creep tests, most damage occurs during triaxial loading. Minor damage accumulation occurs under constant load until the final stage of creep, where damage accelerates and promotes unstable fracturing.

58 GEOSCIENCES↗

A unified finite strain gradient-enhanced micropolar continuum approach for modeling quasi-brittle failure of cohesive-frictional materials

Here, in this work, a novel framework for modeling quasi-brittle crack propagation and shear band dominated failure of cohesive-frictional materials like concrete, mortar, rock, tough ceramics, energetic materials, but also granular materials like sands or powders in terms of a unified continuum approach is proposed. It is based on a combination of the gradient-enhanced continuum with gradients of internal variables for representing quasi-brittle cracking, and the micropolar continuum, accounting for the deformation of the microstructure. For developing the gradient-enhanced micropolar framework, the set of balance equations and the kinematic relations are derived, and the constitutive relations are established in a general manner. The framework is formulated in a geometrically exact setting, based on the thermodynamically sound theory of hyperelasto-plasticity, and the numerical implementation by means of the finite element method is discussed. For assessing the approach, realizations of this new approach in terms of constitutive models for particular materials are developed. They are applied to numerical benchmark examples, investigating various loading conditions, and the obtained results are validated by means of a comparison with experiments from the literature.

36 MATERIALS SCIENCE↗

Single Crystal Plasticity Model with Deformation Twinning for the High Rate Deformation of β-HMX

Deformation twinning is an active deformation mechanism during loading along certain crystallographic directions of β-cyclotetramethylene tetranitramine (β-HMX). In this work, a finite strain thermomechanical model is extended to include twinning as a deformation mechanism in addition to plastic slip. The stress is derived from the free energy expression including a term representing the equation of state. The crystal plasticity framework is used to divide the total strain into inelastic and elastic component, where the elastic part is used in the expression for the free energy. The twin systems are treated as pseudo slip systems and the shear rate on the twin systems is evaluated in terms of the twin resistance and the projection of the stress tensor. The model parameters were calibrated against a set of plate impact experiments performed on β-HMX by Dick et al. The remaining plate impact experiments are used to evaluate the predictive capability of the model. The quality of the model fits and predictions is discussed from a physical and modeling perspective. Particularly, the role of twin modeling on results is highlighted. Finally, the model is used to explore the relationship between the propensity for twinning and crystal orientation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Wrinkling Phenomena of Thin Flat Plates Subjected to Shear Stresses

This report covers a series of tests on thin flat elastic strips restrained at two parallel edges and subjected to shear by conversely directed stresses. Theoretical treatments, particularly those of Lilly, Southwell and Skan, and Timoshenko are briefly outlined. The problem to be solved by these tests was to find out whether, and to what extent the conditions and assumptions upon which the calculations are based are complied with in the tests. Three materials were used: celluloid, duralumin, brass. Owing to the high elastic deformability of celluloid, it was not only possible to observe the beginning but also to ascertain the type of deflection. The test data on celluloid was affirmed by the experiments with duralumin and brass.

Bollenrath, F↗

Cyclic strain is a weak inducer of prostacyclin synthase expression in bovine aortic endothelial cells

Recent studies indicate that hemodynamic forces such as cyclic strain and shear stress can increase prostacyclin (PGI2) secretion by endothelial cells (EC) but the effect of these forces on prostacyclin synthase (PGIS) gene expression remains unclear and is the focus of this study. Bovine aortic EC were seeded onto type I collagen coated flexible membranes and grown to confluence. The membranes and attached EC were subjected to 10% average strain at 60 cpm (0.5 sec deformation alternating with 0.5 sec relaxation) for up to 5 days. PGIS gene expression was determined by Northern blot analysis and protein level by Western blot analysis. The effect of cyclic strain on the PGIS promoter was determined by the transfection of a 1-kb human PGIS gene promoter construct coupled to a luciferase reporter gene into EC, followed by determination of luciferase activity. PGIS gene expression increased 1.7-fold in EC subjected to cyclic strain for 24 hr. Likewise, EC transfected with a pGL3B-PGIS (-1070/-10) construct showed an approximate 1.3-fold elevation in luciferase activity in EC subjected to cyclic strain for 3, 4, 8, and 12 hr. The weak stimulation of PGIS gene expression by cyclic strain was reflected in an inability to detect alterations in PGIS protein levels in EC subjected to cyclic strain for as long as 5 days. These data suggest that strain-induced stimulation of PGIS gene expression plays only a minor role in the ability of cyclic strain to stimulate PGI2 release in EC. These findings coupled with our earlier demonstration of a requisite addition of exogenous arachidonate in order to observe strain-induced PGI2 release, implicates a mechanism that more likely involves strain-induced stimulation of PGIS activity.

Non-NASA Center↗

Internal short circuit and failure mechanisms of lithium-ion pouch cells under mechanical indentation abuse conditions: An experimental study

Electromechanical structural integrity and thermal stability dictate the safety performance of lithium-ion batteries. Progressive deformation and failure across microscopic and macroscopic lengths scales that are responsible for internal short circuit (ISC) in lithium-ion cells under mechanical abuse conditions remains elusive. In this study, a series of indentation tests were conducted on lithium-ion cells with different capacities up to the occurrence of ISC. The external response and internal configuration of these cells were investigated. It is discovered that cells with different capacities and state of charges exhibited different behaviors. Maximum temperature, which is often regarded as the most important parameter related to thermal runaway (TR), varied considerably due to the complicated contact configurations. X-ray computed tomography (XCT) showed that ISC was a collective result of shear band or other strain-localization modes in the electrode assembly, shear offsets in the granular coatings of electrodes, and the accompanying ductile fracture in the metal foils. We believe that the irregular strain-localization modes (kinks, cusps, and buckles), radical mismatches in mechanical properties of different layers, and geometric features of the indenter eventually lead to the tearing/puncture of cell separator at various locations. Furthermore, the results could provide useful guidance for the micromechanical modeling of lithium-ion cells.

25 ENERGY STORAGE↗

Mechanics of Granular Materials (MGM)

The constitutive behavior of uncemented granular materials such as strength, stiffness, and localization of deformations are to a large extend derived from interparticle friction transmitted between solid particles and particle groups. Interparticle forces are highly dependent on gravitational body forces. At very low effective confining pressures, the true nature of the Mohr envelope, which defines the Mohr-Coulomb failure criterion for soils, as well as the relative contribution of each of non-frictional components to soil's shear strength cannot be evaluated in terrestrial laboratories. Because of the impossibility of eliminating gravitational body forces on earth, the weight of soil grains develops interparticle compressive stresses which mask true soil constitutive behavior even in the smallest samples of models. Therefore the microgravity environment induced by near-earth orbits of spacecraft provides unique experimental opportunities for testing theories related to the mechanical behavior of terrestrial granular materials. Such materials may include cohesionless soils, industrial powders, crushed coal, etc. This paper will describe the microgravity experiment, 'Mechanics of Granular Materials (MGM)', scheduled to be flown on Space Shuttle-MIR missions. The paper will describe the experiment's hardware, instrumentation, specimen preparation procedures, testing procedures in flight, as well as a brief summary of the post-mission analysis. It is expected that the experimental results will significantly improve the understanding of the behavior of granular materials under very low effective stress levels.

Alshibli, Khalid A.↗

Experiment 5: Science and Technology of Surface Controlled Oscillations: Report on USML-2 Results

Minuscule amounts (e.g., 1 part in 10,000) of a surface-active material in a liquid can drastically affect the surface behavior of the liquid, influencing how the material flows and mixes with other liquid and solid materials. In many respects, the science of surfactants has been empirical, with trial and error dominating over the ability to predict how surfactant type and concentration influence surface behavior. A program for the modeling of surfactant behavior has been established at Yale. This program combines experimental work performed both on the ground and in space, and theoretical and numerical modeling. By levitating a drop of liquid in air, away from solid container surfaces, and by manipulating the drop with acoustic radiation forces, we have been able to establish idealized conditions for surface behavior studies. The primary experiments involve the study of the free oscillations of initially deformed drops. In STS-73, the USML-2 mission of the Space Shuttle, we performed the following measurements: 1) the oscillation of a spherical drop in its quadrupole mode; 2) the oscillation of a drop about a deformed (oblate) shape; 3) the slow static squeezing of the drop from spherical to nearly flat; and 4) the superoscillations of drops when the radiation forces maintaining the drop in a flattened state are suddenly reduced. Analytic and numerical studies have enabled us to understand the physics of these oscillations and to extract material properties such as the dynamic surface tension and the surface viscosities (shear and dilatational). The relation to ground-based studies is essential, because the knowledge and understanding gleaned from our space studies enable us to interpret ground-based data.

Apfel, Robert E.↗

Three-Dimensional Postbuckling Analysis of Curved Beams

Presented here is a method of solving highly flexible curved beam undergoing huge static or quasi-static deformations. A geometrically exact beam theory based on the use of Jaumann stresses and strains and exact coordinate transformation is presented in terms of 17 first-order ordinary differential equations, and a multiple shooting method is used to solve the corresponding nonlinear two-point boundary value problems. The geometrically exact beam theory accounts far large rotations, large displacements, initial curvatures, extensionality, and transverse shear strains. Four examples are used to demonstrate this method, including a rotating clamped-free beam under the influence of gravity and centrifugal forces, an L-frame subjected to an in-plane tip load, a circular arch subjected to a concentrated load, and a clamped-hinged helical spring subjected to an axial displacement. Results show that the combination of the multiple shooting method and the geometrically exact beam theory works very well. Moreover, the obtained numerically exact solutions can be used to verify the accuracy of nonlinear finite element codes for nonlinear analysis of complex structures.

Pai, P. Frank↗