Response And Stability Of A Stochastic Beam-Column Using Stochastic Fem

A beam-column resting on continuous Winkler foundation and discrete elastic supports is considered. The beam-column is of variable cross-section and the variation of sectional properties along the axis of the beam-column is deterministic. Young's modulus, mass per unit length and distributed axial loadings of the beam-column have a stochastic distribution. The foundation stiffness coefficient of the Winkler model, the stiffnesses of discrete elastic supports, stiffnesses of end springs and the end thrust, are all considered as random parameters. The material property fluctuations and distributed axial loadings are considered to constitute independent, one-dimension uni-variate homogeneous real stochastic fields in space. The foundation stiffness coefficient, stiffnesses of the discrete elastic supports, stiffnesses of end springs and the end thrust are considered to constitute independent random variables. Static response, free vibration and stability behaviour of the beam-column are studied. Hamilton's principle is used to formulate the problem using stochastic FEM. Sensitivity vectors of the response and stability parameters are evaluated. Using these statistics of free vibration frequencies, mode shapes, buckling parameters, etc., are evaluated. A numerical example is given.

Stability of pargasite during ultrahigh-temperature metamorphism:A consequence of titanium and REE partitioning

Orthopyroxene-clinopyroxene-plagioclase needles and symplectite along the cleavage planes and grain boundaries of fluorine-bearing titanian-ferroan pargasite from the Highland Complex, Sri Lanka, are interpreted as evidence for dehydration melting at ultrahigh-temperature conditions. High Ti (up to 0.4 pfu) and F (XF up to 0.56) content in pargasite extends its stability to higher temperatures, and the composition indicates the dehydration melting reaction may take place at ultrahigh-temperatures (~950 °C) at a pressure around 10 kbar, close to peak metamorphic conditions. The increase of Ti content close to the grain boundaries and cleavage planes in pargasite indicates titanium partitioning from the melt during dehydration melting enhanced the stability of the mineral toward ultrahigh-temperature conditions. The REE content in the pargasite shows a similar behavior to that of titanium. The cores with no breakdown assemblage consist of low and flat REE concentrations with respect to the high and Eu-depleted rim. Clinopyroxene in symplectite and needle-shaped lamellae within the pargasite porphyroblasts have similar REE patterns with slightly low-concentrations relative to that of pargasite. In the breakdown assemblage, LREEs are partitioned mainly into plagioclase while the HREEs are partitioned into orthopyroxene. The REE enrichment in the pargasite rims signals their relative partitioning between pargasite rims and melt. Modeling of the partitioning of Ti and REEs associated with pargasite breakdown demonstrates that its stability is greatly enhanced at UHT conditions. This investigation implies that the stability of hydrous minerals such as amphibole can be extended to UHT conditions, and expands our knowledge of metamorphism in the lower crust.

The impact of wall shear stress and pressure drop on the stability of the atherosclerotic plaque

Rupture of vulnerable atheromatous plaque in the carotid and coronary arteries often leads to stroke and heart attack respectively. The mechanism of blood flow and plaque rupture in stenotic arteries is still not fully understood. A three dimensional rigid wall model was solved under steady state conditions and unsteady conditions by assuming a time-varying inlet velocity profile to investigate the relative importance of axial forces and pressure drops in arteries with asymmetric stenosis. Flow-structure interactions were investigated for the same geometry and the results were compared with those retrieved with the corresponding 2D cross-section structural models. The Navier-Stokes equations were used as the governing equations for the fluid. The tube wall was assumed hyperelastic, homogeneous, isotropic and incompressible. The analysis showed that the three dimensional behavior of velocity, pressure and wall shear stress is in general very different from that predicted by cross-section models. Pressure drop across the stenosis was found to be much higher than shear stress. Therefore, pressure may be the more important mechanical trigger for plaque rupture other than shear stress, although shear stress is closely related to plaque formation and progression.

Does calcium deposition play a role in the stability of atheroma? Location may be the key

Background: Rupture of vulnerable atheromatous plaque in the carotid and coronary arteries often leads to stroke and heart attack respectively. The role of calcium deposition and its contribution to plaque stability is controversial. This study uses both an idealized and a patient-specific model to evaluate the effect of a calcium deposit on the stress distribution within an atheromatous plaque. Methods: Using a finite-element method, structural analysis was performed on an idealized plaque model and the location of a calcium deposit within it was varied. In addition to the idealized model, in vivo high-resolution MR imaging was performed on 3 patients with carotid atheroma and stress distributions were generated. The individual plaques were chosen as they had calcium at varying locations with respect to the lumen and the fibrous cap. Results: The predicted maximum stress was increased by 47.5% when the calcium deposit was located in the thin fibrous cap in the model when compared with that in a model without a deposit. The result of adding a calcium deposit either to the lipid core or remote from the lumen resulted in almost no increase in maximal stress. Conclusion: Calcification at the thin fibrous cap may result in high stress concentrations, ultimately increasing the risk of plaque rupture. Assessing the location of calcification may, in the future, aid in the risk stratification of patients with carotid stenosis.

How critical is fibrous cap thickness to carotid plaque stability? A flow-plaque interaction model

Background and Purpose Acute cerebral ischemic events are associated with rupture of vulnerable carotid atheroma and subsequent thrombosis. Factors such as luminal stenosis and fibrous cap thickness have been thought to be important risk factors for plaque rupture. We used a flow-structure interaction model to simulate the interaction between blood flow and atheromatous plaque to evaluate the effect of the degree of luminal stenosis and fibrous cap thickness on plaque vulnerability. Methods A coupled nonlinear time-dependent model with a flow-plaque interaction simulation was used to perform flow and stress/strain analysis in a stenotic carotid artery model. The stress distribution within the plaque and the flow conditions within the vessel were calculated for every case when varying the fibrous cap thickness from 0.1 to 2 mm and the degree of luminal stenosis from 10% to 95%. A rupture stress of 300 kPa was chosen to indicate a high risk of plaque rupture. A 1-sample t test was used to compare plaque stresses with the rupture stress. Results High stress concentrations were found in the plaques in arteries with >70% degree of stenosis. Plaque stresses in arteries with 30% to 70% stenosis increased exponentially as fibrous cap thickness decreased. A decrease of fibrous cap thickness from 0.4 to 0.2 mm resulted in an increase of plaque stress from 141 to 409 kPa in a 40% degree stenotic artery. Conclusions There is an increase in plaque stress in arteries with a thin fibrous cap. The presence of a moderate carotid stenosis (30% to 70%) with a thin fibrous cap indicates a high risk for plaque rupture. Patients in the future may be risk stratified by measuring both fibrous cap thickness and luminal stenosis.

Stability Of Large Damped Flexible Spacecraft With Stored Angular Momentum

Vibrational stability of large flexible structurally damped spacecraft carrying internal angular momentum and undergoing large rigid body rotations is analysed modeling the systems as elastic continua. Initially, analytical solutions to the motion of rigid gyrostats under torque-free conditions are developed. The solutions to the gyrostats modeled as axisymmetric and triaxial spacecraft carrying three and two constant speed momentum wheels, respectively, with spin axes aligned with body principal axes are shown to be complicated. These represent extensions of solutions for simpler cases existing in the literature. Using these solutions and modal analysis, the vibrational equations are reduced to linear ordinary differential equations. Equations with periodically varying coefficients are analysed applying Floquet theory. Study of a few typical beam- and plate-like spacecraft configurations indicate that the introduction of a single reaction wheel into an axisymmetric satellite does not alter the stability criterion. However, introduction of constant speed rotors deteriorates vibrational stability. Effects of structural damping and vehicle inertia ratio are also studied.

Thermal Stability of Polystyrene Peroxide

It has been observed that poly(styrene peroxide) with a high molecular weight is thermally less stable than the same polymer with a low molecular weight. This has been explained as being due to the strain on the O-O bond due to the greater polymer chain length.

Stability of Fe3+ -VO defect pairs in polycrystalline Pb(Ti,Zr)O3

The intensity of the EPR signal with g = 5.985 arising from a ferric ion â oxygen vacancy defect pair (Fe3+ â VO) in PbTiO3, varies with the extent of PbO nonstoichiometry at constant Fe3+ content due to an increased oxygen vacancy concentration. In PZT solid solutions, the signal intensity decreases with an increase in Zr. A lower intensity is also noticed for Fe3+ â VO signals in PbZrO3. This behaviour is explained on the basis of PbO nonstoichiometry arising from independent Pb- and O-vacancies as well as the randomly distributed crystallographic shear (CS) plane defects. The contribution to PbO nonstoichiometry from CS planes is larger in high zirconium compositions of PZT.

Systematic stability analysis of the renormalization group flow for the normal-superconductor-normal junction of Luttinger liquid wires

We study the renormalization group flows of the two terminal conductance of a superconducting junction of two Luttinger liquid wires. We compute the power laws associated with the renormalization group flow around the various fixed points of this system using the generators of the SU(4) group to generate the appropriate parametrization of an matrix representing small deviations from a given fixed point matrix [obtained earlier in S. Das, S. Rao, and A. Saha, Phys. Rev. B 77, 155418 (2008)], and we then perform a comprehensive stability analysis. In particular, for the nontrivial fixed point which has intermediate values of transmission, reflection, Andreev reflection, and crossed Andreev reflection, we show that there are eleven independent directions in which the system can be perturbed, which are relevant or irrelevant, and five directions which are marginal. We obtain power laws associated with these relevant and irrelevant perturbations. Unlike the case of the two-wire charge-conserving junction, here we show that there are power laws which are nonlinear functions of V(0) and V(2kF) [where V(k) represents the Fourier transform of the interelectron interaction potential at momentum k]. We also obtain the power law dependence of linear response conductance on voltage bias or temperature around this fixed point.

The storage stability of passionfruit concentrate

Passionfruit (Passiflora edulis) concentrates (542 g/kg soluble solids) prepared in a wiped-film evaporator were stored for up to 6 months at - 18°, 4° and 20°C. Yeast and mould counts were taken and colour changes noted during storage. When suitable diluted concentrate colour and flavour were acceptable for 1 month at 20°C, 3 months at 4°C and 6 months at -18°C. Commercial short-term storage of concentrate at temperatures above -18°C appears to be feasible. An address presented to the 20th Annual Convention AIFST, Albury NSW, 16th- 20th May, 1987

Helix-coil stability constants for amino acids in nonaqueous solvents. Studies of random poly(-benzyl-L-glutamate-co-L-alanine) and poly(-benzyl-L-glutamate-co-L-leucine) in a mixed solvent

The host-guest technique has been applied to the determination of the helix-coil stability constants of two naturally occurring amino acids, L-alanine and L-leucine, in a nonaqueous solvent system. Random copolymers containing L-alanine and L-leucine, respectively, as guest residues and -benzyl-L-glutamate as the host residue were synthesized. The polymers were fractionated and characterized for their amino acid content, molecular weight, and helix-coil transition behavior in a dichloroacetic acid (DCA)-1,2-dichloroethane (DCE) mixture. Two types of helix-coil transitions were carried out on the copolymers: solvent-induced transitions in DCA-DCE mixtures at 25°C and thermally induced transitions in a 82:18 (wt %) DCA-DCE mixture. The thermally induced transitions were analyzed by statistical mechanical methods to determine the Zimm-Bragg parameters, and s, of the guest residues. The experimental data indicate that, in the nonaqueous solvent, the L-alanine residue stabilizes the -helical conformation more than the L-leucine residue does. This is in contrast to their behavior in aqueous solution, where the reverse is true. The implications of this finding for the analysis of helical structures in globular proteins are discussed.

Development of innovative robust stability enhancement algorithms for distribution systems containing distributed generators

This project was a step forward in improving the voltage profile of traditional low voltage distribution networks with high photovoltaic generation or high peak demand. As a practical and economical solution, the developed methods use a Dynamic Voltage Restorer or DVR, which is a series voltage compensator, for continuous and communication-less power quality enhancement. The placement of DVR in the network is optimised in order to minimise its power rating and cost. In addition, new approaches were developed for grid synchronisation and control of DVR which are integrated with the voltage quality improvement algorithm for stable operation.

Seismic reliability assessment of external stability of reinforced soil walls using pseudo-dynamic method

The paper presents a method for the evaluation of external stability of reinforced soil walls subjected to earthquakes in the framework of the pseudo-dynamic method. The seismic reliability of the wall is evaluated by considering the different possible failure modes such as sliding along the base, overturning about the toe point of the wall, bearing capacity and the eccentricity of the resultant force. The analysis is performed considering properties of the reinforced backfill, foundation soil below the base of the wall, length of the geosynthetic reinforcement and characteristics of earthquake ground motions such as shear wave and primary wave velocity as random variables. The optimum length of reinforcement needed to maintain stability against four modes of failure by targeting various component reliability indices is obtained. Differences between pseudo-static and pseudo-dynamic methods are clearly highlighted in the paper. A complete analysis of pseudo-static and pseudo-dynamic methodologies shows that the pseudodynamic method results in realistic design values for the length of geosynthetic reinforcement under earthquake conditions.

Non-linear resonance in strings under narrow band random excitation, part I: Planar response and stability

Non-linear planar response of a string to planar narrow band random excitation is investigated in this paper. A response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique. It is shown that the response is triple valued, as in the case of harmonic excitation, if the centre frequency of excitation Ω lies in a certain specified range. The triple valued response occurs only if the excitation bandwidth β is smaller than a critical value βcrit which is a monotonically increasing function of the intensity of excitation. An approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the Ω-σ2 plane have been charted. It is shown that planar response can become unstable either due to an unbounded growth of the in-plane component of motion or due to a spontaneous appearance of an out-of-plane component.

Fast Accurate Transient Stability Simulations

The paper describes a Simultaneous Implicit (SI) approach for transient stability simulations based on an iterative technique using traingularised admittance matrix [1]. The reduced saliency of generator in the subtransient state is taken advantage of to speed up the algorithm. Accordingly, generator differential equations, except rotor swing, contain voltage proportional to fluxes in the main field, dampers and a hypothetical winding representing deep flowing eddy currents, as state variables. The simulation results are validated by comparison with two independent methods viz. Runge-Kutta simulation for a simplified system and a method based on modelling damper windings using conventional induction motor theory.