Inverse identification of the bending stiffness of a braided polyethylene twine subject to large deformation: application to the identification of the mesh opening rigidity of fishing nets.

The evaluation of the mesh opening stiffness of fishing nets is an important issue in assessing the selectivity of trawls. It appeared that a larger bending rigidity of twines decreases the mesh opening and could reduce the escapement of fish. Nevertheless, netting structure is complex. A netting is made up of braided twines made of polyethylene or polyamide. These twines are tied with non-symmetrical knots. Thus, these assemblies develop contact-friction interactions. Moreover, the netting can be subject to large deformation. In this study, we investigate the responses of netting samples to different types of solicitations. Samples are loaded and unloaded with creep and relaxation stages, with different boundary conditions. Then, two models have been developed: an analytical model and a finite element model. The last one was used to assess, with an inverse identification algorithm, the bending stiffness of twines. In this paper, experimental results and a model for netting structures made up of braided twines are presented. During dry forming of a composite, for example, the matrix is not present or not active, and relative sliding can occur between constitutive fibres. So an accurate modelling of the mechanical behaviour of fibrous material is necessary. This study offers experimental data which could permit to improve current models of contact-friction interactions [4], to validate models for large deformation analysis of fibrous materials [1] on a new experimental case, then to improve the evaluation of the mesh opening stiffness of a fishing net

Diabetes mellitus affects the biomechanical function of the callus and the expression of TGF-beta1 and BMP2 in an early stage of fracture healing

Transforming growth factor beta 1 (TGF-β1) and bone morphogenetic protein-2 (BMP-2) are important regulators of bone repair and regeneration. In this study, we examined whether TGF-β1 and BMP-2 expressions were delayed during bone healing in type 1 diabetes mellitus. Tibial fractures were created in 95 diabetic and 95 control adult male Wistar rats of 10 weeks of age. At 1, 2, 3, 4, and 5 weeks after fracture induction, five rats were sacrificed from each group. The expressions of TGF-β1 and BMP2 in the fractured tibias were measured by immunohistochemistry and quantitative reverse-transcription polymerase chain reaction, weekly for the first 5 weeks post-fracture. Mechanical parameters (bending rigidity, torsional rigidity, destruction torque) of the healing bones were also assessed at 3, 4, and 5 weeks post-fracture, after the rats were sacrificed. The bending rigidity, torsional rigidity and destruction torque of the two groups increased continuously during the healing process. The diabetes group had lower mean values for bending rigidity, torsional rigidity and destruction torque compared with the control group (P<0.05). TGF-β1 and BMP-2 expression were significantly lower (P<0.05) in the control group than in the diabetes group at postoperative weeks 1, 2, and 3. Peak levels of TGF-β1 and BMP-2 expression were delayed by 1 week in the diabetes group compared with the control group. Our results demonstrate that there was a delayed recovery in the biomechanical function of the fractured bones in diabetic rats. This delay may be associated with a delayed expression of the growth factors TGF-β1 and BMP-2.

The study the properties structurals and elastics of phases lamellar of lipid.

Lamellar systems composed of lipid bilayers have been widely used as model system for investigating properties of biological membranes, interactions between membranes and with biomolecules. The composition of the membrane determines its three dimensional shape and its properties such as rigidity and compressibility which play an important role on membrane fusion, protein adhesion, interactions between proteins, etc. We present a systematic study of a lamellar system composed of lecithin and a commercial co-surfactant (Simusol), which is a mixture of ethoxylated fatty acids. Using X ray scattering and a new procedure to fit X-ray experimental data, we determine relevant parameters characterizing the lamellar structure, varying membrane composition from 100% of lecithin to 100% of Simulsol. We present experimental data illustrating the swelling behavior for the membrane of different compositions and the respective behavior of the Caillé parameter. From and GISAXS experiments on oriented films under controlled humidity we investigate the compressibility of the lamellar phase and the effect of incorporating co-surfactant. Combining the Caillé parameter and compressibility studies we determine the bending rigidity of membranes. The results obtained with this experimental approach and new procedure to fit X-ray experimental allows us to identify structural changes in the bilayer depending both on hydration and co-surfactant content, with implications on elastic properties of membranes.

Structural and elastic properties of DNA and chromatin

We investigate a chain consisting of two coupled worm-like chains withconstant distance between the strands. The effects due todouble-strandedness of the chain are studied. In a previous analyticalstudy of this system an intrinsic twist-stretch coupling and atendency of kinking is predicted. Even though a local twist structureis observed the predicted features are not recovered. A new model for DNA at the base-pair level is presented. Thebase-pairs are treated as flat rigid ellipsoids and thesugar-phosphate backbones are represented as stiff harmonic springs.The base-pair stacking interaction is modeled by a variant of theGay-Berne potential. It is shown by systematic coarse-graininghow the elastic constants of a worm-like chain are related to thelocal fluctuations of the base-pair step parameters. Even though a lotof microscopic details of the base-pair geometry is neglected themodel can be optimized to obtain a B-DNA conformation as ground stateand reasonable elastic properties. Moreover the model allows tosimulate much larger length scales than it is possible with atomisticsimulations due to the simplification of the force-field and inparticular due to the possibility of non-local Monte-Carlo moves. Asa first application the behavior under stretching is investigated. Inagreement with micromanipulation experiments on single DNA moleculesone observes a force-plateau in the force-extension curvescorresponding to an overstretching transition from B-DNA to aso-called S-DNA state. The model suggests a structure for S-DNA withhighly inclined base-pairs in order to enable at least partialbase-pair stacking. Finally a simple model for chromatin is introduced to study itsstructural and elastic properties. The underlying geometry of themodeled fiber is based on a crossed-linker model. The chromatosomesare treated as disk-like objects. Excluded volume and short rangenucleosomal interaction are taken into account by a variant of theGay-Berne potential. It is found that the bending rigidity and thestretching modulus of the fiber increase with more compact fibers. Fora reasonable parameterization of the fiber for physiologicalconditions and sufficiently high attraction between the nucleosomes aforce-extension curve is found similar to stretching experiments onsingle chromatin fibers. For very small stretching forces a kinkedfiber forming a loop is observed. If larger forces are applied theloop formation is stretched out and a decondensation of the fibertakes place.

Theoretical studies of fluid membrane mechanics

Biologische Membranen sind Fettmolekül-Doppelschichten, die sich wie zweidimensionale Flüssigkeiten verhalten. Die Energie einer solchen fluiden Oberfläche kann häufig mit Hilfe eines Hamiltonians beschrieben werden, der invariant unter Reparametrisierungen der Oberfläche ist und nur von ihrer Geometrie abhängt. Beiträge innerer Freiheitsgrade und der Umgebung können in den Formalismus mit einbezogen werden. Dieser Ansatz wird in der vorliegenden Arbeit dazu verwendet, die Mechanik fluider Membranen und ähnlicher Oberflächen zu untersuchen. Spannungen und Drehmomente in der Oberfläche lassen sich durch kovariante Tensoren ausdrücken. Diese können dann z. B. dazu verwendet werden, die Gleichgewichtsposition der Kontaktlinie zu bestimmen, an der sich zwei aneinander haftende Oberflächen voneinander trennen. Mit Ausnahme von Kapillarphänomenen ist die Oberflächenenergie nicht nur abhängig von Translationen der Kontaktlinie, sondern auch von Änderungen in der Steigung oder sogar Krümmung. Die sich ergebenden Randbedingungen entsprechen den Gleichgewichtsbedingungen an Kräfte und Drehmomente, falls sich die Kontaktlinie frei bewegen kann. Wenn eine der Oberflächen starr ist, muss die Variation lokal dieser Fläche folgen. Spannungen und Drehmomente tragen dann zu einer einzigen Gleichgewichtsbedingung bei; ihre Beiträge können nicht mehr einzeln identifiziert werden. Um quantitative Aussagen über das Verhalten einer fluiden Oberfläche zu machen, müssen ihre elastischen Eigenschaften bekannt sein. Der "Nanotrommel"-Versuchsaufbau ermöglicht es, Membraneigenschaften lokal zu untersuchen: Er besteht aus einer porenüberspannenden Membran, die während des Experiments durch die Spitze eines Rasterkraftmikroskops in die Pore gedrückt wird. Der lineare Verlauf der resultierenden Kraft-Abstands-Kurven kann mit Hilfe der in dieser Arbeit entwickelten Theorie reproduziert werden, wenn der Einfluss von Adhäsion zwischen Spitze und Membran vernachlässigt wird. Bezieht man diesen Effekt in die Rechnungen mit ein, ändert sich das Resultat erheblich: Kraft-Abstands-Kurven sind nicht länger linear, Hysterese und nichtverschwindende Trennkräfte treten auf. Die Voraussagen der Rechnungen könnten in zukünftigen Experimenten dazu verwendet werden, Parameter wie die Biegesteifigkeit der Membran mit einer Auflösung im Nanometerbereich zu bestimmen. Wenn die Materialeigenschaften bekannt sind, können Probleme der Membranmechanik genauer betrachtet werden. Oberflächenvermittelte Wechselwirkungen sind in diesem Zusammenhang ein interessantes Beispiel. Mit Hilfe des oben erwähnten Spannungstensors können analytische Ausdrücke für die krümmungsvermittelte Kraft zwischen zwei Teilchen, die z. B. Proteine repräsentieren, hergeleitet werden. Zusätzlich wird das Gleichgewicht der Kräfte und Drehmomente genutzt, um mehrere Bedingungen an die Geometrie der Membran abzuleiten. Für den Fall zweier unendlich langer Zylinder auf der Membran werden diese Bedingungen zusammen mit Profilberechnungen kombiniert, um quantitative Aussagen über die Wechselwirkung zu treffen. Theorie und Experiment stoßen an ihre Grenzen, wenn es darum geht, die Relevanz von krümmungsvermittelten Wechselwirkungen in der biologischen Zelle korrekt zu beurteilen. In einem solchen Fall bieten Computersimulationen einen alternativen Ansatz: Die hier präsentierten Simulationen sagen voraus, dass Proteine zusammenfinden und Membranbläschen (Vesikel) bilden können, sobald jedes der Proteine eine Mindestkrümmung in der Membran induziert. Der Radius der Vesikel hängt dabei stark von der lokal aufgeprägten Krümmung ab. Das Resultat der Simulationen wird in dieser Arbeit durch ein approximatives theoretisches Modell qualitativ bestätigt.

Polymer Models of Meiotic and Mitotic Chromosomes

Polymers tied together by constraints exhibit an internal pressure; this idea is used to analyze physical properties of the bottle-brush–like chromosomes of meiotic prophase that consist of polymer-like flexible chromatin loops, attached to a central axis. Using a minimal number of experimental parameters, semiquantitative predictions are made for the bending rigidity, radius, and axial tension of such brushes, and the repulsion acting between brushes whose bristles are forced to overlap. The retraction of lampbrush loops when the nascent transcripts are stripped away, the oval shape of diplotene bivalents between chiasmata, and the rigidity of pachytene chromosomes are all manifestations of chromatin pressure. This two-phase (chromatin plus buffer) picture that suffices for meiotic chromosomes has to be supplemented by a third constituent, a chromatin glue to understand mitotic chromosomes, and explain how condensation can drive the resolution of entanglements. This process resembles a thermal annealing in that a parameter (the affinity of the glue for chromatin and/or the affinity of the chromatin for buffer) has to be tuned to achieve optimal results. Mechanical measurements to characterize this protein–chromatin matrix are proposed. Finally, the propensity for even slightly chemically dissimilar polymers to phase separate (cluster like with like) can explain the apparent segregation of the chromatin into A+T- and G+C-rich regions revealed by chromosome banding.

Shapes and Dynamics of Blood Cells in Poiseuille and Shear Flows

The dynamics, shape, deformation, and orientation of red blood cells in microcirculation affect the rheology, flow resistance and transport properties of whole blood. This leads to important correlations of cellular and continuum scales. Furthermore, the dynamics of RBCs subject to different flow conditions and vessel geometries is relevant for both fundamental research and biomedical applications (e.g drug delivery). In this thesis, the behaviour of RBCs is investigated for different flow conditions via computer simulations. We use a combination of two mesoscopic particle-based simulation techniques, dissipative particle dynamics and smoothed dissipative particle dynamics. We focus on the microcapillary scale of several μm. At this scale, blood cannot be considered at the continuum but has to be studied at the cellular level. The connection between cellular motion and overall blood rheology will be investigated. Red blood cells are modelled as viscoelastic objects interacting hydrodynamically with a viscous fluid environment. The properties of the membrane, such as resistance against bending or shearing, are set to correspond to experimental values. Furthermore, thermal fluctuations are considered via random forces. Analyses corresponding to light scattering measurements are performed in order to compare to experiments and suggest for which situations this method is suitable. Static light scattering by red blood cells characterises their shape and allows comparison to objects such as spheres or cylinders, whose scattering signals have analytical solutions, in contrast to those of red blood cells. Dynamic light scattering by red blood cells is studied concerning its suitability to detect and analyse motion, deformation and membrane fluctuations. Dynamic light scattering analysis is performed for both diffusing and flowing cells. We find that scattering signals depend on various cell properties, thus allowing to distinguish different cells. The scattering of diffusing cells allows to draw conclusions on their bending rigidity via the effective diffusion coefficient. The scattering of flowing cells allows to draw conclusions on the shear rate via the scattering amplitude correlation. In flow, a RBC shows different shapes and dynamic states, depending on conditions such as confinement, physiological/pathological state and cell age. Here, two essential flow conditions are studied: simple shear flow and tube flow. Simple shear flow as a basic flow condition is part of any more complex flow. The velocity profile is linear and shear stress is homogeneous. In simple shear flow, we find a sequence of different cell shapes by increasing the shear rate. With increasing shear rate, we find rolling cells with cup shapes, trilobe shapes and quadrulobe shapes. This agrees with recent experiments. Furthermore, the impact of the initial orientation on the dynamics is studied. To study crowding and collective effects, systems with higher haematocrit are set up. Tube flow is an idealised model for the flow through cylindric microvessels. Without cell, a parabolic flow profile prevails. A single red blood cell is placed into the tube and subject to a Poiseuille profile. In tube flow, we find different cell shapes and dynamics depending on confinement, shear rate and cell properties. For strong confinements and high shear rates, we find parachute-like shapes. Although not perfectly symmetric, they are adjusted to the flow profile and maintain a stationary shape and orientation. For weak confinements and low shear rates, we find tumbling slippers that rotate and moderately change their shape. For weak confinements and high shear rates, we find tank-treading slippers that oscillate in a limited range of inclination angles and strongly change their shape. For the lowest shear rates, we find cells performing a snaking motion. Due to cell properties and resultant deformations, all shapes differ from hitherto descriptions, such as steady tank-treading or symmetric parachutes. We introduce phase diagrams to identify flow regimes for the different shapes and dynamics. Changing cell properties, the regime borders in the phase diagrams change. In both flow types, both the viscosity contrast and the choice of stress-free shape are important. For in vitro experiments, the solvent viscosity has often been higher than the cytosol viscosity, leading to a different pattern of dynamics, such as steady tank-treading. The stress-free state of a RBC, which is the state at zero shear stress, is still controversial, and computer simulations enable direct comparisons of possible candidates in equivalent flow conditions.

Solid-liquid interactions in microscale structures and devices

Liquid-solid interactions become important as dimensions approach mciro/nano-scale. This dissertation focuses on liquid-solid interactions in two distinct applications: capillary driven self-assembly of thin foils into 3D structures, and droplet wetting of hydrophobic micropatterned surfaces. The phenomenon of self-assembly of complex structures is common in biological systems. Examples include self-assembly of proteins into macromolecular structures and self-assembly of lipid bilayer membranes. The principles governing this phenomenon have been applied to induce self-assembly of millimeter scale Si thin films into spherical and other 3D structures, which are then integrated into light-trapping photovoltaic (PV) devices. Motivated by this application, we present a generalized analytical study of the self-folding of thin plates into deterministic 3D shapes, through fluid-solid interactions, to be used as PV devices. This study consists of developing a model using beam theory, which incorporates the two competing components — a capillary force that promotes folding and the bending rigidity of the foil that resists folding into a 3D structure. Through an equivalence argument of thin foils of different geometry, an effective folding parameter, which uniquely characterizes the driving force for folding, has been identified. A criterion for spontaneous folding of an arbitrarily shaped 2D foil, based on the effective folding parameter, is thus established. Measurements from experiments using different materials and predictions from the model match well, validating the assumptions used in the analysis. As an alternative to the mechanics model approach, the minimization of the total free energy is employed to investigate the interactions between a fluid droplet and a flexible thin film. A 2D energy functional is proposed, comprising the surface energy of the fluid, bending energy of the thin film and gravitational energy of the fluid. Through simulations with Surface Evolver, the shapes of the droplet and the thin film at equilibrium are obtained. A critical thin film length necessary for complete enclosure of the fluid droplet, and hence successful self-assembly into a PV device, is determined and compared with the experimental results and mechanics model predictions. The results from the modeling and energy approaches and the experiments are all consistent. Superhydrophobic surfaces, which have unique properties including self-cleaning and water repelling are desired in many applications. One excellent example in nature is the lotus leaf. To fabricate these surfaces, well designed micro/nano- surface structures are often employed. In this research, we fabricate superhydrophobic micropatterned Polydimethylsiloxane (PDMS) surfaces composed of micropillars of various sizes and arrangements by means of soft lithography. Both anisotropic surfaces, consisting of parallel grooves and cylindrical pillars in rectangular lattices, and isotropic surfaces, consisting of cylindrical pillars in square and hexagonal lattices, are considered. A novel technique is proposed to image the contact line (CL) of the droplet on the hydrophobic surface. This technique provides a new approach to distinguish between partial and complete wetting. The contact area between droplet and microtextured surface is then measured for a droplet in the Cassie state, which is a state of partial wetting. The results show that although the droplet is in the Cassie state, the contact area does not necessarily follow Cassie model predictions. Moreover, the CL is not circular, and is affected by the micropatterns, in both isotropic and anisotropic cases. Thus, it is suggested that along with the contact angle — the typical parameter reported in literature quantifying wetting, the size and shape of the contact area should also be presented. This technique is employed to investigate the evolution of the CL on a hydrophobic micropatterned surface in the cases of: a single droplet impacting the micropatterned surface, two droplets coalescing on micropillars, and a receding droplet resting on the micropatterned surface. Another parameter which quantifies hydrophobicity is the contact angle hysteresis (CAH), which indicates the resistance of the surface to the sliding of a droplet with a given volume. The conventional methods of using advancing and receding angles or tilting stage to measure the resistance of the micropatterned surface are indirect, without mentioning the inaccuracy due to the discrete and stepwise motion of the CL on micropillars. A micronewton force sensor is utilized to directly measure the resisting force by dragging a droplet on a microtextured surface. Together with the proposed imaging technique, the evolution of the CL during sliding is also explored. It is found that, at the onset of sliding, the CL behaves as a linear elastic solid with a constant stiffness. Afterwards, the force first increases and then decreases and reaches a steady state, accompanied with periodic oscillations due to regular pinning and depinning of the CL. Both the maximum and steady state forces are primarily dependent on area fractions of the micropatterned surfaces in our experiment. The resisting force is found to be proportional to the number of pillars which pin the CL at the trailing edge, validating the assumption that the resistance mainly arises from the CL pinning at the trailing edge. In each pinning-and-depinning cycle during the steady state, the CL also shows linear elastic behavior but with a lower stiffness. The force variation and energy dissipation involved can also be determined. This novel method of measuring the resistance of the micropatterned surface elucidates the dependence on CL pinning and provides more insight into the mechanisms of CAH.

Torsional rigidity of single actin filaments and actin–actin bond breaking force under torsion measured directly by in vitro micromanipulation

Knowledge of the elastic properties of actin filaments is crucial for considering its role in muscle contraction, cellular motile events, and formation of cell shape. The stiffness of actin filaments in the directions of stretching and bending has been determined. In this study, we have directly determined the torsional rigidity and breaking force of single actin filaments by measuring the rotational Brownian motion and tensile strength using optical tweezers and microneedles, respectively. Rotational angular fluctuations of filaments supplied the torsional rigidity as (8.0 ± 1.2) × 10−26 Nm2. This value is similar to that deduced from the longitudinal rigidity, assuming the actin filament to be a homogeneous rod. The breaking force of the actin–actin bond was measured while twisting a filament through various angles using microneedles. The breaking force decreased greatly under twist, e.g., from 600–320 pN when filaments were turned through 90°, independent of the rotational direction. Our results indicate that an actin filament exhibits comparable flexibility in the rotational and longitudinal directions, but breaks more easily under torsional load.

Auxin And Physical Constraint Exerted By The Perianth Promote Androgynophore Bending In Passiflora Mucronata L. (passifloraceae).

The androgynophore column, a distinctive floral feature in passion flowers, is strongly crooked or bent in many Passiflora species pollinated by bats. This is a floral feature that facilitates the adaptation to bat pollination. Crooking or bending of plant organs are generally caused by environmental stimulus (e.g. mechanical barriers) and might involve the differential distribution of auxin. Our aim was to study the role of the perianth organs and the effect of auxin in bending of the androgynophore of the bat-pollinated species Passiflora mucronata. Morpho-anatomical characterisation of the androgynophore, including measurements of curvature angles and cell sizes both at the dorsal (convex) and ventral (concave) sides of the androgynophore, was performed on control flowers, flowers from which perianth organs were partially removed and flowers treated either with auxin (2,4-dichlorophenoxyacetic acid; 2,4-D) or with an inhibitor of auxin polar transport (naphthylphthalamic acid; NPA). Asymmetric growth of the androgynophore column, leading to bending, occurs at a late stage of flower development. Removing the physical constraint exerted by perianth organs or treatment with NPA significantly reduced androgynophore bending. Additionally, the androgynophores of plants treated with 2,4-D were more curved when compared to controls. There was a larger cellular expansion at the dorsal side of the androgynophores of plants treated with 2,4-D and in both sides of the androgynophores of plants treated with NPA. This study suggests that the physical constraint exerted by perianth and auxin redistribution promotes androgynophore bending in P. mucronata and might be related to the evolution of chiropterophily in the genus Passiflora.

Rigidez do papelão ondulado: comparação entre resultados experimentais e os obtidos por cálculo analítico

Cardboard packing for horticultural products has as main function to protect them. The design of a cardboard packing request the knowledge of the bending stiffens which is depending on the modulus of elasticity. The objective of this work was to calculate the cardboard modulus of elasticity from data obtained in laboratory using physical characterization test, with different methods, and comparing the results with the values obtained experimentally. Ten samples of each cardboard selected for this study were tested in the paper fabrication direction and in its transverse direction. The papers liner and medium resistance to the traction, used to calculate the bending stiffness, was determined in a universal machine test. To obtaining of the bending stiffens the four points test was accomplished. Expressive variations among the methods from which the modulus of elasticity is obtained were observed and that influence the bending stiffness of the structure. The stiffness values obtained experimentally were always greater than the values obtained from analytical method. This difference can be attributed to two factors, the production processes that assurance a larger rigidity than the components separately and the addition of the adhesive layer that is not taken in consideration in the analytic calculations.

Thermodynamic origin of cooperativity in actomyosin interactions: The coupling of short-range interactions with actin bending stiffness in an Ising-like model

We present Monte Carlo simulations for a molecular motor system found in virtually all eukaryotic cells, the acto-myosin motor system, composed of a group of organic macromolecules. Cell motors were mapped to an Ising-like model, where the interaction field is transmitted through a tropomyosin polymer chain. The presence of Ca(2+) induces tropomyosin to block or unblock binding sites of the myosin motor leading to its activation or deactivation. We used the Metropolis algorithm to find the transient and the equilibrium states of the acto-myosin system composed of solvent, actin, tropomyosin, troponin, Ca(2+), and myosin-S1 at a given temperature, including the spatial configuration of tropomyosin on the actin filament surface. Our model describes the short- and long-range cooperativity during actin-myosin binding which emerges from the bending stiffness of the tropomyosin complex. We found all transition rates between the states only using the interaction energy of the constituents. The agreement between our model and experimental data also supports the recent theory of flexible tropomyosin.

Bending of stochastic Kirchhoff plates on Winkler foundations via the Galerkin method and the Askey-Wiener scheme

In this paper, the method of Galerkin and the Askey-Wiener scheme are used to obtain approximate solutions to the stochastic displacement response of Kirchhoff plates with uncertain parameters. Theoretical and numerical results are presented. The Lax-Milgram lemma is used to express the conditions for existence and uniqueness of the solution. Uncertainties in plate and foundation stiffness are modeled by respecting these conditions, hence using Legendre polynomials indexed in uniform random variables. The space of approximate solutions is built using results of density between the space of continuous functions and Sobolev spaces. Approximate Galerkin solutions are compared with results of Monte Carlo simulation, in terms of first and second order moments and in terms of histograms of the displacement response. Numerical results for two example problems show very fast convergence to the exact solution, at excellent accuracies. The Askey-Wiener Galerkin scheme developed herein is able to reproduce the histogram of the displacement response. The scheme is shown to be a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2009 Elsevier Ltd. All rights reserved.

Chaos-Galerkin solution of stochastic Timoshenko bending problems

This paper presents an accurate and efficient solution for the random transverse and angular displacement fields of uncertain Timoshenko beams. Approximate, numerical solutions are obtained using the Galerkin method and chaos polynomials. The Chaos-Galerkin scheme is constructed by respecting the theoretical conditions for existence and uniqueness of the solution. Numerical results show fast convergence to the exact solution, at excellent accuracies. The developed Chaos-Galerkin scheme accurately approximates the complete cumulative distribution function of the displacement responses. The Chaos-Galerkin scheme developed herein is a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2011 Elsevier Ltd. All rights reserved.

Galerkin Solution of Stochastic Beam Bending on Winkler Foundations

In this paper, the Askey-Wiener scheme and the Galerkin method are used to obtain approximate solutions to stochastic beam bending on Winkler foundation. The study addresses Euler-Bernoulli beams with uncertainty in the bending stiffness modulus and in the stiffness of the foundation. Uncertainties are represented by parameterized stochastic processes. The random behavior of beam response is modeled using the Askey-Wiener scheme. One contribution of the paper is a sketch of proof of existence and uniqueness of the solution to problems involving fourth order operators applied to random fields. From the approximate Galerkin solution, expected value and variance of beam displacement responses are derived, and compared with corresponding estimates obtained via Monte Carlo simulation. Results show very fast convergence and excellent accuracies in comparison to Monte Carlo simulation. The Askey-Wiener Galerkin scheme presented herein is shown to be a theoretically solid and numerically efficient method for the solution of stochastic problems in engineering.