Comparison of finite element reliability methods

The spectral stochastic finite element method (SSFEM) aims at constructing a probabilistic representation of the response of a mechanical system, whose material properties are random fields. The response quantities, e.g. the nodal displacements, are represented by a polynomial series expansion in terms of standard normal random variables. This expansion is usually post-processed to obtain the second-order statistical moments of the response quantities. However, in the literature, the SSFEM has also been suggested as a method for reliability analysis. No careful examination of this potential has been made yet. In this paper, the SSFEM is considered in conjunction with the first-order reliability method (FORM) and with importance sampling for finite element reliability analysis. This approach is compared with the direct coupling of a FORM reliability code and a finite element code. The two procedures are applied to the reliability analysis of the settlement of a foundation lying on a randomly heterogeneous soil layer. The results are used to make a comprehensive comparison of the two methods in terms of their relative accuracies and efficiencies.     

Molecular Mechanisms of the Deregulation of Muscle Contraction Induced by the R90P Mutation in Tpm3.12 and the Weakening of This Effect by BDM and W7

Point mutations in the genes encoding the skeletal muscle isoforms of tropomyosin can cause a range of muscle diseases. The amino acid substitution of Arg for Pro residue in the 90th position (R90P) in γ-tropomyosin (Tpm3.12) is associated with congenital fiber type disproportion and muscle weakness. The molecular mechanisms underlying muscle dysfunction in this disease remain unclear. Here, we observed that this mutation causes an abnormally high Ca²⁺-sensitivity of myofilaments in vitro and in muscle fibers. To determine the critical conformational changes that myosin, actin, and tropomyosin undergo during the ATPase cycle and the alterations in these changes caused by R90P replacement in Tpm3.12, we used polarized fluorimetry. It was shown that the R90P mutation inhibits the ability of tropomyosin to shift towards the outer domains of actin, which is accompanied by the almost complete depression of troponin’s ability to switch actin monomers off and to reduce the amount of the myosin heads weakly bound to F-actin at a low Ca²⁺. These changes in the behavior of tropomyosin and the troponin–tropomyosin complex, as well as in the balance of strongly and weakly bound myosin heads in the ATPase cycle may underlie the occurrence of both abnormally high Ca²⁺-sensitivity and muscle weakness. BDM, an inhibitor of myosin ATPase activity, and W7, a troponin C antagonist, restore the ability of tropomyosin for Ca²⁺-dependent movement and the ability of the troponin–tropomyosin complex to switch actin monomers off, demonstrating a weakening of the damaging effect of the R90P mutation on muscle contractility.     

Green laser sources optimized for highly efficient microdisplay‐based field‐sequential mobile projectors

Abstract— A novel green laser source, based on a monolithic cavity microchip laser platform, has been developed. The laser is designed to be a part of a miniature and efficient RGB light source for microdisplay‐based mobile projector devices. The use of highly efficient, periodically poled MgO‐doped lithium niobate as the non‐linear frequency doubler allows for a significant increase in the overall efficiency of the green microchip laser. Specifically, a 50–150‐mW green output with a wall‐plug efficiency exceeding 10% in the temperature range of greater than 40°C has been demonstrated. A compact package for this laser source with a volume less than 0.33 cm³ is discussed and results of performance tests are presented.     

Estimating the stresses in cantilever beam loaded by a parabolically distributed load with Airy stress functions

This study presents three mathematical methods namely the polynomial stress function approach, the Fourier series form approach and the approximated equations form approach for finding the stress distribution in a cantilever beam with rectangular cross section loaded by a parabolically distributed load. By taking the stress function as a polynomial of the seventh degree, it is attempted to find the coefficients either in complete or in full shape of the polynomial. In the Fourier series approach, the load is discreted to unlimited series of harmonic loads and superposing resultant stresses is the affect of parabolically distributed load on the beam. The resultant stresses are compared with some approximated stress formulas which have been provided before. Finite element analysis are done for square, short, medium and long cantilever beams and the mathematical results of stress distribution in five different height of the beam was compared with FEM results. It was found good results for τ _yy and τ _xy in all cross section of the beams and acceptable results for τ _xx only in y = 0. It is found that discreting loads to even a limit number of harmonic loads and superposing the resultant stresses can give the distribution of τ _yy and τ _xy with the acceptable precision in medium and long cantilever beams with rectangular cross section.     

Joint First-Passage Probability and Reliability of Systems under Stochastic Excitation

The first-passage probability, describing the probability that a scalar process exceeds a prescribed threshold during an interval of time, is of great engineering interest. This probability is essential for estimating the reliability of a structural component whose response is a stochastic process. When considering the reliability of an engineering system composed of several interdependent components, the probability that two or more response processes exceed their respective safe thresholds during the operation time of the system is an equally essential quantity. This paper proposes simple and accurate formulas for approximating this joint first-passage probability of a vector process. The nth order joint first-passage probability is obtained from a recursive formula involving lower order joint first-passage probabilities and the out-crossing probability of the vector process over a safe domain. Interdependence between the crossings is approximately accounted for by considering the clumping of these events. The accuracy of the proposed formulas is examined by comparing analytical estimates with those obtained from Monte Carlo simulations for stationary Gaussian processes. As an example application, the reliability of a system of interconnected equipment items subjected to a stochastic earthquake excitation is estimated by linear programming bounds employing marginal and joint component fragilities obtained by the proposed formulas.     

One dimensional elasto-plastic wave interaction and boundary reflections

Elasto-plastic wave propagation in a one dimensional rod is treated by utilizing finite element analysis. The time dependence is handled by means of a variable time step numerical integration method. Elasto-plastic reflections from a fixed boundary and interaction of plastic waves are discussed.

Theoretical expressions are presented for determining the stress response for a material exhibiting bilinear hardening behavior during elasto-plastic wave interaction and boundary reflection. These expressions are employed to evaluate predictions made by the numerical procedure.

In the computations, steep wave fronts are approximated by ramps. The steepness of these ramps may be increased by refining the finite element grid. Excellent agreement is obtained between numerical and theoretical elastic and inelastic stress response levels.     

Determination of appropriate RF blocking impedance for MRI surface coils and arrays

Surface and phased array receiving coils in MRI typically require that RF excitation be accomplished using the body coil. This process requires that the receiving coils contain blocking circuitry to increase the overall circuit impedance during RF excitation and withstand the electromotive force induced by the applied electromagnetic field. The aim of this study was to determine the optimal impedance range required during RF excitation based on an assessment of image quality. The experimental results are fit by an exponential model and establish criteria that can be applied for general receiver coil design.     

Nonlinear rebound of a rod after impact against a deformable barrier

The nonlinear impact of a vehicle against a deformable barrier and its subsequent rebound from that barrier are simulated. A one-dimensional elastoplastic model represents the vehicle as a series of rod finite elements and the barrier as a single mass, nonlinear spring. The solution procedure utilizes variable time step integration, contains an error control and eliminates numerical instabilities. A limited study assesses the influence of system parameters on both structure and occupants. The chief objective, however, is to establish the feasibility of the proposed treatment of this class of problems. Some results obtained appear, at first, to contradict intuition. It is observed that modelling a deformable barrier as rigid can lead to unconservative results with respect to structural response of the vehicle.