Journal of Engineering Mechanics

A Fourier cum polynomial series solution with correction factors is presented herein for differential equations with variable coefficients. The differential equations correspond to a wide range of boundary value problems. The correction factors included herein are: (1) modified Lanczos correction; (2) Bessel $J$ ; and (3) loading correction factor. These correction factors are introduced in terms of Fourier and polynomial series. The main purpose of using correction factors through a set of series is to improve convergence of the proposed solution, using the first two terms of the series. For the loading correction factor, a Fourier series expansion coupled with orthogonality conditions leads to evaluating undetermined Fourier coefficients of arbitrarily applied loads using concepts of summation equations. Representative boundary value problems are provided to demonstrate the efficiency and accuracy of the first two terms of the proposed solution with correction factors.

Rate-independent and rate-dependent models are presented for the hysteretic shear stress-strain behavior of elastomeric damping materials. A rate-independent hysteretic model, called the general asymptote and power function (GAPF) model, is presented that simulates different types of hysteretic behavior depending on the selected asymptote function. A rate-dependent hysteretic model, formed from a parallel combination of the GAPF model and a dashpot, is also presented which simulates loading frequency dependent behavior in addition to strain amplitude dependent behavior. Closed-form expressions for the shear stress as a function of shear strain are provided for each model. The models are calibrated for three different damping materials, and good correlation between experimental and analytical hysteretic behavior is observed. The models are investigated under variable cyclic loading. To prevent unrealistic stress values (overshooting) after a small strain reversal followed by reloading, a sequential asymptote model is introduced, based on the GAPF model. The hysteretic models were incorporated into a finite-element program within an elastomeric damper element, and the results of nonlinear time history analyses of a building structure with elastomeric dampers under simulated earthquake loading are presented to illustrate behavior of the hysteretic models under several loading histories.

A simple analytical model for calculating the nonlinear deformations of a corrugated core (fluting) during out-of-plane compression is developed. The results from the analytical model are compared to a more comprehensive finite-element model and to experiments. A connection between the boundary conditions and the damage state of the corrugated board is discussed. Including a modified set of boundary conditions gives an almost perfect match of the initial stiffness to the experimental results, indicating that the core might be significantly damaged as a result of the manufacturing process. Possibly, the strength of corrugated boards might be increased about 20% if one could avoid damaging the fluting during the manufacturing process.

Nondimensional parameters and equations governing the buckling behavior of rectangular symmetrically laminated plates are presented that can be used to represent the buckling resistance, for plates made of all known structural materials, in a very general, insightful, and encompassing manner. In addition, these parameters can be used to assess the degree of plate orthotropy, to assess the importance of anisotropy that couples bending and twisting deformations, and to characterize quasi-isotropic laminates quantitatively. Bounds for these nondimensional parameters are also presented that are based on thermodynamics and practical laminate construction considerations. These bounds provide insight into potential gains in buckling resistance through laminate tailoring and composite-material development. As an illustration of this point, upper bounds on the buckling resistance of long rectangular orthotropic plates with simply supported or clamped edges and subjected to uniform axial compression, uniform shear, or pure in-plane bending loads are presented. The results indicate that the maximum gain in buckling resistance for tailored orthotropic laminates, with respect to the corresponding isotropic plate, is in the range of 26–36% for plates with simply supported edges, irrespective of the loading conditions. For the plates with clamped edges, the corresponding gains in buckling resistance are in the range of 9–12% for plates subjected to compression or pure in-plane bending loads and potentially up to 30% for plates subjected to shear loads.

In this paper, first, the technical aspects for applications of finite-element method (FEM) in modeling material forming processes are reviewed, with a final determination of employing the solid formulation explicit finite element code, ANSYS/LS-DYNA, with the arbitrary Lagrangian–Eulerian mesh to simulate upsetting process, which is the uniaxial compression of a cylindrical specimen between two flat platens, of the fresh fiber-cement paste. After combining a previously proposed elasto-viscoplastic constitutive model for the fresh fiber-cement paste into the numerical procedure, satisfactory agreement between experimental and simulated results is observed for the upsetting force-imposed displacement data. The evolution of the deformation within the material flow in the upsetting process is then interpreted based on the calculated results. The study indicates that the present finite-element procedure, as well as the material constitutive model and the boundary condition treatment, are appropriate for modeling the upsetting process of the fresh fiber-cement paste.

A two-dimensional (2D) simulation of flooding from the 1928 failure of St. Francis Dam in southern California is presented. The simulation algorithm solves shallow-water equations using a robust unstructured grid Godunov-type scheme designed for wetting and drying and achieves good results. Flood extent and flood travel time are predicted within 4 and 10% of observations, respectively. Representation of terrain by the mesh is identified as the dominant factor affecting accuracy, and an iterative process of mesh refinement and convergence checks is implemented to minimize errors. The most accurate predictions are achieved with a uniformly distributed Manning $n=0.02$ . A 50% increase in $n$ increases travel time errors to 25% but has little effect on flood extent predictions. This highlights the challenge of a priori travel time prediction but robustness in flood extent prediction when topography is well resolved. Predictions show a combination of subcritical and supercritical flow regimes. The leading edge of the flood was supercritical in San Francisquito Canyon, but due to channel tortuosity, the wetting front reflected off canyon walls causing a transition to subcritical flow, considerably larger depths, and a standing wave in one particular reach that accounts for a 30% fluctuation in discharge. Elsewhere, oblique shocks locally increased flood depths. The 2D dam-break model is validated by its stability and accuracy, conservation properties, ability to calibrate with a physically realistic and simple resistance parametrization, and modest computational cost. Further, this study highlights the importance of a dynamic momentum balance for dam-break flood simulation.

Traditional approaches for repeatedly updating reliability estimates, as needed in reliability-based optimal designs or real-time system control, require the iterative application of a reliability method. This paper explores a new strategy for repeatedly estimating reliability under frequent parameter variations. The central idea is to update the design point in the parameter domain, rather than in the traditional random variable domain, by evaluating several parametric sensitivity measures which are systems of nonlinear first-order ordinary differential equations relating the design point to parameter changes. Four numerical algorithms for evaluating the sensitivity measures are developed using the Euler and the improved Euler algorithms. Two solution procedures are applied. One procedure solves for the updated design point directly, while the other solves for both the unit normal vector at the design point and the reliability index separately, and evaluates the product of these to determine the updated design point. The numerical techniques are thoroughly compared with the classical Hasofer and Lind-Rackwitz and Fiessler (HL-RF) algorithm in five numerical examples regarding efficiency and accuracy. It is found that they are efficient and robust under given conditions.

A novel sensor failure detection method is developed in this paper. Sensor failure considered in this paper can be any type of measurement error that is different from the true structural response. The sensors are divided into two groups; sensors that correctly measure the structural responses are termed “reference sensors” and sensors that may fail to correctly measure the structural responses are termed “uncertain sensors” henceforth. A sensor error function is formulated to detect the instants of failure of the corresponding uncertain sensor, using the measurements from reference sensors and the uncertain sensor examined. The sensor error function is derived using indirect and direct approaches. In the indirect approach, the error function is obtained from the state space model in combination with the inverse model and interaction matrix formulation. The input term is eliminated from the error function by applying the inverse model and the interaction matrix is applied to eliminate the state and all unexamined uncertain sensors except for the one examined from the error function. The direct approach uses the singular value decomposition method to establish the coefficients of the error function from the healthy measured data. The sensor failure detection formulation is investigated numerically using a four degree-of-freedom spring-mass-damper system and experimentally using a $4\text{-}\mathrm{m}$ -long NASA eight-bay truss structure. It is shown by means of numerical and experimental results that the sensor failure formulation developed correctly detects and isolates the instants of sensor failure and can be implemented in real structural systems for sensor failure detection.

The response of a beam-column frame to impulsive ground shock, such as those induced by an underground explosion, has characteristics of both impact and natural earthquake responses. The critical effects may be governed by the dynamic response of individual elements as continuous mass systems, while to a certain extent the global vibration (as of lumped-mass systems) may also be involved. To incorporate both dynamic features, the present study proposes a combined continua and lumped parameter (CCLP) model, which consists of the basic beam-column element with distributed stiffness and mass, along with concentrated mass-springs at element ends to form the reduced dynamic system. To take into account of the shear deformation and rotary inertia which become important in the impulsive response, the governing equations are formulated based on the Timoshenko beam theory. The nonlinearities are described through three mechanisms, namely the distributed nonlinear flexural and diagonal shear behavior, and the direct sliding shear at the member ends. A generic restoring force model is adopted to describe the hysteretic behavior. Comparison with a scaled model test demonstrates that the CCLP model is capable of representing the primary dynamic features in a frame structure under impulsive ground shock. Extended parametric studies indicate that, with increase of the ground shock frequency, the failure tends to become shear dominant. For ground shocks of frequency at $20–30\mathrm{Hz}$ and above, the failure in a reinforced concrete column will require a peak ground velocity (PGV) on the order of $3\mathrm{m}∕\mathrm{s}$ , whereas failure in a beam would occur at PGV of about $1.5\mathrm{m}∕\mathrm{s}$ .

The effects of bending on the modal properties of a stay cable with a transverse damper are analytically studied. Considering that the value of the flexural rigidity in the stay cable is small in practice, an explicit asymptotic formula for the modal damping of a cable with a general type of damper is derived. For a viscous damper, the asymptotic formula obtained is compact, accurate, and thus is very suitable for practical design. Furthermore, for the first few vibration modes of interest, the asymptotic solution is independent of the modal index. It is shown that flexure in the cable reduces the maximum attainable modal damping, possibly up to 20%, while it significantly increases the optimal damping coefficient of the damper.