Journal of Engineering Mechanics

A mathematical model of high-damping rubber materials is developed. First the material experiments necessary for modeling are systematically conducted. Then, on the basis of the results of the material experiments, a constitutive model for rubber materials is proposed. The model is decomposed into two parts. The first part consists of an elastoplastic body with a strain-dependent isotropic hardening law and it represents the energy dissipation of the material, while the second part consists of a hyperelastic body with a damage model and it expresses the evolutional direction of the stress tensor. By comparing the experimental results with the simulation by the model, the model is found to well approximate the behaviors of high-damping rubber materials. Finally, a hybrid analysis method is proposed. In this method, the strain field of laminated rubber bearings measured by image processing is combined with the numerical analysis to confirm the applicability of the proposed model to the bearing. In addition, by this hybrid analysis method, the bulk modulus of rubber material is also computed.

This paper addresses the first generation benchmark problem on structural health monitoring developed by the ASCE Task Group on Structural Health Monitoring. The focus of the problem is a four-story model of an existing physical model at the University of British Columbia where simulated data are used for the system identification. Modal parameters were extracted using the frequency domain decomposition method. Rather than relying on data from the undamaged structure, a new proposed methodology based on ratios between stiffness and mass values from the eigenvalue problem is presented to identify the undamaged state of the structure. Once the structural identification is complete, the damage index method is used to detect the location and severity of damage. By not relying on undamaged structure information, this approach may be applicable to existing structures that may already incorporate some amount of damage.

A numerical model describing two-dimensional fluid motions has been developed on an unstructured grid system. By using a fractional step method, a two-dimensional problem governed by the two-dimensional shallow-water equations is treated as two one-dimensional problems. Thus it is possible to simulate two-dimensional numerical problems with a higher computational efficiency. One-dimensional problems are solved by using an upwind total variation diminishing version of the second-order weighted averaged flux method with an approximate Riemann solver. Numerical oscillations commonly observed in second-order numerical schemes are controlled by exploiting a flux limiter. For the general purpose, the model can simulate on an arbitrary topography, treat a moving boundary, and resolve a shock. Five ideal and practical problems are tested. Very accurate results are observed.

Stochastic characteristics of the surge response of a nonlinear single-degree-of-freedom moored structure subjected to random wave excitations are examined in this paper. Sources of nonlinearity of the system include a complex geometric configuration and wave-induced quadratic drag. A Morison-type model with an independent-flow-field formulation and a three-term-polynomial approximation of the nonlinear restoring force is employed for its proven excellent prediction capability for the experimental results investigated. Wave excitations considered in this study include nearly periodic waves, which take into account the presence of tank noise, noisy periodic waves that have predominant periodic components with designed additive random perturbations, and narrow-band random waves. A unified wave excitation model is used to describe all the wave conditions. A modulating factor governing the degree of randomness in the wave excitations is introduced. The corresponding Fokker–Planck formulation is applied and numerically solved for the response probability density functions (PDFs). Experimental results and simulations are compared in detail via the PDFs in phase space. The PDFs portray coexisting multiple response attractors and indicate their relative strengths, and experimental response behaviors, including transitions and interactions, are accordingly interpreted from the ensemble perspective. Using time-averaged probability density functions as an invariant measure, probability distributions of large excursions in experimental and simulated responses to various random wave excitations are demonstrated and compared. Asymptotic long-term behaviors of the experimental responses are then inferred.

A solution is developed for the buildup, steady, and postarrest dissipative pore fluid pressure fields that develop around a conical penetrometer that self-embeds from free-fall into the seabed. Arrest from free-fall considers deceleration under undrained conditions in a purely cohesive soil, with constant shear strength with depth. The resulting decelerating velocity field is controlled by soil strength, bearing capacity factors, and inertial components. At low impact velocities the embedment process is controlled by soil strength, and at high velocities by inertia. With the deceleration defined, the solution for a point normal dislocation migrating in a poroelastic medium is extended to incorporate the influence of a tapered tip. Dynamic steady pressures, $P_D\text{,}$ develop relative to the penetrating tip geometry with their distribution conditioned by the nondimensional penetration rate, $U_D\text{,}$ incorporating impacting penetration rate, consolidation coefficient, and penetrometer radius, and the nondimensional strength, $N_D\text{,}$ additionally incorporating undrained shear strength of the sediment. Pore pressures may develop to a steady peak magnitude at the penetrometer tip, and drop as $P_D=1/x_D$ with distance $x_D$ behind the tip and along the shaft. Induced pore pressures are singular in the zone of tip taper for the assumed zero radius of the penetrometer, negating the direct evaluation of permeability magnitudes from pressures recorded on the cone face. However, peak induced pressure magnitudes may be correlated with sediment permeabilities, postarrest dissipation rates may be correlated with consolidation coefficients, and depths of penetration may be correlated with shear strengths. The magnitudes of fluid pressures evaluated on the shaft may be correlated with sharp penetrometer data (reported by Urgeles et al. in 2000) to independently evaluate magnitudes of strength and transport parameters.

The assessment of safety for structures subjected to earthquake excitation is a time-variant reliability problem whose practical solution, when the structure behaves inelastically and uncertainty in the mechanical parameters is taken into account, is traditionally sought by means of simulation. In this paper the feasibility of an alternative solution based on the first order reliability method is explored. The problem is expressed in terms of first-excursion event within a conceptual framework, established in recent years, in which random vibration problems are discretized to make them tractable by the well-established methods of time-invariant structural reliability. The necessary extensions to apply the methodology to reinforced concrete frame structures are presented. Applications to a simple spring-mass system and to a complete three-dimensional bridge structure are presented.

A Bayesian probabilistic approach is presented for selecting the most plausible class of models for a structural or mechanical system within some specified set of model classes, based on system response data. The crux of the approach is to rank the classes of models based on their probabilities conditional on the response data which can be calculated based on Bayes’ theorem and an asymptotic expansion for the evidence for each model class. The approach provides a quantitative expression of a principle of model parsimony or of Ockham’s razor which in this context can be stated as “simpler models are to be preferred over unnecessarily complicated ones.” Examples are presented to illustrate the method using a single-degree-of-freedom bilinear hysteretic system, a linear two-story frame, and a ten-story shear building, all of which are subjected to seismic excitation.

We propose a procedure to obtain a consistent, mesh-objective, continuous model starting from chains composed of discrete springs exhibiting strain softening. Observing the size-dependent response of tensile chains and the corresponding scaling law, recent results for the variational convergence of discrete functionals (Γ convergence) are used to pass from a molecular to a continuum theory. The limit model, where softening and fracture are interpreted by the dichotomy of bulk and surface energies, reproduces the same overall properties of the discrete system. In particular, fracture energy does not vanish in the limit and the discrete approximations of the resulting continuum model are mesh objective.

The numerical solution of problems of curved rods can be formulated using rod elements developed within the context of the theory of a Cosserat point. It is well known that the buckling of shallow arches presents a formidable challenge to theoretical models because it necessarily requires accurate modeling of the nonlinear coupling of membrane and bending effects as well as the accurate prediction of prebuckled deformations. This paper shows that the Cosserat theory predicts buckling loads and deformed shapes of elastic clamped circular arches which are in excellent agreement with the experiments over the full range of arch geometries that were tested. This success suggests that the Cosserat theory can be used to obtain reliable results for nonlinear deformations of curved elastic rods. Moreover, the analysis of these experiments indicates that variations in the thicknesses of shallow arch structures due to standard tolerances have a strong influence on buckling loads and should be measured and controlled in accurate buckling experiments.

A damage identification procedure for Euler-Bernoulli beams under static loads is proposed. Use is made of an integral formulation for the static problem of damaged Euler-Bernoulli beams. This formulation originates from the observation that a variation in the bending stiffness of a linear elastic beam can be modeled as a superimposed curvature depending on damage parameters as well as on the actual bending moment distribution. Using the superposition principle, the problem is reduced to the solution of a Fredholm integral equation of the second kind characterized by a Pincherle-Goursat kernel. It is shown that the solution of this equation can always be obtained in an analytical form that may be used to set up a damage identification procedure based on the minimization of a nonlinear function of damage parameters.

Peak values in time histories of wind effects may be obtained by using the entire information inherent in the time series of the wind effect, a method entailing the estimation of the probability distribution of the peak through the application of the classical Rice procedure extended for non-Gaussian time histories. We present estimates of the sampling errors inherent in this method. These are needed for structural reliability calculations and for decisions on the requisite length of wind tunnel pressure records, especially for database-assisted design. If based on the analysis of 1-h-long records generated by Monte Carlo simulation, typical sampling errors in the estimation of peaks of time histories corresponding to windstorms of 1-h duration are about 5%. If based on 30- or 20-min records, they are about 1.5 times or twice as large, respectively. Consideration of the sampling errors in reliability calculations entails an estimated increase in the requisite safety margins with respect to wind loading of roughly 2, 3, and 5% if 1-h, 30-min, or 20-min records are used, respectively.

The paper explores the time-wise evolution of selected turbulence parameters during gravity-driven flow establishment of incompressible fluids in rigid circular pipes. Two initial conditions are considered: flow starting from rest, passing through laminar-to-turbulent transition, and terminating in a turbulent steady state; and transient flow between two turbulent steady states. It is found that, in the second case, the properties considered, i.e., local temporal mean velocity and its transverse distribution, axial turbulence intensity, and wall shear stress, are monotonically increasing with time. However, for flow starting from rest, all properties are strongly affected by the development of turbulence. In particular, at the critical moment when laminar-to-turbulent transition is complete, the wall shear stress changes abruptly from one to the other, identifying wall shear stress as a very sensitive indicator of criticality.