Journal of Engineering Mechanics

Stochastic finite-element analysis of shells is performed using the spectral representation method for the description of the random fields in conjunction with the local average method for the formulation of the stochastic stiffness matrix of the elements. A stochastic formulation of the nonlinear triangular composites facet triangular shell element is implemented for the stability analysis of cylindrical panels with random initial imperfections. The imperfections are described as a two-dimensional univariate homogeneous stochastic field. The elastic modulus and the shell thickness are also described as two-dimensional uni-variate homogeneous stochastic fields. The variability of the limit load of the cylindrical panel is then computed using the Monte Carlo simulation. Useful conclusions for the buckling behavior of cylindrical panels with random initial imperfections are derived from the numerical tests presented in this paper. These tests also demonstrate the applicability of the proposed methodology in realistic problems.

A novel system identification procedure is proposed for nondestructive damage evaluation of structures. It is a finite element-based time-domain linear system identification technique capable of identifying structures at the element level. The unique features of the algorithm are that it can identify a structure without using any input excitation information and it can consider both viscous and Rayleigh-type proportional damping in the dynamic models. The consideration of proportional damping introduces a source of nonlinearity in the otherwise linear dynamic algorithm. However, it will also reduce the total number of damping coefficients to be identified, reducing the size of the problem. The Taylor series approximation is used to transform a nonlinear set of equations to a linear set of equations. The proposed algorithm, denoted as the modified iterative least square with unknown input algorithm, is verified with several examples considering various types of structures including shear-type building, truss, and beams. The algorithm accurately identified the stiffness of structures at the element level for both viscous (linear) and proportional (nonlinear) damping cases. It is capable of identifying a structure even with noise-contaminated response information. An example shows how the algorithm could be used in detecting the exact location of a defect in a defective element. The algorithm is being developed further and is expected to provide an economical, simple, efficient, and robust system identification technique that can be used as a nondestructive defect detection procedure in the near future.

The traditional approach for assessing the stability of slopes is using limit equilibrium methods. Recently, many efforts have been made to utilize limit analysis methods based on the upper bound and lower bound limit theorems in plasticity. In this paper, an upper bound limit analysis method using rigid finite elements is presented. Rigid finite elements are used to discretize the slope media. Kinematically admissible velocity discontinuities are permitted to occur at all interelement boundaries. The traditional definition of factor of safety is adopted in the present method so that the results from the limit analysis can be directly compared with those from methods of slices. The presence of water can be considered through work terms in the energy–work balance equation. To do this effectively, the pore water pressure is considered as an external force, similar to gravity and surface tractions. The proposed method formulates the slope stability problem as a nonlinear optimization problem with constraints based on the yield criterion, flow rule, boundary conditions, and the energy–work balance equation. The optimization problem is solved by a sequential quadratic algorithm. Two numerical examples are presented to illustrate the validation and potential applications of the present method.

Recognizing the importance of limiting residual deformations that are usually associated with the response of full hysteretic systems under seismic loading, a number of energy dissipating devices and innovative structural systems exhibiting a full recentering response have recently been developed. Although these systems encompass the highly desirable self-centering characteristic, they inherently have less energy dissipation capacity when compared to more traditional fuller hysteretic systems. Little information is available on the nonlinear dynamics of systems exhibiting this flag-shaped hysteresis. In this paper, the frequency response of single degree of freedom (SDOF) systems exhibiting the flag-shaped hysteresis is computed in a closed form using the method of slowly varying parameters. The solution is derived for two independent variables representing the postyielding stiffness and energy dissipation capacity that define all self-centering hysteretic systems. The hysteretic systems covered by this formulation range from bilinear elastic systems (with no energy dissipation) to full bilinear elastoplastic. The frequency response exhibits a softening branch with multiple solution regions. A relationship between the system properties and bounded response at resonance for a given amplitude of excitation is also derived. Further analysis is carried out to assess the stability of these multiple solution regions. It is found that both stable solution branches can be achieved depending on the nature of the excitation. An amplitude jump phenomenon is also present both in increasing frequency and decreasing frequency sweeps. The concept of theoretical versus likely response curve is discussed for less idealized excitation functions.

Application of Crank–Nicolson (CN) discretization to the hydrostatic (or shallow-water) free-surface equation in two-dimensional or three-dimensional Reynolds-averaged Navier–Stokes models neglects a second order term. The neglected term is zero at steady state, so it does not appear in steady-state accuracy analyses. A new correction term is derived that restores second-order accuracy. The correction is significant when the amplitude of the surface oscillation is within two orders of magnitude of the water depth and the barotropic Courant–Friedrichs–Lewy (CFL) stability condition is less than unity. Analysis shows that the CN accuracy for an unforced free-surface oscillation is degraded to first order when the barotropic CFL stability condition is greater than unity, independent of whether or not the new correction term is applied. The results indicate that the semi-implicit Crank–Nicolson method, applied to the hydrostatic free-surface evolution equation, is only first-order accurate for the time and space scales typically used in lake, estuarine, and coastal ocean studies.

An advanced generalized plasticity soil model and bounding surface geosynthetic model, in conjunction with a dynamic finite element procedure, are used to analyze the behavior of geosynthetic-reinforced soil retaining walls. The construction behavior of a full-scale wall is first analyzed followed by a series of five shaking table tests conducted in a centrifuge. The parameters for the sandy backfill soils are calibrated through the results of monotonic and cyclic triaxial tests. The wall facing deformations, strains in the geogrid reinforcement layers, lateral earth pressures acting at the facing blocks, and vertical stresses at the foundation are presented. In the centrifugal shaking table tests, the response of the walls subject to 20 cycles of sinusoidal wave having a frequency of 2 Hz and of acceleration amplitude of $0.2g$ are compared with the results of analysis. The acceleration in the backfill, strain in the geogrid layers, and facing deformation are computed and compared to the test results. The results of analysis for both static and dynamic tests compared reasonably well with the experimental results.

Experimental modal analysis (EMA) has been explored as a technology for condition assessment and damage identification of constructed structures. However, successful EMA applications such as damage detection to constructed systems pose certain difficulties. The properties of constructed systems are influenced by temperature changes as well as other natural influences such as movements in addition to any deterioration and damage. Writers were challenged in their attempts to measure the dynamic properties of an aged bridge by EMA due to inconsistencies within the data set due to short-term variations in ambient conditions. A complex interaction was observed between the dynamic properties of the bridge, hour-to-hour changes in temperature, and controlled damages applied to the bridge. Inconsistencies in the data set made curve fitting difficult for some common parameter estimation algorithms that have been designed to handle consistent data sets. Although the quality of measurements within the entire data set was affected by time variance and nonlinearity, increasing the number of reference measurements significantly improved the reliability of the information which could be extracted. In conjunction with the multiple-input multiple-output technique, a parameter estimation method using complex mode indicator function (CMIF) was developed and implemented in this study to determine the modal properties with proper scaling to obtain modal flexibility. This method proved to be very successful among many others with the data acquired from the aged and deteriorated highway bridge. In this paper, challenges in reliable identification of modal parameters from large structures are reviewed and the new CMIF based algorithm is documented. The method is evaluated on actual bridge data sets from a damage detection research study.

The ultimate strength of structures made of brittle materials—such as microconcrete—strongly depends on microstructural defects, the structure size, and the loading pattern. Probabilistic approaches allow one to take account of such dependencies. By using a Weibull model, cracking of ferrocement panels is analyzed. Provided the behavior of the reinforcement remains elastic, it is shown that the Weibull parameters identified on unreinforced microconcrete samples tested in flexure may be used to predict multiple cracking in ferrocement panels tested in tension. A key aspect of the analysis is related to the understanding and modeling of the stress heterogeneity effect on the local failure probability of unreinforced as well as reinforced microconcrete by the use of a so-called Weibull stress.

A new method is proposed for the description and simulation of nonstationary random processes based on Hilbert spectra of their sample observations. A sample of a random process is first decomposed into intrinsic mode functions (IMFs) by the method of empirical mode decomposition. The Hilbert transforms of the IMFs yield the instantaneous amplitude and frequency, from which the Hilbert spectrum can be obtained as a function of time and frequency. The average of the Hilbert spectra over the samples is then defined as the Hilbert spectrum of the process and used as the target in the simulation of the process. The method is also extended to vector random processes. Unlike current procedures such as those based on the evolutionary process, no assumptions of functional forms for the spectra are necessary which are unknown a priori; and no assumptions of piecewise stationarity and egodicity of the process are required in parameter estimation. Applications to spectral characterization and simulation of multivariate earthquake ground motions show that the Hilbert spectra give a clear description of the time-varying spectral content of the motions and the simulated samples represent an accurate statistical image of the records. The response spectra compare well with those of the records and retain the jagged look. The method has great potential for engineering applications when dealing with nonstationary, nonlinear random processes.

A wavelets-based method is developed to estimate the evolutionary power spectral density (EPSD) of nonstationary stochastic processes. The method relies on the property that the continuous wavelet transform of a nonstationary process can be treated as a stochastic process with EPSD given in terms of the EPSD of the process in a closed form. This yields an equation in the frequency domain relating the instantaneous mean-square value of the wavelet transform to the EPSD of the process. A number of these equations are considered, each related to a certain scale of the wavelet transform, in conjunction with representing the target EPSD as a sum of time-independent shape functions modulated by time-dependent coefficients; the squared moduli of the Fourier transforms of the wavelets associated with the selected scales are taken as shape functions. This leads to a linear system of equations which is solved to determine the unknown time-dependent coefficients; the same system matrix applies for all time instances. Numerical examples demonstrate the accuracy and computational efficiency of the proposed method.

The increasingly widespread use of fiber-reinforced polymers as an alternative to conventional materials makes it necessary to formulate theoretical models which adequately evaluate the influence of the anisotropy of such composites on the structural behavior. While the cross section shapes adopted for compressed members are generally the same as in steel structures, the anisotropy which characterizes these polymers may reduce the critical loading threshold due to local buckling phenomena. A procedure to study the buckling of glass fiber reinforced polymer pultruded members by means of an homogenization approach is proposed here. A two-stage buckling model permits the determination of both global and local critical loads as explicit functions of the member geometry and its material behavior. These functions may be used for optimization of the shape of the above-mentioned members. Besides the model shows its reliability as it fits the results of experimental testson members with different slenderness ratios.

Duckbill-shaped elastomer valves are often installed on wastewater effluent diffusers, stormwater outfalls, and industrial flow systems to prevent backflow and sediment/salt water intrusion. Unlike fixed diameter nozzles, the flow from a duckbill valve (DBV) depends both on the driving pressure and the size of the valve opening. A nonlinear large deformation finite element analysis of a prototype DBV is reported herein. The elastomer is modeled as a hyperelastic incompressible solid, and the flow inside the DBV, shaped like a converging nozzle, is treated as energy conserving. The deformed valve is computed iteratively from sequential standard large deformation analysis of the internal flow and pressure loading. The calculations show that the valve opening is lip shaped, and the maximum stress occurs around the two sides of the saddle of the DBV; maximum strains are on the order of 5%. In contrast to the traditional square-root head–discharge dependence, a linear pressure–discharge relation is predicted for a range of elastomer thickness; the jet velocity/valve opening area varies nonlinearly with discharge. The normalized predictions of valve discharge flow and opening area as a function of the driving pressure are in excellent agreement with experimental data.

A compressive postbuckling analysis is presented for a functionally graded cylindrical panel with piezoelectric actuators subjected to the combined action of mechanical, electrical, and thermal loads. The temperature field considered is assumed to be of uniform distribution over the panel surface and through the panel thickness and the electric field considers only the transverse component $E_Z\text{.}$ The material properties of the presently considered functionally graded materials (FGMs) are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, whereas the material properties of the piezoelectric layers are assumed to be independent of the temperature and the electric field. The governing equations are based on a higher-order shear deformation theory with a von Kármán-Donnell-type of kinematic nonlinearity. A boundary layer theory for shell buckling is extended to the case of hybrid FGM cylindrical panels of finite length. The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the compressive postbuckling behavior of perfect and imperfect FGM cylindrical panels with fully covered piezoelectric actuators, under different sets of thermal and electrical loading conditions. The effects due to temperature rise, volume fraction distribution, applied voltages, panel geometric parameters, in-plane boundary conditions, as well as initial geometric imperfections are studied.