Journal of Engineering Mechanics

Published by American Society of Civil Engineers
Print ISSN: 0733-9399
Efficient design techniques are presented for improving the response of seismic-excited buildings under actuators with limited capacity. Information, regarding the actuator capacity and estimated peak ground acceleration, is used to fine tune the controller and reduce conservatism. Both state feedback and observer-based controllers are discussed. The observer-based controller is based on measurement of the ground acceleration, though this requirement can be removed easily. The sufficient conditions for feasibility of a feedback controller are expressed in terms of linear matrix inequalities. Performance of the proposed techniques is illustrated through simulations of a six-story building subjected to earthquake
When design factors are considered as random variables and the failure condition cannot be expressed by a closed form algebraic inequality, computations of risk (or probability of failure) may become extremely difficult or very inefficient. This study suggests using a simple and easily constructed second degree polynomial to approximate the complicated limit state in the neighborhood of the design point; a computer analysis relates the design variables at selected points. Then a fast probability integration technique (i.e., the Rackwitz-Fiessler algorithm) can be used to estimate risk. The capability of the proposed method is demonstrated in an example of a low cycle fatigue problem for which a computer analysis is required to perform local strain analysis to relate the design variables. A comparison of the performance of this method is made with a far more costly Monte Carlo solution. Agreement of the proposed method with Monte Carlo is considered to be good.
Three recent developments in the sensitivity analysis for thermomechanical postbuckling response of composite panels are reviewed. The three developments are: (1) effective computational procedure for evaluating hierarchical sensitivity coefficients of the various response quantities with respect to the different laminate, layer, and micromechanical characteristics; (2) application of reduction methods to the sensitivity analysis of the postbuckling response; and (3) accurate evaluation of the sensitivity coefficients to transverse shear stresses. Sample numerical results are presented to demonstrate the effectiveness of the computational procedures presented. Some of the future directions for research on sensitivity analysis for the thermomechanical postbuckling response of composite and smart structures are outlined.
This paper considers the development of an improved constrained time stepping scheme which can efficiently and stably handle the pre-post-buckling behavior of general structure subject to high temperature environments. Due to the generality of the scheme, the combined influence of elastic-plastic behavior can be handled in addition to time dependent creep effects. This includes structural problems exhibiting indefinite tangent properties. To illustrate the capability of the procedure, several benchmark problems employing finite element analyses are presented. These demonstrate the numerical efficiency and stability of the scheme. Additionally, the potential influence of complex creep histories on the buckling characteristics is considered.
A computational procedure is presented for reducing the size of the model used in the buckling and vibration analyses of symmetric anisotropic panels to that of the corresponding orthotropic model. The key elements of the procedure are the application of an operator splitting technique through the decomposition of the material stiffness matrix of the panel into the sum of orthotropic and nonorthotropic (anisotropic) parts and the use of a reduction method through successive application of the finite element method and the classical Rayleigh-Ritz technique. The effectiveness of the procedure is demonstrated by numerical examples.
An analysis reported by Veletsos et al. (1972) concerning the free vibrational characteristics of circular arches vibrating in their own planes is considered. The analysis was based on a theory which neglects the effects of rotatory inertia and shearing deformation. A supplementary investigation is conducted to assess the effects of the previously neglected factors and to identify the conditions under which these effects are of practical significance or may be neglected. A simple approximate procedure is developed for estimating the natural frequencies of arches, giving due consideration to the effects of the previously neglected factors.
Hysteretic damping is often modeled by means of linear viscoelastic approaches such as "nearly constant Attenuation (NCQ)" models. These models do not take into account nonlinear effects either on the stiffness or on the damping, which are well known features of soil dynamic behavior. The aim of this paper is to propose a mechanical model involving nonlinear viscoelastic behavior for isotropic materials. This model simultaneously takes into account nonlinear elasticity and nonlinear damping. On the one hand, the shear modulus is a function of the excitation level; on the other, the description of viscosity is based on a generalized Maxwell body involving non-linearity. This formulation is implemented into a 1D finite element approach for a dry soil. The validation of the model shows its ability to retrieve low amplitude ground motion response. For larger excitation levels, the analysis of seismic wave propagation in a nonlinear soil layer over an elastic bedrock leads to results which are physically satisfactory (lower amplitudes, larger time delays, higher frequency content).
We combine Bayesian networks (BNs) and structural reliability methods (SRMs) to create a new computational framework, termed enhanced Bayesian network (eBN), for reliability and risk analysis of engineering structures and infrastructure. BNs are efficient in representing and evaluating complex probabilistic dependence structures, as present in infrastructure and structural systems, and they facilitate Bayesian updating of the model when new information becomes available. On the other hand, SRMs enable accurate assessment of probabilities of rare events represented by computationally demanding, physically-based models. By combining the two methods, the eBN framework provides a unified and powerful tool for efficiently computing probabilities of rare events in complex structural and infrastructure systems in which information evolves in time. Strategies for modeling and efficiently analyzing the eBN are described by way of several conceptual examples. The companion paper applies the eBN methodology to example structural and infrastructure systems.
The eBN model and the corresponding reduced rBN for the unconditional reliability problem. The shaded area is the Markov envelope.
Probabilistic model for the infrastructure example.
Sequence of observations in the infrastructure system example.
Reliability indexes computed for different evidence cases that include measurements of element capacities.
Example transportation system.  
The enhanced Bayesian network (eBN) methodology described in the companion paper facilitates the assessment of reliability and risk of engineering systems when information about the system evolves in time. We present the application of the eBN (a) to the assessment of the life-cycle reliability of a structural system, (b) to the optimization of a decision on performing measurements in that structural system, and (c) to the risk assessment of an infrastructure system subject to natural hazards and deterioration of constituent structures. In all applications, observations of system performances or the hazards are made at various points in time and the eBN efficiently includes these observations in the analysis to provide an updated probabilistic model of the system at all times.
A new method for the free-vibration analysis using the boundary element technique is presented. The method utilizes a fictitious vector function to approximate the inertia forces and then uses the well-known concept of complementary functions and particular integrals to solve the resulting governing differential equations. The necessary particular integrals are defined for the two and three-dimensional analyses, and the present formulation is applied to a number of two-dimensional problems to show its accuracy and efficiency in the solution of realistic engineering problems.
(a) Scheme of the system associated with the 2-DoF model (16). m is the system mass. (b)
Elasto-damaged BW model, uniaxial stress σ 11 = 3 2 [dev(σ)] 11. (a) Strain-history ε 11 and ε 22. (b) σ 11 stress evolution. (c) Stress-strain loops. (d) The damage evolution with the corresponding dissipated energy.
In this paper, a thermodynamic analysis of Bouc-Wen models endowed with both strength and stiffness degradation is provided. It is based on the relationship between the flow rules of these models and those of the endochronic plasticity theory with damage, discussed in a companion paper (Erlicher and Point, 2008). Using the theoretical framework of that extended endochronic theory, it is shown that an elastic Bouc-Wen model with damage, i.e. without plastic strains, can be formulated. Moreover, a proper definition of the dissipated energy of these Bouc-Wen models with degradation is given and some thermodynamic constraints on the parameters defining the models behavior are emphasized and discussed. In particular, some properties of the energetic linear stiffness degradation rule as well as the so-called pivot rule, well-known in the seismic engineering field, are illustrated and commented upon. An improved energetic stiffness degradation rule and a new stiffness degradation rule are proposed.
The thermoelasto viscoplastic buckling behavior of cylindrical shells under axial compression is investigated. The analysis is based on nonlinear kinematic relations and nonlinear rate-dependent unified constitutive equations. Bodner-Partom's model is employed to represent the thermoelasto viscoplastic material behavior. The material model does not separate the inelastic deformation into time-dependent (creep) and time-independent (plastic) deformations. It can cover elastic and inelastic material behavior, and temperature effects simultaneously. A finite-element approach with a two-phase solution scheme for the unified constitutive equations is employed to predict the inelastic buckling behavior of the structure. Numerical examples are given to demonstrate the change of critical load, deformation mode, and the load-carrying capability in the postbuckling stage. The effects of several parameters, which include temperature, small initial imperfections, and the thickness of the shell, are assessed. The creep buckling is also studied as an example of the time-dependent deformation.
A creep and creep damage theory is presented for metallic composites with strong fibers. Application is to reinforced structures in which the fiber orientation may vary throughout but a distinct fiber direction can be identified locally (local transverse isotropy). The creep deformation model follows earlier work and is based on a flow potential function that depends on invariants reflecting stress and the material symmetry. As the focus is on the interaction of creep and damage, primary creep is ignored. The creep rupture model is an extension of continuum damage mechanics and includes an isochronous damage function that depends on invariants specifying the local maximum transverse tension and the maximum longitudinal shear stress. It is posited that at high temperature and low stress, appropriate to engineering practice, these stress components damage the fiber/matrix interface through diffusion controlled void growth, eventually causing creep rupture. Experiments are outlined for characterizing a composite through creep rupture tests under transverse tension and longitudinal shear. Application is made to a thin-walled pressure vessel with reinforcing fibers at an arbitrary helical angle. The results illustrate the usefulness of the model as a means of achieving optimal designs of composite structures where creep and creep rupture are life limiting.
Criteria for the incipient motion of a rigid body initially resting on a rigid surface are formulated from first principles in this work. A modified Coulomb friction model and an associated distribution of reaction forces are proposed. There exists a surprisingly large category of general motions, however, which subscribe to a more conventional analysis; an analysis made possible by identifying so-called ``significant reaction surfaces''. In this way a model which caters for the majority of combined translations and rotations is devised. Some introductry results demonstrate the accuracy with which fluids can be numerically modelled for the purposes of entrainment. This work is an extension of previous work by the same author.
This paper presents a study on the postbuckling response of a shear deformable functionally graded cylindrical shell of finite length embedded in a large outer elastic medium and subjected to axial compressive loads in thermal environments. The surrounding elastic medium is modeled as a tensionless Pasternak foundation that reacts in compression only. The postbuckling analysis is based on a higher order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity. The thermal effects due to heat conduction are also included and the material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent. The nonlinear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the postbuckling response of the shells and an iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region between the shell and the elastic medium. Numerical solutions are presented in tabular and graphical forms to study the postbuckling behavior of FGM shells surrounded by an elastic medium of tensionless Pasternak foundation, from which the postbuckling results for FGM shells with conventional elastic foundations are also obtained for comparison purposes. The results reveal that the unilateral constraint has a significant effect on the postbuckling responses of shells subjected to axial compression in thermal environments when the foundation stiffness is sufficiently large.
Drag force law acting on a moving circular disk in a two-dimensional granular medium is analyzed based on the discrete element method (DEM). It is remarkable that the drag force on the moving disk in moderate dense and pure two-dimensional granular medium can be well reproduced by a perfect fluid with separation from the boundary. A yield force, being independent of the moving speed of the disk, appears if a dry friction between the granular disks and the bottom plate exists. The perfect fluidity is violated in this case. The yield force and the drag force diverge at the jamming point.
Analytic three-dimensional thermoelasticity solutions are presented for static problems of simply supported sandwich panels and cylindrical shells subjected to mechanical and thermal loads. The panels and shells have laminated composite face sheets of arbitrary thickness separated by a core. Each of the individual layers of the face sheets and the core is modeled as a three-dimensional continuum. Analytic first-order sensitivity coefficients are evaluated to assess the sensitivity of the responses to variations in material parameters of the face sheets and the core, as well as to variations in the curvatures and thicknesses of the sandwich and face sheets. Also, the strain energy associated with various stress components in the face sheets and core are calculated and compared. The information obtained in the present study can aid the development and assessment of two-dimensional models for sandwich structures and illuminate the role of particular material parameters in an equivalent model for the core.
An eigenvector updating method is proposed to fit modal test data. The calculated eigenvectors are updated by coinciding some of them with the corresponding measured eigenvectors as a result of an orthogonal transformation. The advantage of the method is the applicability to large complex structures without necessity of recomputation of the eigendata.
Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.
The Sequential Unconstrained Minimization Technique (SUMT) offers an easy way of solving nonlinearly constrained problems. However, this algorithm frequently suffers from the need to minimize an ill-conditioned penalty function. An ill-conditioned minimization problem can be solved very effectively by posing the problem as one of integrating a system of stiff differential equations utilizing concepts from singular perturbation theory. This paper evaluates the robustness and the reliability of such a singular perturbation based SUMT algorithm on two different problems of structural optimization of widely separated scales. The report concludes that whereas conventional SUMT can be bogged down by frequent ill-conditioning, especially in large scale problems, the singular perturbation SUMT has no such difficulty in converging to very accurate solutions.
: The effects of calcium nitrite (CN), fly ash, microsilica and their combination on alkalisilica reaction (ASR) have been studied according to ASTM C227 (mortar bar test). To explore the mechanism of such effects, chemically combined water and X-ray diffraction tests were conducted additionally. The microstructural information provided by these experiments was in agreement with the microscopic observations. A neural network analysis was also conducted to study the feasibility of prediction of a theoretical model. The results showed that a cascade-correlation algorithm could predict very reasonable outputs that coincide with the experimental results after a proper training. Introduction It is well known that mineral admixtures such as fly ash and silica fume are effective in controlling expansion due to ASR (Hooton 1986). However, the influence of chemical admixtures on ASR is a mixed blessing. Bleszynski and Thomas(1998) concluded that the addition of Ca(OH) 2 could promote expansi...
this paper is to address the e#ect of the opening of microcracks on the di#usive and advective transports in a saturated porous medium. This question is encountered in various situations and at di#erent scales, from civil to petroleum engineering, such as chlorides penetration in concrete or #uid #ows in reservoirs. The crack network in the considered representative elementary volume #r.e.v.# is constituted by parallel circular cracks. The connected porous space comprises both the porosity of the uncracked porous medium and the crack porosity which may vary as a function of the loading to which the r.e.v. is subjected. We consider the case of a traction applied in the direction of the normal e z to the cracks, which is referred to as vertical direction in the sequel, so that the e#ective macroscopic stress state can be described by a uniaxial tensor
The response of a cylindrical elastic bar (pile) partially embedded in a homogeneous poroelastic medium and subjected to a time-harmonic vertical load is considered. The bar is modeled using one-dimensional elastic theory valid for long bars in the low frequency range, and the porous medium is treated using Biot's three-dimensional elastodynamic theory. The problem is formulated by decomposing the bar-porous medium system into a fictitious bar and an extended porous medium. A Fredholm's integral equation of the second kind governs the axial force in the fictitious bar. The governing integral equation is solved by applying numerical quadrature. Numerical results for vertical impedance is presented to portray the influence of frequency of excitation and poroelastic properties on the response. INTRODUCTION A theoretical formulation presented by Muki and Sternberg (1970) is considered as the most rigorous mathematical model based on classical theory of elasticity for static axial load tr...
An investigation into the calculation of peaks of non-Gaussian processes, representative of #uctuating internal forces induced by wind in low-rise building frames, is presented. The aim is to develop a simple procedure which can be easily included in computer programs that use surface pressure databases to obtain peak internal forces. In general the processes of interest are non-Gaussian, and we apply translation models to estimate the distribution of their peaks. To illustrate the procedure we calibrate a translation model to the record of a one-hour time history of the bending moment at the upwind bentofalow-rise frame. Introduction Time series of internal forces in low-rise building frames are generally non-Gaussian. An example is shown in Figure 1. It represents, in arbitrary non-dimensional units, a one-hour time history of the bending moment at the upwind bent of the two-hinge, center bay frame of a building in open terrain, 11 m high, 27.5 m wide, 45 m long, anda5 # pitched ro...
First mode damping vs. damper coefficients.
Natural frequency and damping ratio in the first mode for the linear designs.
RMS displacement for semiactive, passive viscous, and active dampers.
Long cables, such as are used in cable-stayed bridges, are prone to vibration due to their low inherent damping characteristics. Several studies have investigated the use of an optimal viscous damper attached transversely to dampen such vibration. This paper investigates the potential for improved damping using a semiactive device. The equations of motion of the cable/damper system are reviewed and an improved modeling formulation is introduced to dramatically reduce computational burden. The response of a cable with linear viscous, active, and semiactive dampers is studied. A semiactive damper is found to decrease response by 51% compared to the optimal linear viscous damper, thus demonstrating the efficacy of a semiactive damper for absorbing cable vibratory energy. Introduction Long steel cables, such as are used in cable-stayed bridges and other structures, are prone to vibration induced by the structure to which they are connected and by weather conditions, particularly wind com...
. The paper reports on wind tunnel experiments with an elastically suspended circular cylinder vibrating under the excitation of natural wind of high turbulence degree. The natural wind turbulence was simulated by superposing the low frequency part of the natural wind turbulence on the background high frequency turbulence of the wind tunnel flow. This was done by controlling the propeller rotation speed according to an artificially generated low frequency speed sample function drawn from a suitable random process model. The experiment provided statistical data on the intermittend random occurrence and size of strong lock-in vibrations in resonanse with the vortex shedding excitation. The purpose of the experiment was to obtain data support for the formulation of a su#ciently detailed stochastic model to allow computer simulation of reasonably realistic fatigue damage accumulation at "hot spots" of tubular structural elements subject to the natural wind. The engineering relevance of th...
A method based on adaptive estimation approaches is presented for the on-line identification of hysteretic systems under arbitrary dynamic environments. The availability of such an identification approach is crucial for the on-line control and monitoring of timevarying structural systems. Previous work by the authors is extended to handle the general case when no information is available on the system parameters, even the mass distribution. A robust, least-squares based adaptive identification algorithm, incorporating a Bouc-Wen hysteresis element model with additional polynomial-type nonlinear terms, is used to investigate the effects of persistence of excitation and of under-and over-parameterization: challenging problems in realistic applications. In spite of the challenges encountered in the identification of the hereditary nature of the restoring force of such nonlinear systems, it is shown through the use of simulation studies of SDOF and certain MDOF systems that the proposed ap...
In 1965, a book was published with the title Research Frontiers in Fluid Dynamics, edited by Raymond Seeger and G. Temple. It was intended to give a panoramic view of some exciting vistas in fluid dynamics. It covered the following areas: (1) High-speed aerodynamics; (2) magnetophydrodynamics (MHD); (3) physics of fluids (low or high density, low or high temperature, etc); (4) constitutive properties of fluids (viscosity, viscoelasticity, etc.); (5) oceanography and meterology; (6) astrophysical and planetary fluid mechanics; and (7) mathematical aspects and numerical aspects. A few of these areas, such as MHD, have blossomed and faded away within a short decade. Some others, such as high-speed aerodynamics, have reached maturity and hope to keep their momentum. In the intervening years, we have witnessed that a number of fields in fluid mechanics have revived from their old times into a new life; still, some have emerged with brand new growth. For instance, the subject of long waves has had a colorful development, with the result of improving our understanding of at least seven different physical phenomena, though originally the solitary water wave was its home base. Low Reynolds number flows have again received new stimuli from many needed applications such as aerosol physics, two-phase flows, rheology, geophysics of the earth interior, as well as micro and molecular biology. Oil exploration has motivated various aspects of marine-related research and development, giving ever-increasing activities in ocean engineering. The energy program, a new glamorous field by its own importance, has brought forth investigations of fluid mechanical problems pertaining to nuclear, geothermal, solar, wind, ocean wave, and other forms of energy sources. Riding on the waves of these broad movements that have carried us thus far, we now hope to forecast the future of fluid mechanics research in 1986. We may like to put the focus at a slightly different depth and ask: What will be the most significant areas of fluid mechanics that by 1986 will enjoy the best prospects of vigorous development, most rewarding not only to the fluid dynamicist but also to mankind, and by then, still offer the expectation of longevity into the 1990's? The task is almost as hard as to make a prophecy on what the political world will be in 1986.
Observed Order of Convergence for Various Tests
The behavior of two stress update algorithms for shear-free large deformation paths is analyzed. The first algorithm has a truncation error of order 1. The second algorithm has a truncation error of order 2. As a consequence, the global performance of the second algorithm is clearly superior. However, for the particular case of shear-free deformation paths, the first algorithm correctly predicts null shear stresses, while the second one does not. This behavior was reported in a previous paper for an extension-rotation test. In this note a general shear-free deformation path is considered in full detail. Peer Reviewed Postprint (author’s final draft)
When an elastic wave propagates through a rock mass, its amplitude is attenuated and velocity is slowed due to the presence of fractures. During wave propagation, if the shear stress at a fracture interface reaches the fracture shear strength, the fracture will experience a large shear displacement. This paper presents a study of the normal transmission of S-waves across parallel fractures with Coulomb slip behavior. In our theoretical formulation, the method of characteristics combined with the Coulomb slip model is used to develop a set of recurrence equations with respect to particle velocities and shear stress. These equations are then solved numerically. In a comparison with the theoretical study, numerical modeling using the universal distinct element code (UDEC) has been conducted. A general agreement between UDEC modeling and theoretical analysis is achieved. The magnitude of the transmission coefficient is calculated as a function of shear stress ratio, nondimensional fracture spacing, normalized shear stiffness, and number of fractures. The study shows that the shear stress ratio is the most important factor influencing wave transmission, and the influence of other factors becomes more apparent when the shear stress ratio is small.
In this paper an algorithm is implemented for the control of uncertain nonlinear dynamical systems. The control algorithm is adaptive and consists of two phases. First, a system identification phase is implemented to develop a predictive model of the system based on its observed behavior. Second, a controller is designed to steer the predicted system response into a desired configuration. The control strategy to be presented in this paper is related to the well-known concepts of sliding mode control and variable structure control. Furthermore, the implementation of this control strategy utilizing smart materials is also addressed. Numerical examples are presented for the trajectory tracking and stabilization of uncertain nonlinear dynamical systems. Control strategies based on externally powered actuators and adaptive components are considered.
Two algorithms for the stress update (i.e., time integration of the constitutive equation) in large-strain solid mechanics are discussed, with particular emphasis on two issues: (1) The incremental objectivity; and (2) the implementation aspects. It is shown that both algorithms are incrementally objective (i.e., they treat rigid rotations properly) and that they can be employed to add large-strain capabilities to a small-strain finite element (FE) code in a simple way. A set of benchmark tests, consisting of simple large deformation paths, have been used to test and compare the two algorithms, both for elastic and plastic analyses. These tests evidence different time-integration accuracy for each algorithm. However, it is also shown that the algorithm that is less accurate in general gives exact results for shear-free deformation paths. Peer Reviewed Postprint (author’s final draft)
Exact explicit eigenvalues are found for compression buckling, hygrothermal buckling, and vibration of sandwich plates with dissimilar facings and functionally graded plates via analogy with membrane vibration. These results apply to simply supported polygonal plates using the first-order shear deformation theory and the classical theory. A Winkler-Pasternak elastic foundation, a hydrostatic inplane force, hygrothermal effects, and rotary inertias are incorporated. Bridged by the vibrating membrane, exact correspondence is readily established between any pairs of eigenvalues associated with buckling and vibration of sandwich plates, functionally graded plates, and homogeneous plates. Positive definiteness is proved for the critical buckling hydrostatic pressure and, in the range of either tension loading or compression loading prior to occurrence of buckling, for the natural vibration frequency.
The paper describes beam elements with inelastic hinges capable of modeling softening due to damage in building frames under severe loadings. A condition for uniqueness on the element level is derived, and the behavior of the model is compared to analytical solutions of simple structures (a single column and a portal frame). An application to postpeak analysis of a multibay frame is presented. Depending on the beam-to-column stiffness ratio and on a certain ductility parameter, various failure modes can occur, ranging from distributed to highly localized ones. This leads to a special type of size effect on the peak load, which is assessed numerically and related to analytically derived solutions valid in extreme situations-the elastic limit and the plastic limit.
An accurate and rapid estimation of the pavement temperature field is desired to better predict pavement responses and for pavement system design. In this paper, an innovative method to derive the theoretical solution of an axisymmetric temperature field in a multilayered pavement system is presented. The multilayered pavement system was modeled as a two-dimensional heat transfer problem. The temperature at any location r , z and any time t in an N-layer pavement system can be calculated by using the derived analytical solution. The Hankel integral transform with respect to the radial coordinate is utilized in the derivation of the solution. The interpolatory trigonometric polynomials based on discrete Fourier transform are used to fit the measured air temperatures and solar radiation intensities during a day, which are essential components in the boundary condition for the underlying heat transfer problem. A FORTRAN program was coded to implement this analytical solution. Measured field temperature results from a rigid pavement system demonstrate that the derived analytical solution generates reasonable temperature profiles in the concrete slab. Illinois Department of Transportation published or submitted for publication is peer reviewed
A buckling analysis of anisotropic composite layered plates is presented. The analysis employs finite strips in conjunction with a perturbation technique and is applicable to rectangular plates with one pair of opposite edges simply supported. The perturbation technique plays the vital role of decoupling the harmonics characterizing the solution. The perturbation parameter is θ, the ply angle, which gives the orientation of the piles with reference to the plate axis. The technique is seen to be a powerful one, producing rapidly converging solutions solutions over a considerable range of θ. The results obtained using this technique are compared with currently available analytical and experimental results.
A numerical method is presented for determining scattered pressures from a submerged infinite cylindrical shell with radial plate appendages subjected to a transverse incident plane Heaviside pressure wave. Inside a cylindrical fluidcontrol surface circumscribing the appendages, finite-difference equations in the cylindrical domain govern the fluid-structure interaction. The infinite region outside the control surface is transformed mathematically into a finite rectangular domain, within which finite-difference equations with unequal spacing govern. A conditionally stable explicit scheme is used to solve the array. Numerical results indicate that the characteristic transient echo of the cylinder is obscured when the appendages are present.
Most previous investigations on tide-induced watertable fluctuations in coastal aquifers have been based on one- dimensional models that describe the processes in the cross- shore direction alone, assuming negligible along-shore variability. A recent study proposed a two-dimensional approximation for tide-induced watertable fluctuations that took into account coastline variations. Here, we further develop this approximation in two ways, by extending the approximation to second order and by taking into account capillary effects. Our results demonstrate that both effects can markedly influence watertable fluctuations. In particular, with the first-order approximation, the local damping rate of the tidal signal could be subject to sizable errors.
Simple analytical formulas are presented for the approximate calculation of the first-passage probabilities for the random response of a linear single-degree-of-freedom system. Specifically, results are given for the first passage of the zero-start response of a simple single-degree-of-freedom oscillator excited by stationary white noise with a normal probability distribution. The short-time nonstationary situation is included as well as the long-time stationary behavior. There are no essential limitations on the parameter values of the simple oscillator considered, and the only limitation on the crossing level is that it not be smaller than the rms value of the stationary response process.
A nonlinear finite element procedure for arch dams is described in which the gradual opening and closing of vertical contraction joints and predetermined horizontal cracking planes are considered. A special joint element approximately represents the deformations due to plane sections not remaining plane at each open joint and allows a single shell element discretization in the thickness direction to be used for the dam. Compressive and sliding nonlinearities are not included. Finite element treatments are also used for the water, assumed incompressible, and for the foundation rock, assumed massless, with all degrees of freedom (dof) off the dam condensed out. For efficiency in the computations, the condensed water and foundation matrices are localized in a way which maintains good accuracy. The response of Pacoima Dam to the 1971 San Fernando ground motion recorded on a ridge over one abutment and scaled by two-thirds is computed first for water at the intermediate level that existed during the 1971 earthquake and then for full reservoir. In the first analysis, the dam exhibits pronounced opening and separation of the contraction joints, allowing violation of the no-slip assumption. The presence of a full reservoir greatly increases the dam response, enough to bring some of the assumptions of the analysis into question. Reducing the ground motion scale to 0.44 with full reservoir drops the response back to a reasonable level, but the contraction joint separations remain.
This paper is concerned with the in-plane elastic stability of arches with a symmetric cross section and subjected to a central concentrated load. The classical methods of predicting elastic buckling loads consider bifurcation from a prebuckling equilibrium path to an orthogonal buckling path. The prebuckling equilibrium path of an arch involves both axial and transverse deformations and so the arch is subjected to both axial compression and bending in the prebuckling stage. In addition, the prebuckling behavior of an arch may become nonlinear. The bending and nonlinearity are not considered in prebuckling analysis of classical methods. A virtual work formulation is used to establish both the nonlinear equilibrium conditions and the buckling equilibrium equations for shallow arches. Analytical solutions for antisymmetric bifurcation buckling and symmetric snap-through buckling loads of shallow arches subjected to this loading regime are obtained. Approximations for the symmetric buckling load of shallow arches and nonshallow fixed arches and for the antisymmetric buckling load of nonshallow pin-ended arches, and criteria that delineate shallow and nonshallow arches are proposed. Comparisons with finite element results demonstrate that the solutions and approximations are accurate. It is found that the existence of antisymmetric bifurcation buckling loads is not a sufficient condition for antisymmetric bifurcation buckling to take place.
Recently, considerable efforts have been devoted to the phenomenon of wave-seabed-pipeline interaction. However, conventional investigations for this problem have been concerned with a uniform seabed, despite the strong evidences of variable permeability and shear modulus. In this paper, a finite-element model is proposed to investigate the wave-induced pore pressure, effective stresses, and soil displacements in the vicinity of a buried pipeline in a porous seabed with variable permeability and shear modulus. The numerical results indicate that the inclusion of variable permeability and shear modulus significantly affects the wave-induced soil response around the pipeline. The influence of the variable permeability and shear modulus and geometry of the pipe on the wave-induced soil response around a buried pipeline are also detailed.
This paper presents an application of a coupled thermo/hydro/chemical/mechanical model via simulation of a laboratory experiment in order to investigate the transport behavior of ions in bentonite pore water. Chemical reactions considered include ion exchange reactions involving major cations Na+, K+, Mg2+, and Ca2+ and precipitation-dissolution of trace minerals calcite, dolomite, anhydrite, and halite. The following conclusions are drawn based on the numerical results. The development of both the temperature and moisture fields was captured by simulation, and a good correlation with the experimental water uptake results was observed. For all ions, the model showed a good qualitative and reasonable quantitative agreement with the experimental results.
This paper presents an investigation of the inclusion of some aspects of chemical behavior within a model of coupled thermo/hydro/chemical/mechanical behavior of unsaturated soils. In particular, multicomponent reactive chemical transport behavior is addressed. The chemical transport model is based on the advection/dispersion/reaction equation, while geochemical reactions are considered via coupling with an established geochemical speciation model. A numerical solution of the governing differential equations is achieved by the use of the Galerkin-weighted residual method for spatial discretization and an implicit backward Eulerian finite-difference method for temporal discretization. The solution of the geochemical reactions is achieved externally to the main solution procedure. Coupling between the chemical transport and geochemical models is achieved via the implementation of both sequential iterative and sequential noniterative techniques. Three application problems are then presented to demonstrate the capability of the coupled model.
An asymptotic approximation is developed for evaluating the probability integrals which arise in the determination of the reliability and response moments of uncertain dynamic systems subject to stochastic excitation. The method is applicable when the probabilities of failure or response moments conditional on the system parameters are available, and the effect of the uncertainty in the system parameters is to be investigated. In particular, a simple analytical formula for the probability of failure of the system is derived and compared to some existing approximations, including an asymptotic approximation based on SORM methods. Simple analytical formulas are also derived for the sensitivity of the failure probability and response moments to variations in parameters of interest. Conditions for which the proposed asymptotic expansion is expected to be accurate are presented. Since numerical integration is only computationally feasible for investigating the accuracy of the proposed method for a small number of uncertain system parameters, simulation techniques are also used. A simple importance sampling method is shown to converge much more rapidly than straightforward Monte-Carlo simluation. Simple structures subjected to white noise stochastic excitation axe used to illustrate the accuracy of the proposed analytical approximation. Results from the computationally efficient perturbation method are also included for comparison. The results show that the asymptotic method gives acceptable approximations, even for systems with relatively large uncertainty, and in most cases, it outperforms the perturbation method.
A novel method of Bayesian learning with automatic relevance determination prior is presented that provides a powerful approach to problems of classification based on data features, for example, classifying soil liquefaction potential based on soil and seismic shaking parameters, automatically classifying the damage states of a structure after severe loading based on features of its dynamic response, and real-time classification of earthquakes based on seismic signals. After introduction of the theory, the method is illustrated by applying it to an earthquake record dataset from nine earthquakes to build an efficient real-time algorithm for near-source versus far-source classification of incoming seismic ground motion signals. This classification is needed in the development of early warning systems for large earthquakes. It is shown that the proposed methodology is promising since it provides a classifier with higher correct classification rates and better generalization performance than a previous Bayesian learning method with a fixed prior distribution that was applied to the same classification problem.
This research project has taken the micromechanics approach to model the strength and deformation behavior of inherently anisotropic sand subjected to stresses non-coaxial with the material axes. Asymmetric sand grains, such as elongated sand grains, are likely to develop a preferred orientation when deposited during the process of alluvial sedimentation, creating an inherently anisotropic material fabric with horizontally oriented bedding planes. Sand thus exhibits different strength and stress-strain behavior dependent on the direction of loading with respect to the axes of the soil. Accounting for non-coaxiality between the stress and material axes is paramount for the accurate prediction of soil's response to applied loads; however, despite the numerous advancements in constitutive models and numerical methods for geotechnical analysis, the problem of accounting for the effect of non-coaxiality between stress and material axes on soil behavior has not been satisfactorily addressed. Drained hollow cylinder torsional shear (HCTS) compression tests on Toyoura sand were simulated, where the direction of the major principal stresses were applied at various angles to the material axes ranging from 0° to 90° from vertical (i.e., ranging from normal to parallel with the bedding plane). Anisotropic behavior has been attributed to interlocking of the sand particles, where the interlocking is least and sliding occurs most easily on the bedding plane. The degree of interlocking was taken as a material property which varies in three dimensions with respect to the material axes, and has been shown to account for observed anisotropy of material strength. Anisotropy of elastic and plastic strain was accounted for, as was the volumetric strain behavior. The developed micromechanics model has been shown to be capable of predicting anisotropy of strength and stress-strain behavior resulting from non-coaxiality of the stress and material axes.
In recent years, Bayesian model updating techniques based on measured data have been applied to system identification of structures and to structural health monitoring. A fully probabilistic Bayesian model updating approach provides a robust and rigorous framework for these applications due to its ability to characterize modeling uncertainties associated with the underlying structural system and to its exclusive foundation on the probability axioms. The plausibility of each structural model within a set of possible models, given the measured data, is quantified by the joint posterior probability density function of the model parameters. This Bayesian approach requires the evaluation of multidimensional integrals, and this usually cannot be done analytically. Recently, some Markov chain Monte Carlo simulation methods have been developed to solve the Bayesian model updating problem. However, in general, the efficiency of these proposed approaches is adversely affected by the dimension of the model parameter space. In this paper, the Hybrid Monte Carlo method is investigated (also known as Hamiltonian Markov chain method), and we show how it can be used to solve higher-dimensional Bayesian model updating problems. Practical issues for the feasibility of the Hybrid Monte Carlo method to such problems are addressed, and improvements are proposed to make it more effective and efficient for solving such model updating problems. New formulae for Markov chain convergence assessment are derived. The effectiveness of the proposed approach for Bayesian model updating of structural dynamic models with many uncertain parameters is illustrated with a simulated data example involving a ten-story building that has 31 model parameters to be updated.
(a) Variation of Runup Function R(, ) with Increasing = kl.-, for Parabolic Beach h(x) = 2x/l (x/l ) 2 ;-, for Plane Beach h(x) = x/l, at Incidence Angle = 0, 45, and 89. (b) Variation of Runup Function R(, = 0) with Increasing = kl for Parabolic Beaches, h(x) = mx/l (1 m)(x/l ) 2 , m = 0.6, 0.8, 1.0, 1.5, and 2.0 (See Inset)
Variations of Wave Elevation over Range of x/l for A = 1: (a) = 45, = 0.5, 2, 5, and 10; (b) = 10, = 0, 30, 60, 70, 80, and 89.-, Present Theory;-, Asymptotic Formula [Eq. (56b)]
This study considers the 3D runup of long waves on a uniform beach of constant or variable downward slope that is connected to an open ocean of uniform depth. An inviscid linear long-wave theory is applied to obtain the fundamental solution for a uniform train of sinusoidal waves obliquely incident upon a uniform beach of variable downward slope without wave breaking. For waves at nearly grazing incidence, runup is significant only for the waves in a set of eigenmodes being trapped within the beach at resonance with the exterior ocean waves. Fourier synthesis is employed to analyze a solitary wave and a train of cnoidal waves obliquely incident upon a sloping beach, with the nonlinear and dispersive effects neglected at this stage. Comparison is made between the present theory and the ray theory to ascertain a criterion of validity. The wave-induced longshore current is evaluated by finding the Stokes drift of the fluid particles carried by the momentum of the waves obliquely incident upon a sloping beach. Currents of significant velocities are produced by waves at incidence angles about 45 [degrees] and by grazing waves trapped on the beach. Also explored are the effects of the variable downward slope and curvature of a uniform beach on 3D runup and reflection of long waves.
Top-cited authors
Zdenek P Bazant
  • Northwestern University
Billie F. Spencer
  • University of Illinois, Urbana-Champaign
G. Pijaudier-Cabot
  • Université de Pau et des Pays de l'Adour
Niels Lind
  • University of Waterloo
Sami Masri
  • University of Southern California