Showing papers in "Journal of Engineering Mechanics-asce in 1992"

Steady-state and multiple cracking of short random fiber composites

Abstract: This paper analyzes the pseudostrain‐hardening phenomenon of brittle matrix composites reinforced with discontinuous flexible and randomly distributed fibers, based on a cohesive crack‐mechanics approach. The first crack strength and strain are derived in terms of fiber, matrix, and interface micromechanical properties. Conditions for steady‐state cracking and multiple cracking are found to depend on two nondimensionalized parameters that embody all relevant material micromechanical parameters. The results are therefore quite general and applicable to a variety of composite‐material systems. Phrased in terms of a failure‐mechanism map, various uniaxial load‐deformation behaviors for discontinuous fiber composites can be predicted. The influence of a snubbing effect due to local fiber/matrix interaction for randomly oriented crack‐bridging fibers on the composite properties is also studied.

Active Structural Control: Theory and Practice

Abstract: Actively controlled structures control algorithms - practical considerations control mechanisms optimization of actively controlled structures. Appendices.

High‐Order Theory for Sandwich‐Beam Behavior with Transversely Flexible Core

Abstract: A general high-order theory based on variational principles is presented for the bending behavior of a sandwich beam with a core that is vertically flexible. The theory embodies a rigorous and systematic approach to the analysis of such structures, which have high-order effects caused by the nonlinearity of the longitudinal and the transverse deformations of the core through the height. As such, it improves on the available classical and superposition theories. Beam construction consists of the upper and lower skin, metallic or composite laminated symmetric, with nonidentical mechanical and geometrical properties, and a soft core made of foam or honeycomb. The formulation uses a beam theory for the skins and a two-dimensional elasticity theory for the core. The behavior is presented in terms of internal resultants and displacements in skins, peeling and shear stresses in skin-core interfaces, and stress and displacement fields in the core, even in the vicinity of concentrated loads. The method is applicable to any type of loading exerted on the skins and to any type of boundary or continuity conditions, including cases in which at the same section the conditions at the upper skin are different from those at the lower. Some typical cases are studied numerically.

Tuned liquid damper (TLD) for suppressing horizontal motion of structures

Abstract: A new kind of passive mechanical damper, tuned liquid damper (TLD). is studied that relies upon the motion of shallow liquid in a rigid tank for changing the dynamic characteristics of a structure and dissipating its vibration energy. A nonlinear model of two‐dimensional liquid motion inside a rectangular TLD subjected to horizontal motion is developed on the basis of shallow‐water wave theory, where the damping of the liquid motion is included semianalytically. Using the model, the response of a structure with TLD is also computed. The liquid motion inside the TLD under harmonic base excitation and, furthermore, the response of a single‐degree‐of‐freedom structure with TLD, subjected to harmonic external force, are experimentally investigated. The agreement is good between the experiment and the prediction.

Control of Along-Wind Response of Structures by Mass and Liquid Dampers

Abstract: An investigation is made of the possible application of tuned liquid column dampers and tuned liquid column/mass dampers in reducing the along-wind response of wind-sensitive structures. The structure is modeled as a lumped mass multi-degree-of-freedom system taking into account both bending and shear. The wind turbulence is modeled as a stochastic process that is stationary in time and nonhomogeneous in space. A random vibration analysis utilizing transfer matrix formulation is carried out to obtain response statistics. The nonlinear damping term in the fundamental equation of the tuned liquid damper is treated by an equivalent linearization technique. Numerical examples show that tuned liquid dampers, which have significant practical advantages, are as effective as the traditional tuned mass dampers if the parameters of the liquid dampers are properly selected. However, excessive liquid motion in a tuned liquid column/mass damper may reduce the effectiveness of this damper. It is also shown that the wind-induced force- and acceleration-type responses of the structure with a damper, which is usually tuned to the fundamental frequency of the structure, should involve more than one vibration mode as higher-mode responses may become as large or even larger than the controlled-mode response.

Theoretical study of crack-induced eigenfrequency changes on beam structures

Abstract: The theoretical relationships between eigenfrequency changes and magnitudes and the locations of crack-induced damage are developed for beam structures with either simply supported or cantilever boundary conditions. For uniform beams, a physical model of a massless rotational spring is used to represent the local flexibility introduced by the crack. A characteristic equation is derived as a base for the development of the relationship. A symbolic computational package, MACSYMA, is used to facilitate the computations of the higher-order determinant and the corresponding derivatives involved in the characteristic equations. For nonuniform beams, the concept of receptance is used for a system linked with two coordinates (axial and rotational coordinates). Numerical experiments involving the use of a finite-element program, SAP, to determine the eigenfrequencies of both uniform and nonuniform beams with a variety of damage scenarios are used to validate the derived theoretical relationships. The comparisons between the predicted and simulated damage conditions are satisfactory. Two important assumptions are involved in the derived relationship: one is that the structure is considered to behave linearly, and the other one is that the elastic properties of the structure member are time-invariant. The application of the theoretical model is discussed at the end of the paper.

Frequency Domain Analysis of Undamped Systems

Abstract: A numerical tool commonly used in digital signal processing, the exponential window method, is briefly reviewed in this paper and applied to problems in structural dynamics. This method allows one to carry out analyses of undamped structures in the frequency domain, and yields highly accurate results for both discrete and continuous systems. In essence, the solution involves: (1) Finding both the transfer function and the forward Fourier transform of the excitation for complex frequencies; (2) performing a standard inverse Fourier transformation into the time domain; and (3) removing the effect of the complex frequencies by means of an exponential factor (or window). Excellent results are obtained when this factor is chosen so that the power of the excitation and response signals at the end of the window are attenuated by some three orders of magnitude. In such case, it is found that a quiet zone (a tail of trailing zeroes) is not needed for accurate computations, and that temporal aliasing (folding) is n...

Response of Systems with Uncertain Parameters to Stochastic Excitation

Abstract: This paper presents a method for the dynamic analysis of linear systems with uncertain parameters to stochastic excitation. The applied forcing function is modeled as a modulated Gaussian white-noise process in time. A procedure to derive the random state-space equation for the response covariance matrix of the system is presented. The covariance equation is then integrated in time and the response variability is computed. The proposed method is applied to the random response of a five-degree-of-freedom primary-secondary system. Five different values of the ratio of the fundamental natural frequency of the primary to secondary system are considered along with two different ratios of primary- to secondary-system mass. Two types of uncertainty are considered: uncertain primary-system stiffness and damping, and uncertain secondary-system stiffness and damping. Results are reported for the effect of system uncertainty on both the relative displacement and absolute acceleration response of the secondary system. It is concluded that uncertainty in the stiffness of the primary and secondary systems has a very strong influence on the response of the secondary system and its reliability, and must be properly accounted for in the analysis of such systems.

Point-Estimate Method for Calculating Statistical Moments

Abstract: A number of approximate methods exist in the literature for estimating the statistical moments of a random function. The usual approach is based on Taylor series expansion about the mean values of the random variables. This approach requires the calculation of the derivatives of the random function. For complex functions or functions that cannot be expressed in an explicit form, it is desirable to use the so-called point-estimate methods, which do not require the calculation of the derivatives. Point-estimate methods enable the calculation of the expectation of a random function to be calculated based on the values of the function at a specific set of input parameters. In this paper, an efficient point-estimate method is developed, which requires only (\In\N²+3\In\N+2)/2 evaluations of a random function with \In\N random variables. The method is applicable to correlated random variables, and is more accurate than the commonly used Rosenblueth method, which requires a total of 2\I\un\N evaluations of the random function.

Analysis and Implementation of Thin‐Layer Element for Interfaces and Joints

Abstract: An analysis and implementation of the thin‐layer element of Desai et al. for interfaces and joints shows that the planar approximation of the element treated as a solid element can provide satisfactory simulation of the finite‐sized interface zone, and in the limit, its results approach those from the zero‐thickness element. Advantages and limitations of the thin‐layer element are identified, and it is implemented in a nonlinear finite element procedure with the hierarchical single surface plasticity model. The computed results are compared with those from laboratory tests on joints in concrete with different asperity angles. The nonassociative version provides highly satisfactory correlation with laboratory observations.

Frequency Domain Optimal Control of Wind‐Excited Buildings

Abstract: An optimal frequency‐domain approach to active control of wind‐excited buildings is proposed in which the H2 norm of the transfer function from the external disturbance to the regulated output is minimized. A wind‐excitation model established by factorizing the cross‐spectral density matrix of the wind fluctuation is included in the control design. The control of a 60‐story building under an along‐wind excitation by one mass damper, two mass dampers, and active tendon mechanisms is presented in the numerical examples. As an improvement over previous results in civil‐engineering structural control studies, measurement and minimization of building accelerations is achieved. The effects of using constant and frequency‐dependent weighting functions in the control design are also shown. In this case, the frequency‐dependent weighting functions are designed based on the frequency domain response characteristics of the building. The frequency‐domain‐based‐design approach is shown to be both flexible and powerful.

Optimal Importance‐Sampling Density Estimator

Abstract: Importance‐sampling technique has been used in recent years in conjunction with Monte Carlo simulation method to evaluate the reliability of structural systems. Since the efficiency of the importance‐sampling method depends primarily on the choice of the importance‐sampling density, the use of the kernel method to estimate the optimal importance‐sampling density is proposed. This method deviates from the current practice of prescribing the importance‐sampling density from a given parametric family of density functions. Instead, the data obtained from an initial Monte Carlo run are utilized to determine the required importance‐sampling density. The kernel method yields unbiased estimates of the probability of failure. Two measures are developed to quantify the efficiency of the kernel method relative to the basic Monte Carlo method. The first measure, called the marginal efficiency, is used as an indicator of the effectiveness of the kernel method, whereas the second measure, the overall efficiency, define...

Shear‐Band Analysis in Idealized Granular Material

Abstract: Two‐dimensional particles experience shear bands as real granular materials; they form a convenient vehicle to investigate shear bands within granular soils. Numerical simulations on these idealized materials are used to assess the assumptions and limitations of the shear‐band analyses that are based on linear stability theory and micropolar continua. These shear‐band analyses are found to be applicable in the postbifurcation range, and they describe the thickness of shear bands and the displacements and rotations of the particles within the shear bands of idealized granular materials. The influence of particle rotation within shear bands validates the use of micropolar models. The thickness of shear bands is strongly influenced by the model parameters controlling the micropolar effects. The constitutive models based on the deformation and flow theories of plasticity predict similarly the emergence and inclination of shear bands, but give different shear‐band thicknesses.

Damage diagnosis of steel frames using vibrational signature analysis

Abstract: This paper presents a structural diagnosis technique using “vibrational signature” analysis and the concept of strain mode shape (SMS). When a structure experiences a damage or change, a new state of force equilibrium is realized. This change of force distribution can be noted from the SMSs of the structure measured before and after the damage. The magnitude of the changes reflects the degree of forces redistributed. Since force redistribution is, in general, greatest near the damaged area, the location of damage is implicitly identified by the severity of the SMS change. A steel model frame was tested in the laboratory to substantiate this approach. Results show that locations of minor damage (specified change) in the frame can be pinpointed.

Coupled Vertical and Horizontal Galloping

Abstract: Galloping can occur when wind blows on ice‐coated conductors. In this paper, the linearized coupled vertical‐horizontal galloping equations are derived and the eigenvalues defining the motion are determined analytically. The intrinsic coupling between the vertical and horizontal equations requires that there be no vertical motion if the horizontal motion is constrained. Furthermore, vertical galloping may be initiated by a horizontal displacement or velocity. The solution of the eigenvalue equation indicates that the coupled galloping criterion may be either more or less stringent than Den Hartog's criterion. The galloping trajectory is either a straight line at a small angle to the vertical, or under more extreme conditions, defines an elliptical envelope. Solutions are obtained for four cases chosen from the literature to illustrate the effect of different combinations of values of the aerodynamic parameters.

Three-dimensional solutions for thermal buckling of multilayered anisotropic plates

Abstract: Analytic three‐dimensional elasticity solutions are presented for the thermal buckling problem of multilayered anisotropic plates. The plates are assumed to have rectangular geometry and an antisymmetric lamination with respect to the middle plane. The temperature is assumed to be independent of the surface coordinates, but it has an arbitrary symmetric variation through the thickness of the plate. No external loads are present, but the motion of the plate is partially restrained in its plane. A mixed formulation is used, with the fundamental unknowns consisting of the six stress components and the three displacement components of the plate. The prebuckling deformations are taken into account. Each of the plate variables is decomposed into symmetric and antisymmetric components in the thickness direction, and is expressed in terms of a double Fourier series in the Cartesian surface coordinates. Extensive numerical results are presented showing the effects of the prebuckling deformation on the critical tem...

Stable Controllers for Instantaneous Optimal Control

Abstract: Recently, instantaneous optimal control algorithms were proposed and developed for applications to control of seismically excited linear, nonlinear, and hysteretic structural systems. In particular, these control algorithms are suitable for aseismic hybrid control systems, for which the linear quadratic optimal control theory is not applicable. Within the framework of instantaneous optimal control, the weighting matrix Q should be assigned to guarantee the stability of the controlled structure. A systematic way of assigning the weighting matrix by use of the Lyapunov direct method is investigated. Based on the Lyapunov method, several possible choices for the weighting matrix are presented, and their control performances are examined and compared for active and hybrid control systems under seismic loads. It is shown that the performance of the stable controllers presented herein are remarkable.

Buckling of Pressurized Axisymmetrically Imperfect Cylinders under Axial Loads

Abstract: It has long been recognized that the strength of a thin, axially compressed, unstiffened cylinder is governed by bifurcation into a nonsymmetric displacement mode, that the strength is acutely sensitive to very small geometric imperfections of the surface, and that internal pressure increases the strength markedly. In many practical applications, axially compressed cylinders are simultaneously subject to internal pressure, so the problem is a common one. Despite many theoretical and experimental studies, the strength gains due to internal pressure cannot yet be defined with confidence, and a match between laboratory testing, field imperfection measurement, theoretical bifurcation prediction, and allowable design strength has not yet been achieved. The conservatism of current designs is thus still in doubt. This paper addresses the problem of elastic unstiffened thin cylinders with axisymmetric imperfections, as some field measurements indicate that these imperfections are common in civil engineering struc...

Aseismic hybrid control of nonlinear and hysteretic structures. II

Abstract: Instantaneous optimal control for nonlinear and inelastic systems is formulated incorporating the specific hysteretic model of the system. The resulting optimal control vector is obtained as a function of the total deformation, velocity, and the hysteretic component of the structural response. The hysteretic component of the response can be estimated from the measured structural response and the hysteretic model used. It is shown that the optimal control vector satisfies not only the necessary conditions, but also the sufficient condition of optimality. Specific applications of the optimal algorithm to two types of hybrid control systems are demonstrated. These include: (1) Active control of base-isolated buildings using frictional-type sliding base isolators; and (2) active control of base-isolated buildings using lead-core rubber bearings. Numerical examples are worked out to demonstrate the applications of the proposed control algorithm. It is shown that the performance of such an optimal algorithm is an improvement over that of the algorithm that does not consider the hysteretic components in the determination of the control vector.

Stochastic FEM based on local averages of random vector fields

Abstract: The formula for the covariances of the local averages of homogeneous random scalar fields over rectangular domains is first generalized to include the case of homogeneous random vector fields with quadrant symmetry. For nonhomogeneous random fields and/or nonrectangular domains, Gaussian quadrature is proposed to evaluate the means and covariances of the local averages of random vector fields. The stochastic finite‐element analysis based on the local averages of random vector fields is then formulated for static, eigenvalue, and stress‐intensity factor problems. The present stochastic finite‐element method (SFEM) is a generalization of the SFEM based on the local averages of random scalar fields and can be applied to any configuration of structure with several correlated random parameters and several correlated random loads. Numerical examples are examined to show the advantages of the present SFEM over the SFEM based on midpoint discretization, i.e., more rapid convergence and more efficiency.

Microplane Model for Cyclic Triaxial Behavior of Concrete

Abstract: A recently proposed microplane model, which describes not only cracking but also general nonlinear triaxial response, is extended to cyclic loading and the rate effect, and is implemented in a three‐dimensional finite element code. The material properties are characterized separately on planes of various orientations within the material, called the microplanes, on which no tensorial invariance requirements need to be observed. The state of each microplane is described by normal deviatoric and volumetric strains, and by shear strain. To avoid spurious localization instabilities due to strain softening and the consequent mesh‐sensitivity problems, the concept of nonlocal continuum with local strain is adopted. The rate effect is introduced by combining the damage model on each microplane with the Maxwell rheologic model. The results of finite element analysis of some basic cases on the material level, as well as of plain concrete specimens loaded in bending and compression, are demonstrated. The calculated ...

Analytical Solutions for Thick, Doubly Curved, Laminated Shells

Abstract: The state equations for orthotropic, doubly curved shells are established in an orthogonal curvilinear coordinate system. Simplifying hypotheses about displacement models or stress distribution that were assumed in early work are not introduced in this paper. The continuity conditions of stresses and displacements at the interfaces between the contacting layers are satisfied, and analytical solutions for statics and dynamics of the simply supported, doubly curved shells with ortho‐tropic layers are presented by means of the Cayley‐Hamilton theorem. For any number of layers considered, the problem reduces to solving a set of linear algebraic equations with three unknowns. A unified analytical solution is given for thin, moderately thick, and thick laminated shells. The solution satisfied all the equations of elasticity, and each of nine elastic constants is considered. Arbitrary precision of the desired order can be obtained. Numerical results are given to compare with solutions available in the literature.

Rate Effects in Uniaxial Dynamic Compression of Concrete

Abstract: Corrections for stress‐wave dispersion in a 76.2‐mm‐diameter split Hopkinson pressure bar (SHPB) system have produced more accurate data in the regime between yield point (elastic limit) and maximum stress of dynamic stress‐strain curves of concrete, so that the rate dependence of the stress on the inelastic strain rate in this regime could be determined. Such results are published here for the first time, based on SHPB tests of two kinds of high‐strength plain concrete specimens. In addition to rate dependence of the dynamic compressive strength (to more than twice the static strength), the critical strain to failure and the yield stress are reported. Records from axial and circumferential strain gages mounted on some specimens permitted estimation of lateral inertia effects and were useful in determining yield. It is shown that, in these ramp‐loaded tests, the lateral acceleration of the specimen surface between yield and maximum stress was very small, so that the induced radial confinement stresses wer...

Quantitative NDE technique for assessing damages in beam structures

Abstract: A physical model using a massless rotational spring to represent the crack-induced local flexibility is adopted as a basis for developing a quantitative nondestructive evaluation (NDE) technique for assessing the damage in a beam structure. Expressions relating changes in eigenfrequencies of the structure and the quantitative damage index S\I\de\N are formulated via an influence matrix h. The coefficients in the h matrix can be determined from the knowledge of the modal shapes of the undamaged structure. The damage index matrix S\I\de\N can be solved by the resulting system of linear algebraic equations using the measured eigenfrequencies of existing structure. Methods of solution for the system of equations are discussed along with special cases where a pseudo-inverse technique is necessary to solve the system of equations. Series of case studies involving simply supported, cantilevered, and continuous beams are presented to demonstrate the validity of the formulation.

FEM Modeling of Fictitious Crack Propagation in Concrete

Abstract: Using a mixed‐mode extension of the Hillerborg fictitious crack model, a practical interface finite element approach is used to model discrete crack propagation. The fictitious crack tip propagates perpendicular to the maximum tensile principal stress at its tip when the tensile strength is exceeded. A dynamic relaxation method is employed. Interface elements have been used before to model such cracks; however, the software technology is in a state of rapid development, making possible improvements in the modeling of discrete nonlinear crack propagation. The concept of fracture process zone is broadened to one of interface process zone, which includes the nonlinear behavior of the fracture process zone as well as the crack face interference behind the fracture process zone. A development makes the method efficient while preserving the accuracy of the fictitious crack model. The fictitious crack is represented by interface elements with linearly varying displacements; however, the traction distribution is ...

Load‐Space Formulation for Time‐Dependent Structural Reliability

Abstract: A Monte Carlo procedure for reliability estimation of structural systems, subject to multiparameter timevarying loading and formulated in the space of the load processes, is described. For most rea...

Buckling of skew plates and corner condition for simply supported edges

Abstract: The paper considers the elastic buckling of skew plates subjected to in‐plane loadings. The buckling analysis is performed using the Rayleigh‐Ritz method with the newly proposed pb‐2 Ritz functions, which consist of the product of a two‐dimensional polynomial function and a basic function. The basic function is formed from taking the product of the equations of the boundaries, with each equation raised to the power of 0,1, or 2 corresponding to free, simply supported, or clamped edges; thus satisfying the kinematic boundary conditions at the outset. With pb‐2 Ritz functions, the analyst avoids the difficulty of searching for the appropriate function for any arbitrarily shaped plates with various combinations of supporting‐edge conditions. Using this efficient and accurate pb‐2 Rayleigh‐Ritz method, buckling solutions are obtained and presented in the form of design charts for skew plates with different edge conditions, angles, and aspect ratios. In addition, the differing viewpoints on the kinematic condition for a corner formed by two simply supported edges are discussed.

Vibration control of beams by beam-type dynamic vibration absorbers

Abstract: Dynamic vibration absorbers with one degree of freedom are generally applied to the passive control of beam vibration. These absorbers are useful to control a single mode of vibration under harmonic excitation. In this paper, a beam-type dynamic vibration absorber is presented and is composed of a beam (dynamic absorbing beam) under the same boundary conditions as the main beam and uniformly distributed, connecting spring and damper between the main beam and absorbing beam. Equations of motion of the system in modal coordinates of the main beam become equal to those of the two-degrees-of-freedom system with two masses and three springs. Formulas for optimum design of the beam-type dynamic vibration absorber are proposed by using the optimum design method of a dynamic absorber in two degrees of freedom, obtained by Den Hartog’s method. Numerical calculations indicated the response of the main beam without damping is reduced with the exception of the response of the second, and the one with damping is remarkably reduced.