Showing papers in "Journal of Engineering Mechanics-asce in 1986"

Structural reliability under incomplete probability information

Abstract: A comprehensive framework is set forth for the analysis of structural reliability under incomplete probability information. Under stipulated requirements of consistency, invariance, operability, and simplicity, a method is developed to incorporate in the reliability analysis incomplete probability information on random variables, including moments, bounds, marginal distributions, and partial joint distributions. The method is consistent with the philosophy of Ditlevsen’s generalized reliability index and complements existing second-moment and full-distribution structural reliability theories.

Bounding surface plasticity, i: mathematical foundation and hypoplasticity

Abstract: The mathematical foundation of the general bounding surface constitutive formulation in plasticity is presented. Along these lines the concept of hypoplasticity is formally introduced, and it is shown that a particular class of hypoplastic formulations arises naturally from certain bounding surface models, with the distinguishing feature being the dependence of the elastoplastic moduli and/or the plastic strain rate direction on the stress rate direction. The general analytical perspective allows the better understanding and improvement of existing bounding surface plasticity and hypoplasticity models, which are briefly discussed, and suggests the proper way to construct new ones for future applications.

Stochastic Variation of Earthquake Ground Motion in Space and Time

Abstract: Consideration of the spatial as well as temporal variation of earthquake ground motions may be important in the design of structures with spatially extended foundations and lifeline systems. In this paper, the ground motion during a specific earthquake event is conceived as the realization of a space‐time random field. Following a brief review of pertinent results from the second‐order theory of random fields and a description of spectral estimators, accelerograms recorded by the SMART 1 seismograph array in Lotung, Taiwan, are examined to determine the frequency‐dependent spatial correlation of earthquake ground motions. A scheme for processing seismograph array data is proposed, and similarities and differences in the motions recorded during different events are noted. Finally, key parameters characterizing the correlation structures are identified and a preliminary mathematical model is suggested for the space‐time correlations.

Bounding surface plasticity. II: application to isotropic cohesive soils

Abstract: The radial mapping version of the bounding surface plasticity formulation is applied to isotropic cohesive soils. While some aspects of this constitutive model have appeared in the past, a number of important novel features, including closed form analytical relations for certain loadings and the complete analytical formulation, are presented here for the first time. Based on the new aspects a much improved predictive capability is obtained, as shown by successful comparison with experimental data under different loading conditions. The analytical formulation and the significance of the different model constants are carefully investigated in order to have a better understanding of the simulated material response as obtained by numerical methods.

Bounding Surface Plasticity Model for Sands

Abstract: Using bounding surface plasticity, a constitutive equation is constructed to simulate the nonlinear behaviors of loose and dense sands subjected to various types of loadings. The critical state, wh...

Time domain flexural response of dynamically loaded single piles.

Abstract: Adopting a Winkler assumption, a simple mechanical soil model is developed for the flexural response analysis of dynamically loaded piles. The model is defined by examining a frequency-domain analytical expression of the dynamic response of a massless cylinder in an infinite previously developed medium. The expression is based on the plane strain assumption. Using this soil model, the time-domain transfer matrix is developed for the flexural response of a single pile. The steady-state harmonic response of a single pile is computed by both the present approach and a previously developed frequency-domain solution. Good agreement between the two computed results validates the present approach. The dynamic response of single piles subjected to the lateral impulse load is computed for piles in both homogeneous and inhomogeneous soil, in order to demonstrate the capability of the present approach. It is confirmed that the developed soil model and pile response formulation are very efficient in numerical computation.

Bounding Surface Plasticity. III: Application to Anisotropic Cohesive Soils

Abstract: A rate‐independent elasto‐plastic bounding surface constitutive model applicable to anisotropic cohesive soils is presented. It is shown that the theory is capable of realistically accounting for the initial anisotropy and its subsequent evolution in a manner consistent with our current understanding of anisotropy. While retaining the capabilities of the bounding surface theory developed for isotropic cohesive soils, a more general hardening behavior, which includes rotational and shape‐hardening features, is introduced in this anisotropic theory in order to simulate the evolution of material anisotropy. By comparing the predictions with experimental data, the anisotropic theory is shown to provide satisfactory results under stress paths involving strong development of anisotropy.

3D Beam‐Column Element with Generalized Plastic Hinges

Abstract: Beam‐column elements in which plastic hinges may form are commonly used for elastic‐plastic analysis of frames. The concept of a zero‐length plastic hinge (lumped plasticity) is a mathematical abstraction, because it implies infinite strains. Nevertheless, the concept is convenient computationally, and can be sufficiently accurate for many practical applications. For simple beams, plastic hinges can be introduced easily into a mathematical model. For 3D beam‐columns, however, the concept of a “generalized” hinge is needed, accounting for interaction among axial, torsional and biaxial bending effects. A theory and computational procedure based on plasticity concepts are presented. Numerical examples indicate how the element might be used, and show that results in agreement with more elaborate models can be obtained. Because the lumped plasticity assumption is not necessarily accurate, caution is advised in use of the element.

Fracture processes in concrete and fiber reinforced cementitious composites

Abstract: This paper discusses the fracture processes of concrete and fiber reinforced cementitious composites with special focus on the development of the fracture process zone with respect to the stress-separation constitutive relation of such materials. The suggestion is that the overall mechanical behavior of a concrete or FRC structure could be strongly influenced by the stress-separation constitutive relation, which in turn could be altered by engineering the microstructure of the material, especially in FRC. The process zone length is found not to be a material property, but depends on the geometry of the specimen and the loading configurations. All these results are shown explicitly by a simple numerical model of a center-cracked panel subject to remote edge loading or to wedge loading on the crack faces. These calculations also provide further understanding to the validity of certain failure criteria.

Free Vibration Analysis by BEM Using Particular Integrals

Abstract: 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

Free vibration of combined dynamical systems

Abstract: A method for analyzing the free vibration of combined linear undamped dynamical systems attached at discrete points is shown. The method uses separation of variables to exhibit the harmonic motion of the system and to derive a generalized differential equation for the normal modes. Green’s functions for the vibrating component systems are used to solve the generalized differential equation and derive the characteristic equation for the natural frequencies of the system. The characteristic equation can then be solved for the exact natural frequencies and exact normal modes. The method is demonstrated for two types of dynamical systems involving beams and oscillators. For two particular systems, approximate natural frequencies determined through a Galerkin’s method and the finite element method are compared to the exact natural frequencies. The generalized orthogonality relation for each system is derived.

Spline Finite Strip Analysis of General Plates

Abstract: The spline finite strip method was developed recently as a complement to the semi-analytical finite strip method in dealing with problems involving mixed boundary conditions, concentrated loads, and continuous spans. In this paper, the spline strip method is further extended to the analysis of arbitrary shaped general plates. The versatility and accuracy of the method are amply demonstrated through a number of numerical examples.

Harmonic rocking of rigid block on flexible foundation

Abstract: A study of the rocking response of a rigid block resting on a foundation of independent springs and dashpots is made. To simulate the lack of appreciable tension strength in soil foundations, uplifting of the block base from the foundation is allowed when the springs are in tension. Two piecewise equations of motion are derived, and they are also coupled and nonlinear. Due to uplifting the system behaves as a softening system. An approximate analytical solution combining static condensation and the method of averaging is used to predict the rocking amplitude when the foundation moves horizontally due to a harmonic acceleration. The analysis shows that relatively large rocking amplitudes, compared to the model with perfect bonding, can occur at excitation frequencies below the natural rocking frequency. Further, an approximate method for predicting the maximum tilt-angle under horizontal earthquake excitation by relying on the linear seismic response spectra is developed. The predicted results are found in reasonable agreement with data obtained from numerical integration of the exact equations of motion.

Non-Normal Stochastic Response of Linear Systems

Abstract: Conventional analysis of mean squared values is extended to calculation of the fourth moment of the response of a linear system. This provides a way to investigate the non‐normality of structural response, due to a non‐normal excitation. Studies are made for a linear SDF structure subjected to fairly simple non‐normal forces, which include a “white noise” process and filtered processes. Each filtered non‐normal process is generated by passing a “white noise” non‐normal process through a linear second‐order filter. The non‐normality of the structural response is investigated by integration in both the time domain and the frequency domain and by a more efficient technique that is an extension of the Lyapunov equation. This latter method reduces the calculation of the fourth moment of the response to solving a set of simultaneous linear algebraic equations.

Static Stability of Curved Thin‐Walled Beams

Abstract: Starting from a continuum mechanics basis, the principle of virtual displacements is used for deriving the differential equations of equilibrium for a horizontally curved I‐beam. In the present formulation, the effect of curvature is considered, while the condition of inextensibility, usually adopted in conventional analyses, is not required. The cross‐sectional displacements for the curved I‐beam are derived through employment of Vlasov's thin‐walled beam assumptions. Due to the inclusion of nonlinear strains in the virtual work equation, the instability effects caused by various loads, including the axial force, transverse shears, torque, bending moments, and bimoment are generally taken into account. The solutions are presented and compared with existing ones for two special cases.

Effect of Sediment on Earthquake-Induced Reservoir Hydrodynamic Response

Abstract: In typical reservoir a sediment layer of considerable depth may be deposited on top of exposed bedrock foundation. The effect of sediment on the dissipation and damping of earthquake induced hydrodynamic waves is by and large ignored in earlier studies of dam-reservoir-foundation system. The present work models the sediment as a poroelastic material. For vertical excitations, analytical solutions are sought with the aid of computer algebra (MACSYMA). As a result, the bottom damping coefficients are explicitly expressed as functions of material properties and earthquake frequency. For a modest amount of sediment and slight desaturation of pore water, significant changes in the hydrodynamic response curves are observed.

Constitutive Model for Nonassociative Behavior

Abstract: A simplified approach for the nonassociative behavior of granular (geological) materials is proposed. The basic concept is that the plastic potential can be obtained by controlling or correcting the yield function used for associative plasticity. This is achieved by correcting the hardening, evolution or growth function, which involves only one additional parameter above those for the associative model. Determination of constants and verification with respect to two granular soils tested under a variety of multiaxial stress paths are presented. It is shown that incorporation of the nonassociative behavior through the correction of the growth function yields remarkably satisfactory predictions for volumetric and stress‐strain responses of the material response.

Thermodynamic Consequences of Strain Softening in Tension

Abstract: The strain softening behavior of a tension bar loaded by an increasing elongation is analyzed. The constitutive model consists of linear elasticity in combination with associated plasticity theory using a maximum tensile stress criterion as yield surface. The resulting mechanical stability criterion is augmented by considerations of the use of the second law of thermodynamics. These thermodynamical considerations imply a significant reduction in the possible strain softening responses. Moreover, for very brittle material behavior, it is shown that the softening region cannot be considered to have a specific strain state, but rather is described by a strrss-elongation relation. This result provides strong physical support for a fictitious crack model. This crack model is then reevaluated in the spirit of a smeared crack approach and the resulting expressions turn out to be identical with those of a composite fracture model.

Analysis of Kinked Crack under Uniform Heat Flow

Abstract: A thermo‐elastic problem is analyzed for an infinite plate with a kinked crack, which occurs from an end of a linear initial crack. The plate is subjected to a uniform heat flow in an arbitrary direction. The rational mapping function of a sum of fractional expressions, thermal dislocation and the complex variable method are used in the analysis. A closed solution is obtained for the shape represented by the rational mapping function. Distributions of heat flow, temperature and stress, the stress intensity factor and singularity of heat flow are investigated, both before and after the occurrence of a kinked crack.

Rough Crack Model for Analysis of Concrete

Abstract: The theory of a rough crack model for nonlinear finite element analysis of reinforced concrete is presented. The model accounts for shear dilation, degradation under cyclic loading, and other effects. The smeared crack approach is used in the derivation, but the model could also be used for discrete cracks. The concept, theory, and computational procedure are described, and examples are presented.

Convexity of smooth yield surface of frictional material

Abstract: Existing formulations for the deviatoric cross section of a smooth yield surface for a frictional material such as concrete, soil, or rock are examined. It is shown that the simplest avail formulae do not guarantee convexity of the yield surface for all combinations of material parameters, while the formula developed by later research does.

Effect of Fatigue on Fracture Toughness of Concrete

Abstract: An experimental study utilizing 4‐point bending SENB specimens was carried out to determine the effect of fatigue on the fracture toughness of plain concrete. In addition to fourteen static tests of beams with a midspan precast notch, nine specimens with an initial precast notch of a depth to height ratio of l/d=0.20 were fatigued until a certain crack length was reached. Crack growth was successfully monitored by the CMOD compliance measurements. Independent surface crack length measurements by a hand‐held scope and observations of the crack front with the use of a fluorescent dye‐penetrant injected into the notch root were also performed. The fracture toughness, GIC, under fatigue appears to be higher than under static loading and shows an increasing trend with increasing crack length and number of loading cycles. The observed behavior is most likely related to the presence of a microcracking zone that evolves with fatigue.

Three‐Dimensional Motion of Buried Pipeline. I: Analysis

Abstract: Dynamic response of a long, continuous pipeline buried at a depth, h, below the free surface of the ground is analyzed. It is assumed that the pipe is disturbed by plane seismic waves traveling at an arbitrary angle to its axis. Thus, the problem is three dimensional. The pipe has been modeled as a cylindrical shell. Both the pipe and the surrounding ground are assumed elastic, isotropic, and homogeneous. The solutions of equations of elastodynamics governing the motions of both are obtained in terms of cylindrical eigenfunctions modified to satisfy the boundary conditions on the free surface of the ground. Numerical results are presented in the accompanying paper.

Vibration of Damped Plate‐Oscillator Systems

Abstract: A classical method for obtaining the exact natural frequencies, natural modes, orthogonality relation and response due to arbitrary loading of undamped beam-oscillator systems presented earlier by the writers is extended to viscously damped plate-oscillator systems. The natural modes are expressed in terms of the Green’s function for the vibrating plate. Damping is present in both the plate and oscillators. Modal analysis allows the determination of a closed form expression for the system response to arbitrary loading. Oscillators attached to a simply supported rectangular plate have been considered, but the method is applicable to any plate-oscillator system, provided the Green’s function for the undamped vibrating plate is known. An example involving a single oscillator attached to the plate shows the natural frequencies, natural modes and response due to two special types of loading.

Response of linear systems to quadratic gaussian excitations

Abstract: Probability density functions, mean crossing rates, and other descriptors are developed for the response of linear systems to squares of Gaussian excitations. The analysis is based on discrete approximations of the spectrum of the Gaussian excitation. Accordingly, the response can be expressed as a finite quadratic form in Gaussian variables, whose characteristic function has a closed form. The characteristic function can be inverted by Fast Fourier Transform algorithms to find the first order probability of the response. Several approximations are applied to determine crossing and peak characteristics of the response. The proposed methodology is applied to estimate structural response to wind loads and the mean failure rate of systems subjected to bivariate Gaussian stress processes.

Vibrations of Footings on Zoned Viscoelastic Soils

Abstract: Most finite element solutions of soil‐structure interaction problems assume a horizontally layered soil that unavoidably extends to infinity and is bounded at the bottom by a bedrock. In this paper, a model consisting of a soil deposit included in a viscoelastic half‐space is used to analyze numerically the effects of the shape of the soil deposit and the existence of a compliant bedrock on the dynamic compliances of strip footings. The soil deposit is assumed to be semielliptical and in order to achieve a parametric study several aspect ratios going from infinity (boundless horizontal layer) to one (semi‐circle) are considered. The rigidity of the half‐space is given several values including infinity (rigid bedrock). The foundation compliances are computed using a frequency domain formulation of the Boundary Element Method for zoned viscoelastic media.

Formulations of Structural System Reliability

Abstract: Two formulations are developed for the determination of the reliability of general redundant structural systems. One is the failure mode approach, which is based on ways in which a structure may fail. The other is the stable configuration approach, which is based on the possible configurations in which a structure may carry an applied load. Conceptually, the stable configuration approach has the advantage over the failure mode approach in that neglecting possible configurations will be conservative, whereas neglecting potential failure modes will be unconservative. For a class of structures, in which the load effects on a surviving element never decrease with the failure of other elements (consistent redistribution), simplified formulations are obtained. Such simplifications for this type of structure result from the fact that the exact sequence in which the elements will fail is irrelevant. Results of the simplified formulations are conservative for structures in which the load effect on a member may be ...

Z-transform modeling of P-M wave spectrum

Abstract: The approximation of the Pierson‐Moskowitz (P‐M) wave spectrum as the output of digital filters to white noise excitation is considered. It is shown that the mathematical peculiarity of this spectrum is the source of the numerical difficulties encountered in approximating it by autoregressive (AR) models. Further, it is shown that a reasonably accurate initial AR approximation leads to quite efficient autoregressive moving average (ARMA) models. This is accomplished by employing two new techniques. Numerical data are given in a dimensionless form so that they are applicable to a variety of structural dynamics applications.

Random Vibration of Rotating Machines under Earthquake Excitations

Abstract: Random vibration of rotating machines subjected to seismic excitations is analyzed in which the six-component earthquake ground motions are modeled as nonstationary random processes. The six-component earthquake inputs, including the rotational components of base excitations, result in not only nonhomogeneous excitations but also parametric excitations. Thus, the classical spectral analysis of random vibration is not applicable. Furthermore, both nonhomogeneous and parametric random excitations are correlated random processes, making the problem even more difficult to solve analytically. To date random vibration of such a complicated problem has not been investigated. The method of Monte Carlo simulation is used to simulate the six-component nonstationary earthquake ground motions and to determine the statistics of the response of rotating machines. The significance of seismic base rotations on the overall structural response is examined. A numerical example is worked out to demonstrate the methodology employed.

Cumulants of stochastic response for linear systems

Abstract: The magnitudes of response cumulants are investigated for linear systems excited by stochastic inputs. This extension of the classical study of mean and covariance (i.e., first and second cumulants), provides basic information regarding the non‐normality of a response process. The dependence of the response cumulants on the parameters of the linear system is emphasized, as are approximations and order‐of‐magnitude results which reveal the nature of this dependence without numerical computation of response values. New information is provided regarding the phenomenon of a linear system having a nearly normal response to a non‐normal excitation. Conditions are determined under which a complicated stochastic excitation may be adequately approximated by a process which is delta correlated and a numerical example is given to illustrate one particular situation. Conditions are also derived under which a stationary process may adequately approximate an excitation that is nonstationary.