Journal of Engineering Mechanics

A combined plasticity and damage mechanics model for concrete is developed within the general framework of the internal variable theory of thermodynamics. The necessity of using both plasticity and damage mechanics is discussed and the corresponding surfaces are developed via the internal dissipation inequality. The damage surface is a consequence of a damage evolution law based on the physical aspects associated with two modes of cracking. Both hardening and softening features are displayed by the damage surface. The plasticity surface is the classical one of von Mises with strain hardening but not strain softening. The combined theory is capable of accommodating the anisotropy induced by mi‐crocracking and is very suitable for computer implementation. The simultaneous use of the damage surface, which is pressure dependent, and the plasticity surface, which is chosen here to be pressure insensitive, leads to a constitutive model that displays the essential features of concrete inelasticity. These features, which include dilatation with shear and enhanced ductility with increased values of mean pressure, are shown together with comparisons of theoretical and experimental data.

This paper presents the experimental results obtained from the study of two similar cylindrical water tanks. One of the tanks was directly fixed to the earthquake simulator, the other was mounted on the base of a scaled nine‐story steel structure. The structure was isolated on eight multilayered elastomeric bearings. Due to the reduction in the ground accelerations, the dynamic pressure is reduced for the tank in the isolated structure. Free‐surface water elevation was slightly increased due to the lower frequency that characterizes the motion of base‐isolated structures. This problem can be overcome by appropriate selection of the isolation system or by the addition of dampers at the location of maximum water particle velocities. A theoretical solution developed from linear wave theory correlates very well with the experimental results. Further study is carried out to investigate the advantages of using base isolation for large storage tanks.

A technique based on time‐series modeling is used to determine modal forces arising from wind pressures recorded at various levels of a building model during a wind‐tunnel experiment. The complexities of the wind flow pattern around a building, coupled with limitations in the instrumentation, may make it difficult to monitor a sufficient number of pressure transducers to obtain such forces in only one wind‐tunnel experiment. Transfer function models are used to create a statistically consistent ensemble of wind pressures using partial records available from several separate wind‐tunnel experiments, in which the instrumentation is reconfigured in each experiment but conditions otherwise are unchanged. Statistics of wind forces acting on the building model in the alongwind, acrosswind, and torsional directions, and their correlations are considered. This technique, if used judiciously, can overcome some of the difficulties caused by limitations on the number of available instrumentation.

A model is proposed with a probabilistic evolution of damage in the material. The constitutive law is built through the development of a two‐level approach. The micro‐level is assumed to be constituted of elastic‐brittle springs whose strength follows a probabilistic distribution. The representative macro‐volume of material contains a given number of these elementary defects and its damage (loss of elastic properties) is computed from the knowledge of the local states. The macro‐behavior results from the interactions between all the micro‐defects. The model may be considered as representative of the behavior of brittle and almost brittle materials. It exhibits scattering and size effect. A Weibull distribution law is assumed for the local probabilities of failure and a parallel loose bundle connects the micro‐defects. These simple hypotheses lead to analytical expressions of the probabilistic constitutive law. The approach developed appears as an intermediate model between continuous damage mechanics and probabilistic brittle fracture. The knowledge of a single parameter $N_t\text{,}$ number of defects in a given volume, provides the degree of ductility of the material.

This paper deals with the nonaxisymmetric dynamic behavior of fluid‐filled buried orthotropic cylindrical shells/pipes excited by plane longitudinal waves. A thick shell model including the effects of shear deformation and rotary inertia is taken. A perfect bond between the shell and the surrounding soil is assumed. The linear acoustic equation is used for wave propagation in the fluid inside the pipe. Results are presented for the axisymmetric as well as the flexural mode for different orthotropy parameters of the shell and also for different soil conditions around the pipe/shell. Results of the empty and fluid‐filled shells are compared. Effects of changes in the fluid density are also discussed. The presence of fluid inside the shell significantly alters the shell response. The effect of fluid, in general, is comparable to the effects of variation in the orthotropy parameters of the shell and also to the effects due to changes in the soil condition. In the flexural mode, deformations in the fluid‐filled shell are normally more than those in the empty shell. Finally, it is concluded that it may not always be safe to assume that the consideration of fluid presence will give only a lower and conservative dynamic/seismic response compared to the empty shell.

Two methods are examined for simulating samples of a diffusion process ${\mathbf{X}}_t\text{.}$ The methods are based on: (1) The Itô differential equation of ${\mathbf{X}}_t;$ and (2) differential equations with colored noises for processes ${\mathbf{Y}}_t^n$ converging to ${\mathbf{X}}_t$ as the memory of colored noises decreases. The Wong‐Zakai theorem can be applied to establish these differential equations. One‐ and two‐dimensional diffusion processes are used to illustrate and evaluate the simulation methods. Results show that both methods are satisfactory, provided that numerical methods for solution and integration time step are adequate. Use of processes ${\mathbf{Y}}_t^n$ allows one to determine the sensitivity of the response of a nonlinear system to input correlation and allows use of a broader range of numerical integration techniques.

The research here deals with the development of an analytical method for the computation of large deflections and rotations of members with varying stiffness along their length. The member may be statically determinate, or statically indeterminate, and its loading may be arbitrary. This method involves the use of equivalent nonlinear and equivalent pseudolinear systems of uniform stiffness that replace the original variable‐stiffness member. The large deflections and rotations of the equivalent system are identical to the corresponding ones of the original variable‐stiffness member, and they can be obtained by either: (1) Using the equivalent pseudolinear system and applying elementary linear analysis; or (2) using a simplified equivalent nonlinear system and applying nonlinear analysis. A mathematical proof regarding the existence of equivalent nonlinear and equivalent pseudolinear systems is obtained by using the nonlinear second‐order differential equation. The use of equivalent systems simplifies a great deal the mathematical complexity of the variable‐stiffness problem. The Young's modulus of elasticity is assumed to be constant, but the method applies equally well when this modulus varies along the length of the member.

A combined crack closure‐shear transfer model of the fracture‐process zone (FPZ) of concrete was developed through an interactive use of fracture‐test data and finite element analyses of crack‐line wedge‐loaded, double‐cantilever beam (CLWL‐DCB) specimens subjected to additional diagonal compression loading. The diagonal compression loading caused the crack to veer in the diagonal direction. The numerical simulation of those mixed‐mode‐fracture results showed that the load‐carrying capacity of the specimens was governed only by the crack‐closure stress on the FPZ, because the initial direction for the cracks coincided with the minimum principal stress direction and that direction remained essentially the same until the maximum wedge load was exceeded. The effect of shear‐transfer modeling was demonstrated by numerical simulation of published fracture‐test data for eccentrically loaded, four‐point‐bend specimens.

This paper investigates the accuracy of a simplified model for the description of elastic‐plastic response of wide flange shapes under three‐dimensional loading. The model uses the average effect of moment‐axial force curvature equations in each bending direction to compute the terms in the element stiffness matrix. While this approach is exact for planar response computations, it is an approximation in describing three‐dimensional response. Another problem that arises for rolled shapes is that the model must describe the effect of differential bending on the member's response. This is accomplished by using the elastic stress variation to measure the extent of flange yielding. A large deflection, displacement‐control procedure is used to compute the elastic‐plastic‐failure load of the system and trace the unloading path. Comparison with analytical and experimental work on flexural‐torsional buckling of columns is used to verify the accuracy of the proposed model. Agreement with previously published results is excellent.

A complete solution is given for the first time to the problem of an inclined circular punch bonded to a transversely isotropic elastic half‐space. Explicit expressions are derived for the field of stresses and displacements around such punch subjected to a shifting load and a tilting moment. The method of solution is based on the new results in potential theory obtained by the writer earlier. The complete solution is initially expressed in terms of three potential functions. The displacements are defined through first derivatives of the potential functions, while the stresses are given by second derivatives. The complete solution for an isotropic body is obtained as a limiting case of the general solution. Specific computations are performed in order to compare the elastic field in the vicinity of a bonded punch with similar parameters for a smooth punch. It is found that the influence of bonding on normal displacement is relatively small, while its influence on tangential displacements may be quite significant.

On‐line, pseudodynamic tests are becoming increasingly popular for large‐scale seismic performance testing of structures. Such tests provide a means of simulating the effect of compliance of the structure on the inertial loads it will experience in the event of an earthquake, without the need to use a shaking table. One of the difficulties encountered is that the results from pseudodynamic tests can be extremely sensitive to measurement and control errors. Error analyses available to date have focused on implementations based on explicit time‐integration schemes. Recently, however, researchers have successfully implemented an implicit integration scheme, which will probably become the preferred technique for pseudodynamic testing. An error analysis for this implicit scheme is presented, using a systematic approach. It is shown that the effect of measurement and control errors can in most cases be greatly reduced by a suitable adjustment of the measured displacements at every time step. The reduction in errors for this case is similar to that achieved in the explicit implementation by using the computed instead of the measured displacements.

Error propagation characteristics for the pseudodynamic test method based on implicit time‐integration schemes are evaluated and compared to those for an explicit time‐integration scheme. For random errors and a linear structure with one degree of freedom, the error amplification factor for the implicit scheme is generally lower than that for the explicit scheme. The difference is small when the time step is small compared to the period of oscillation of the structure, and increases for larger time steps. The advantages of the implicit scheme become more apparent for an N‐degree‐of‐freedom structure consisting of N equal masses connected by shear springs of equal stiffness, and errors that occur independently from one story to the next. In this case, the error amplification factor at first increases as the number of degrees of freedom is increased, but then decreases and appears to approach an asymptotic value of unity when the number of degrees of freedom becomes very large. As an example of an inelastic system, the effect of random measurement errors on the response of an elastic‐perfectly plastic oscillator is evaluated. This example serves to verify the range over which linearity of the error structure is applicable.

A transmitting boundary for semi-infinite fluid is developed. Displacements instead of pressures are used to describe fluid motion. Singularity problems in fluid are overcome by using penalty function method and selective integration scheme. The proposed method is particularly convenient for computer implementation; moreover, the method can be extended readily to include semi-infinite solid-fluid media.