Journal of Engineering Mechanics

The use of multidimensional random fields to model real engineering systems is gaining acceptance as personal computer systems become increasingly powerful. The accuracy of such models depends directly on the accuracy of the algorithm used to generate realizations of the representative random fields; there is a need to evaluate and compare various random‐field generators. To address the issue, three common random field generators are considered in this paper: (1) The fast Fourier transform (FFT) method; (2) the Turning bands method (TBM); and (3) the local average subdivision (LAS) method. For each, an ensemble of realizations of a two‐dimensional homogeneous Gauss‐Markov process is generated and the field mean, variance, and covariance structures are checked for statistical accuracy. Concerns such as ease of use and efficiency are also considered. All three methods have distinct advantages and disadvantages, and the choice of algorithm will depend on the particular application. A number of guidelines and suggestions are made to help avoid or minimize problems associated with each method.

This paper presents a frequency domain method to estimate the second‐order statistics of the response of complex hysteretic structures under stationary stochastic excitation. The nonlinear constitutive relations are dealt with by means of a stochastic linearization approach of an iterative nature. Since the first iteration has been accomplished, a criterion is established that allows location of the regions where inelastic deformations progress. Other regions of potential plastic behavior, which actually remain elastic, may thus be removed from the structural equation of motion with a tremendous computational advantage. Hinged frames and shear‐beam models are numerically investigated to illustrate the effectiveness of the proposed scheme.

The main nonlinear phenomena that govern the deformational behavior of early‐age concrete are the evolution of the stiffness properties, the development of thermal strains, creep, and cracking. A general approach for numerically simulating this type of behavior is presented. The thermomechanical problem is decoupled such that first a thermal analysis is carried out and then a stress calculation is performed. An interface program is used to map the results from the thermal analysis onto the input data required for the stress analysis. A brief review of the relations for the thermal‐stress analysis is given, followed by a more elaborate treatment of the algorithm used for the combination of thermal strains, creep, and smeared cracking. To properly accommodate these effects in a finite‐element analysis, a smeared‐crack model is used that is rooted in a decomposition of the strain increments. The emphasis is on the general approach for properly and efficiently handling these phenomena. A special case, namely a power‐type creep law, is elaborated. It is shown that this relationship reasonably fits experimental data. A detailed description of an example calculation that demonstrates the potential of the numerical simulation strategy follows.

The optimal design of circular plates of elastic‐perfectly plastic material and subjected to variable repeated loads is studied according to the shakedown criterion. Two different types of design problem are formulated: one searches for the minimum volume design whose shakedown limit load is assigned; the other searches for the maximum shakedown limit load design whose volume is assigned. In both cases the design problem is formulated by means of a statical approach on the grounds of the shakedown lower‐bound theorem, and by means of a kinematical approach on the grounds of the shakedown upper‐bound theorem. The Euler‐Lagrange equations of these problems are found by a variational approach. The equivalence of the two types of design problem is proved and the design optimality condition is shown to constitute an extension to the shakedown context of the well‐known Drucker‐Prager‐Shield‐Rozvany theorem of optimal plastic design; namely, a modified unit cost is envisaged, the sum of the plate unit cost with some energy density, whose gradient with respect to the thickness equals, at the optimum, the analogous gradient of the plate plastic dissipation density. A few numerical applications are presented.

A general analytical solution is obtained for the stresses and displacements of an elastic body consisting of an assembly of coaxial hollow circular cylinders made of orthotropic material, with or without a core, and subjected to bending, tensile and torsion loads. Two types of conditions are considered at the interfaces between cylinders: no slip and no friction. A numerical application is used to illustrate the theoretical results. Results show that there is no coupling between bending and tension‐torsion and that there is no deviation in the bending curvature. It was finally found that some warping of the cross section develops under bending, meaning that the Bernoulli‐Euler hypothesis would not strictly apply in the case of orthotropic cylinders.

Linearized potential wave theory is applied in the present paper to investigate the phenomenon of wave scattering by a submerged porous disk. By means of the eigenfunction expansion method, harmonic expressions of the velocity potential in terms of unknown constants are obtained in two subregions of the domain by taking into account the boundary conditions on the free surface, the porous disk surface, and sea bottom surface, as well as the Sommerfeld condition at infinity. These unknown constants are then determined by the matching conditions. Variation of the wave height around the disk and the wave load on the disk versus the dimensionless disk radius, the relative water depth, and the porous‐effect parameter is discussed. It is found that the wave scattering by a disk includes a process of focusing wave energy near the rear of the disk for small dimensionless porous‐effect parameters. An increase of the dimensionless porous‐effect parameter decreases the wave height, and the behavior of a porous disk is similar to that of a wave absorber that may lead to setdown for a large disk radius.

A relatively simple and general constitutive model of interface behavior in quasi‐brittle materials is presented. It is assumed that both hardening and softening behaviors are governed by the same Mohr‐Coulomb‐type fracture criterion. The hardening‐softening level is specified by a single parameter $\kappa \left(v_n^p\text{,}{v}_t^p\right)$, so that the coupling effect of normal and tangential directions are naturally reflected. The whole fracture criterion is established mainly on two basic tests: pure tension and pure shear on interface specimens. A simplified nonassociated flow rule is employed. Simple examples have shown that the model is capable of predicting a variety of interface behaviors in quasi‐brittle materials.

This paper presents several new results in the studies of the fictitious‐crack model. First, an engineering version of the stability theory of the fictitious‐crack model is presented in the framework of the finite element method. Then, the rupture condition of the fictitious‐crack model is extended to the case of multiple loads for the linear softening materials, which leads to a new formula to predict tensile strength. In addition, a new semianalytic model is proposed to study beams without notch, from which a very simple size‐effect formula is derived. This new formula currently has been adopted in a German code to predict the concrete response under multiple loads. Extensive experimental results are collected and compared with our theoretical predictions. In view of the comparison, it appears that, for normal concrete, a linear softening relation is sufficient for the purpose of describing its modulus of rupture.

In this paper a total stress‐strain constitutive model is employed to simulate concrete response prior to cracking. A smeared crack approach is used to simulate the effect of cracking in concrete, and the model is capable of depicting the effect of multiple nonorthogonal cracks. Tension stiffening is considered part of the concrete in each reinforcing direction. A variable crack interface shear‐stiffness model, based on crack‐confining normal stresses, is employed. The effect of compression softening in cracked concrete is considered through the use of both stress‐ and strain‐based softening procedures. The capabilities of the analytical model are evaluated by analyzing several panel elements under uniform membrane stresses and a shear‐wall element under in‐plane stress action.

Fibers with inclination angles of 0°, 14°, 27°, and 37°, respectively, were pulled out from a cementitious matrix. For each inclination angle, two types of specimens with 16 and eight steel fibers, respectively, were tested. Effects of fiber inclination and number of fibers on peak pullout load and corresponding slip were experimentally examined. Based on failure mechanisms experimentally observed, a fracture mechanics model was developed to predict pullout resistance of aligned and inclined fibers. A rising $R‐\mathrm{curve}$ is proposed to account for different embedded lengths of fibers. The predicted peak loads match quite well with the experimental results from different studies. The proposed theoretical model can predict reasonably accurately both the peak load as well as the corresponding slip displacement. Predictions are compared with the data for both metallic and synthetic fibers.

A new approach for first‐order reliability analysis of structures with material parameters modeled as random fields is presented. The random field is represented by a series of orthogonal functions, and is incorporated directly in the finite‐element formulation and first‐order reliability analysis. This method avoids the difficulty of selecting a suitable mesh for discretizing the random field. A general continuous orthogonal series expansion of the random field is derived, and its relationship with the Karhunen‐Loeve expansion used in recent stochastic finite‐element studies is examined. The method is illustrated for a fixed‐end beam with bending rigidity modeled as a random field. A set of Legendre polynomials is used as the orthogonal base to represent the random field. Two types of correlation models are considered. The Karhunen‐Loeve expansion leads to a lower truncation error than does the Legendre expansion for a given number of terms, but one or two additional terms in the Legendre expansion yields almost the same results and avoids some of the computational difficulties associated with the use of the Karhunen‐Loeve expansion.

The problem of interaction among cracks, including the effects of process zones, is studied. The Dugdale‐type cohesive‐zone model is extended to mixed‐modes of loading and is then used to evaluate the size of process zones. The interaction is considered by applying uniform normal and shear tractions on each crack surface caused by the remaining cracks. The magnitude of these interaction tractions relative to far‐field stresses reflects the intensity of the interaction. The effect of process zones on the magnitude of interaction tractions is studied by comparing them with the corresponding elastic values. It is shown that process zones generally enhance the interaction, but effective properties are not altered significantly.

The dynamic behavior of a geometrically nonlinear cable system is studied. Vector‐valued, nonwhite, correlated, stationary random excitation is used. The excitation has both additive and parametric components. The equations for the statistical moments of response are solved by numerical integration and by continuation. Simulation results are presented to assess the accuracy of the analytically predicted moments. The mean‐square response of the dominant coordinate decreases with increasing positive correlation between the excitation components. Increasing the prestrain of the system increases the linearized fundamental frequency and lowers responses. For some values of the parameters, the system has multiple stable and unstable mean‐square responses. Digital simulation shows that the system switches randomly in time from one stable branch to the other. The responses remain finite, so that the system can function safely in such regions. In general, the analytical predicted moments and those computed from simulation agree very well. Moreover, the multiple stable mean‐square responses predicted using Gaussian closure also match simulation results.