Journal of Engineering Mechanics

In this work, the response analysis of a randomly excited nonlinear system is considered. The system resembles a frictional base isolation system under random earthquake excitation. The equivalent linearization technique and the stochastic averaging method are used to estimate the response statistics. The applicability of the recently suggested method of equivalent nonlinear system is also examined. The resulting mean‐square responses as evaluated by various approximation techniques are compared with those obtained from the performed Monte Carlo digital simulations. It is shown that the stochastic averaging method leads to more accurate stationary response statistics when compared with the equivalent linearization technique. Furthermore, the accuracy of the results obtained by the method of equivalent nonlinear system is quite sensitive to the form of equivalent system selected.

This paper concerns the optimal distribution of a given volume of material in I‐beams so as to maximize the elastic flexural‐torsional buckling capacities. The material distribution has been restricted to different top‐to‐bottom flange‐width ratios, linear tapering of flange width, or linear tapering of web depth. Based on the Rayleigh‐Timoshenko energy method, a canonical form of the Ray‐leigh quotient is derived for the three types of design considered. For the maximum buckling capacity, the quotient is first minimized with respect to the displacement function and then maximized with respect to the design parameter. To avoid inelastic behavior and a small cross‐sectional area in the optimal beam designs, a maximum permissible normal‐stress constraint is imposed. Optimal designs of simply supported I‐beams under general moment gradient are presented. A comparison study is made to determine which of the three design types is the most effective way of distributing material for maximum buckling capacities.

A multiple‐mechanism elasto‐plastic model for soils applicable to general three‐dimensional stress states and cyclic loadings is presented. The model uses the concept of mobilized friction angles to define yielding. In stress space, the postulated yielding mechanisms define an elastic domain whose boundary is, in general, nonsmooth and possesses comers. Theoretical and computational aspects of the model are discussed in detail. Numerical implementation of the model is performed using the cutting plane algorithm. The model accuracy is demonstrated using triaxial soil test data and previously determined material parameters. The model is accurate in characterizing soil behavior and able to capture both com‐pactive and dilative responses of soil. Also, the accuracy of the stress‐point algorithm used for the update of the stress state is analyzed and found to be acceptable. Finally, the model is used to compute the response of a semi‐infinite saturated soil deposit consisting of loose and dense layers subjected to earthquake base excitation. Resulting changes in pore fluid pressure, accompanied by changes in vertical effective normal stress, are illustrated.

The category of problems that examines the dynamic behavior of inclusions embedded in elastic media is of particular interest to the study of dynamic soil‐structure interaction. In a majority of investigations, the interface between the inclusion and the surrounding elastic medium is assumed to be perfectly bonded. This paper examines the elastodynamic problem pertaining to the steady rectilinear oscillations of a spherical rigid inclusion that is embedded in smooth bilateral contact with an isotropic elastic medium of infinite extent. The bilateral contact is maintained by the application of a uniform radial stress field at infinity. The inclusion is subjected to a harmonic oscillation. The analytical solution for the resulting elastodynamic problem is developed in exact closed form. The numerical results presented in the paper illustrate the manner in which the dynamic compliance of the embedded rigid spherical inclusion is influenced by the frictionless boundary conditions at the inclusion‐elastic medium interface.

The functioning of lifeline systems after a major earthquake is critical to the modern urban center. A system study of lifeline response to catastrophic earthquakes is the essential prerequisite for the emergency management authority to form a mitigation and reconstruction plan to minimize the total loss caused by the earthquake. This paper develops an applied formulation of lifeline‐restoration processes in the post‐earthquake period, on the basis of a discrete‐state, discrete‐time Markov process. There are a finite number of damaged lifelines that each require a resource for reconstruction. The lifelines have values associated with their functioning capacity. We wish to assign limited resources to lifelines so as to minimize the total loss caused by malfunction of damaged lifelines. Dynamic programming is used to optimize the distribution of limited reconstruction resources. By computer simulation, various scenarios are examined, and useful information that is important to the emergency management authority is obtained.

A hypoplastic model is formulated to simulate the nonlinear and irreversible behavior of loose and dense sands. Hypoplasticity provides a theoretical framework that is simpler than elastoplasticity. The failure surface that is assumed fixed in stress space is chosen as the bounding surface. All the hypoplastic properties (flow and yield directions and plastic modulus) are defined as functions of the distance to the bounding surface. The model is formulated in terms of stress invariants', the influence of Lode angle is accounted for by using an adjustable Lode dependence. The incremental stress‐strain relationships are inverted and derived in a format compatible with solution techniques, such as finite element methods. The model has 12 material constants calibrated from triaxial tests. Based on the comparison of predicted and experimental results on loose and dense Sacramento River sands, it is concluded that the model is capable of predicting the drained and undrained behavior of loose and dense sands.

An elastic‐viscoplastic model for large deformation of metals (Rubin 1987b) has been generalized to include the major features of cap‐type models for geological materials. Specifically, the effects of shear‐enhanced compaction and dilation are conveniently modeled using kinematics that naturally separate plastic distortion from plastic dilatation (volume change). The constitutive equation for stress is hyperelastic in the sense that the stress is a function of elastic deformation and is equal to a derivative of the Helmholtz free energy. Although the theory is formulated without the explicit use of a yield function, the flow rule for plastic deformation rate can best be described as nonassociated. In this regard, special attention is focused on satisfying a physically plausible thermodynamic restriction on the constitutive equations, which ensures that the rate of plastic dissipation is nonnegative. Specific constitutive equations are proposed, and the material constants are determined by matching experimental data for Yuma clayey sand.

A bimaterial problem is considered for shapes that are symmetrical with respect to an interface that is finite and straight. A rational mapping function and complex stress functions are used to obtain a general solution for bonded half‐planes with cracks at an end of the interface. A stress analysis is carried out for a state of uniform tension at infinity, which is either symmetrical or antisymmetrical with respect to the interface. Stress distributions and stress‐intensity factors are obtained for various crack length and elastic constants. When one material is in tension and the other is free from traction, stress‐intensity factors are also investigated. The bond effects on the stress‐intensity factors are studied. The elastic constant's effects on the stress‐intensity factor for a short crack and the stress function for special material constants are also investigated.

A Theological model of the normal consolidation behavior of viscous clays is presented. The approach adopted combines elasto‐plastic behavior with structural viscosity effects. In particular, a modified Cam‐clay yield surface, employed to describe plasticity effects, is analyzed in conjunction with viscous resistance characteristics based on the use of a thixotropy law. The whole is placed in the context of Biot's two‐dimensional consolidation framework and solved using the finite element method. An application of the model, to the one‐dimensional consolidation of a clay that had previously been tested in the laboratory, is presented. Good correlation is achieved, indicating clearly the ability of the proposed model to reproduce real consolidation behavior during both the primary and the secondary phases. Various features of the model are then addressed via numerical predictions of the consolidation of thicker samples of the same clay. The model's scaling law is determined together with the form of the variation of deformation predictions, as drainage path lengths are increased. The importance of viscous resistance effects in the model's performance is also demonstrated.

The hydrodynamic pressure acting on the upstream face of arch dams is explored by a special boundary element method based on the use of a complete and nonsingular set of Trefftz functions. The arch dam, bounded by a limited, arbitrary irregular part and an unlimited regular part of the river valley, is considered to be in an arbitrary shape. Using this method, one can, with minimal effort, accurately model the compressibility of the water and the gravity waves on the water surface. Numerical examples are presented to illustrate the results obtained from this method. Comparisons with other numerical solutions are provided.

The secondary influences, besides the transverse shear deformation and the rotatory inertia, that affect the bending behavior of beams are identified. Incorporating these influences, a shear-deformation theory is developed for beams of solid circular cross section. Because an a-priori knowledge of the stresses is necessary to account for the secondary influences, a procedure is developed to obtain a statically equivalent three-dimensional stress field. Using this procedure, an engineering stress field is developed, and is compared with an exact solution for the beams of circular cross section. The stress field is later used to develop the shear-deformation theory that accounts for all the bending-related secondary influences. The theory is evaluated considering the propagation of traveling flexural waves.