Journal of Engineering Mechanics

The extended distinct‐element method (EDEM) is used to construct models of multi‐degrees‐of‐freedom systems for particles of concrete frames and to conduct a series of numerical simulations in which the particles collapsed due to seismic forces. When a concrete frame collapses, it is reduced to a pile of debris. If the debris is rejoined to form the concrete frame, the original shape is restored; i.e., the frame prior to collapse is considered to be an assembled body of concrete debris. The EDEM is a method for analyzing discontinuous bodies, but here we report on an analysis in which concrete debris is considered to contain the elements of a discontinuous body. For convenience, we assumed that the particle shape in the debris is circular and that the parts are connected by springs that satisfy the Mohr‐Coulomb yield conditions. The results of our simulations are in good agreement with records of damage done by past earthquakes.

This paper presents a comprehensive analytical treatment of the three‐dimensional response of a transversely isotropic elastic half space subjected to time‐harmonic excitations. General solutions for equations of equilibrium expressed in terms of displacements are derived by applying Fourier expansion with respect to the circumferential coordinate and Hankel integral transforms with respect to the radial coordinate. The general solutions are used to derive the explicit solutions for Green's functions (displacements and stresses) corresponding to a set of time‐harmonic circular ring loads acting inside a half space. The circumferential variation of the ring loads are assumed to be $\cos m\theta$ for loadings in the vertical and radial directions and $\sin m\theta$ for the loading in the circumferential direction. These Green's functions can be used as the kernel functions of the boundary‐integral‐equation method and in the development of solutions for a variety of elastodynamic boundary value problems. Comparisons with existing numerical solutions for an isotropic half space are presented to confirm the accuracy of the present solutions. Selected numerical results for displacements and stresses are presented to portray the dependence of the response of the half space on the frequency of excitation and the degree of anisotropy of the medium.

Research in seismic numerical modeling of liquid‐storage tanks has been concentrated on tanks with single curvature, such as cylindrical tanks. This paper outlines the development of a numerical model for the seismic analysis of tanks with single and double curvatures, which is achieved through the use of a combined finite‐element‐boundary‐element numerical procedure. The coupled seismic liquid‐shell interaction problem is solved using a shell finite element for the tank structure and the boundary‐element method to model the fluid region. The boundary‐element equations for the liquid region are used to obtain an equivalent finite element fluid mass matrix. This equivalent fluid mass matrix is then combined with the shell structure mass matrix and the coupled equations of motion are then solved. The computer program developed can handle both single‐ and double‐curvature axisymmetric tanks such as cylindrical tanks and spherical tanks. Free‐surface sloshing of liquid and tank‐wall flexibility are included in the model. Frequency‐domain analysis is required if sloshing is included.

A linear theory that may be used to predict the primary responses (stress, strain displacement) of continuous pavements to moving dynamic loads is presented. The theory is derived from the well‐known convolution integral and its formulations in moving and stationary frames of reference are derived. A detailed solution, in the frequency/wave‐number domain, is given for a quarter‐car vehicle‐model driving up a step on an elastic beam resting on a damped elastic foundation. The effects of speed and frequency on predicted stresses and displacements are observed to be consistent with those measured by other writers. The convolution's practical implementation is explained. The results of validation experiments, involving impulse response measurements to check the assumptions of the theory, and an instrumented vehicle driving over an instrumented test track, are described. The results demonstrate that the theory can be used to predict accurately the strains generated in a road as a vehicle drives over, including the effects of vehicle speed and dynamic tire forces.

In this paper a numerical model for the minimum‐weight design of a rectangular machine foundation under a harmonic vertical load is presented. The analysis of the dynamics of foundation‐soil interaction is based on frequency‐dependent dynamic properties of a semi‐infinite supporting medium and includes the shape of the foundation plan, the embedment of the foundation into the soil, and hysteretic material damping of the soil. Dimensions of the concrete block are assumed as design variables. Constraints are placed on resonant frequency, vertical displacement amplitude, stresses in the soil and dimensions of the foundation concrete block. A sequential programming method with variable move limits is used to obtain the optimal solution, which is affected by inertia properties of the machine‐foundation‐soil system, damping from dynamic soil‐foundation interaction and local soil conditions. Numerical examples are given to demonstrate the applications of the proposed approach.

Most of diagnostic techniques used within the class of beam‐like structures are based on the requirement that the damage location closely matches with the calculated and the observed frequency changes. Since these variations are usually mild, one expects that frequency sensitivity to damage plays an important part in the crack identification. Here we show that frequency sensitivity for any beam‐like structure can be explicitly evaluated on the basis of the undamaged system by using a general perturbation approach. The usual jump conditions are taken along with the Freund‐Herrmann concept of using a “spring” to represent the effect of the crack in a section. Then, frequency sensitivity turns to be proportional to the potential energy stored, for the relevant mode shape, at the cross section where the crack occurs. Moreover, the ratios of the frequency changes of various orders are independent of the severeness of the crack and this seems to explain their usefulness in the localization of the damage in practical situations.

Wave scattering over a horizontally submerged circular disk is analyzed by the linear potential wave theory. By means of the method of separation of variables, harmonic expressions of the velocity potential in terms of unknown constants are obtained in three subregions of the domain occupied by the fluid. A simple approach is employed to match these harmonic expressions at the common boundary of the subregions. The velocity potential is thus obtained, and consequently, the water‐surface elevation is determined. Variation of the wave height around the submerged disk versus the dimensionless disk radius, the relative water depth, and the submerged depth ratio of the disk to the total water depth is presented and discussed. The results show an effect of wave focusing around the rear of the disk. It is also noted that shallower‐water waves undergo more significant scattering when the ratio of the disk radius to the incident wavelength is fixed. The pattern of the wave‐height distribution is found to be closely related to the size of the disk but less dependent on the relative water depth.

This paper presents an efficient method for calculating the response statistics of dynamic systems subjected to Poisson‐distributed (non‐Gaussian) pulse processes. The procedure to be followed is based on an extension of the traditional method of the Itô stochastic differential equation, in which the increment of the Wiener process associated with the Itô stochastic differential equation has been substituted by the increment of a compound Poisson process. One major achievement here is the derivation of a general moment equation suitable to Poisson‐distributed pulse excitations. Two examples of application (for linear and nonlinear systems) are given to illustrate the use of the derived moment equation. Exact response moments for linear systems can be calculated efficiently. In studying a nonlinear oscillator with a use of fourth‐order cumulant‐neglect method, it is found that the calculation for response moments of second order is reasonably accurate, although this is not so for moments of fourth order.

Scaling laws are the most fundamental aspect of every physical theory. Recently, the problem of scaling law and size effect in the theories of structural failure has received considerable attention, particularly with regard to distributed damage and nonlinear fracture behavior. The paper presents a rigorous mathematical analysis of scaling in various types of failure theories in structural mechanics. First it is shown that the scaling law is a power law if, and only if, a characteristic dimension is absent. For all the theories in which the failure condition is expressed in terms of stress or strain only, including elasticity with a strength limit, plasticity, and continuum damage mechanics, the nominal strength of the structure is shown to be independent of its size. For linear‐elastic fracture mechanics, in which the failure criterion is expressed in terms of energy per unit area, the scaling law for the nominal strength is shown to be (size)^−1/2, provided that the cracks in structures of different sizes are geometrically similar. When the failure condition involves both the stress (or strain) and the energy per unit area, which is typical of quasibrittle materials, the scaling law represents a gradual transition from the strength theory, which is asymptotically approached for very small sizes, to LEFM, which is asymptotically approached for very large sizes. The size effect described by Weibull statistical theory of random material strength is also considered, and the reasons for its inapplicability to quasibrittle materials are explained. Finally, floating elastic plates with large bending fractures and a negligible process‐zone size are shown to exhibit an anomalous scaling law, such that the nominal strength is proportional to (size)^−3/8, and another anomalous size effect of the type (size)^−2/5, pertinent to one recent theory of borehole breakout, is pointed out.

This paper describes the experimental and analytical study of a friction‐controllable sliding base isolation system. To overcome the problems associated with conventional passive sliding isolation systems that have hindered their practical effectiveness, a hybrid sliding base isolation system is developed using friction‐controllable bearings. This innovative hybrid system uses a variable friction force that is computer controlled by changing the pressure in the fluid chamber of the bearing. The variable friction force makes the sliding isolation system more effective in controlling the structural response under earthquakes with a broad range of intensity. A prototype hybrid sliding isolation system is physically developed and tested on a shaking table using a structural model equipped with this system. Control algorithms specially developed for controlling the frictional force that has an inherent nonlinear feature are used in this study, and their effectiveness is verified. Simulation of structural response under passive or hybrid control technique shows good agreement with the experimental results.

A continuum damage mechanics model for monotonic and cyclic behavior of concrete is developed. The model adopts a bounding surface concept in which the introduced bounding surface, loading surface, and initial fracture surface are chosen to be functions of the maximum accumulated damage ever experienced by the material. The initial fracture surface is the onset of fracture propagation, i.e., damage growth occurs only when the loading surface lies outside the initial fracture surface. The proposed model recognizes the different behavior of concrete in tension and compression, hence the damage due to tensile stresses is assumed to grow independently from the damage due to compressive stresses and separate compliance matrices are introduced for tension and compression. Both hardening and softening behavior of concrete are displayed by the proposed damage‐bounding surface. The model successfully predicts the essential characteristics of concrete behavior such as the nonlinearity, stiffness degradation, shear compaction dilatancy, different behavior of concrete in tension and compression, and the strain‐softening behavior.