Journal of Engineering Mechanics

Results are discussed from experimental and theoretical studies on the tensile failure of short, steel fiber‐reinforced mortar/concrete (SFRC) composites. A displacement‐controlled test method for conducting stable fracture tests on tension‐weak brittle materials developed in an earlier study has been used for conducting uniaxial tension tests. Several concrete, mortar, paste, and SFRC mixes were tested. Fracture of SFRC in tension is observed to be influenced largely by the matrix softening behavior, the fiber‐matrix interfacial response, and its composition parameters. The theoretical model proposed for the idealized SFRC composite takes into account these two primary nonlinear aspects of the failure mechanism in such composites, i.e.: (1) The inelastic behavior of the fiber‐matrix interface; and (2) the softening characteristics of the matrix. The model, in addition, is also realistically sensitive to the reinforcement parameters like fiber volume content, aspect ratio, and the elastic properties of the fiber.

An eigenfunction expansion is used to calculate a solution for wave movement in an axisymmetric tank of liquid that is accelerated horizontally by an earthquake. Fluid motion is assumed to be irrotational and incompressible, and tank boundaries are assumed to be rigid. A major portion of the solution is obtained from the numerical solution of an integral equation eigenvalue problem. A comparison between solutions calculated for a cylindrical tank and a conical tank, both filled with equal volumes of liquid, shows that solutions for free surface displacements and pressure forces are similar in magnitude and behavior, but that moments created by the fluid pressure differ considerably.

A new boundary element formulation is introduced for the treatment of gravitational and centrifugal body forces in axisymmetric elastic media. This new formulation is based on the method of particular integrals, which require neither volume nor surface integration for the treatment of body forces. Particular integrals for both gravitational and centrifugal body forces are derived and all kernel functions are defined in an appendix. The formulation is implemented into a multiregion system that utilizes quadratic isoparametric shape functions to model the geometry and field variables on the boundary of the body. A number of examples of practical interest have been included to demonstrate the power and versatility of the present formulation.

A simplified analytical‐numerical method for analyzing the nonlinear earthquake response of earth dams, modeled as two‐dimensional, nonhomogeneous shear wedges in rectangular canyons, is presented. The method takes into account the nonlinear, hysteretic, and strain‐dependent characteristics of the dam materials. The hysteretic stress‐strain behavior of the material is modeled using elastoplastic constitutive equations based on multisurface kinematic plasticity theory; no viscous or numerical (artificial) damping is employed. The method is based on a Galerkin formulation of the equation of motion in which the solution is expanded using the eigenmodes of the two‐dimensional linearized problem defined over the spatial domain occupied by the dam. The analysis can be used to calculate the entire time history of the response quantities, including permanent deformations of earth dams subjected to ground shaking. Finally, the efficiency and low computational cost make the technique very attractive.

The method presented in the companion paper is applied herein to analyze the nonlinear earthquake response of an earth dam; the entire time history of the response quantities, including permanent deformation of the dam, are calculated. Two different input ground motion cases are considered: a moderate and a strong shaking with very different frequency characteristics. Comparative studies are conducted to examine the influence of two‐dimensionality, nonlinearity, nonhomogeneity, modal expansion, modal coupling, and the multidimensional stress interaction on the response. The results are also compared to those obtained by an elaborate finite element analysis. The comparative study reveals significant response differences between one‐ and two‐dimensional analyses, homogeneous and nonhomogeneous models, moderate and strong shakings, and one‐ and multi‐mode solution expansions. In addition, the comparison indicates that the simplified method proposed can be used to reliably estimate the nonlinear earthquake response of earth dams modeled as 2‐D shear wedges.

The suppression of the flutter instability of a suspension bridge by means of feedback control is studied. To this end, the mathematical model considered consists of the midsection of a bridge, assumed to be fixed at the bridge towers. The partial differential equations of motion can be converted into a set of second‐order ordinary differential equations by using Galerkin's method. The design of optimal control is carried out by the independent modal‐space control method. The closed‐loop eigenvalues are selected so that the unstable flutter mode acquires a negative real part while the open‐loop frequency remains unchanged. A numerical example is given in which the flutter of a suspension bridge deck having aerodynamic characteristics similar to those of the original Tacoma Narrows Bridge is controlled.

Physical modeling to quantify wind effects for either wind‐engineering design or research requires simultaneous similarity for two distinct physical phenomena. The initial consideration is similarity of the desired natural wind characteristics. When this requirement is satisfied, similarity of specific wind effects must then be considered. Advancements in both aspects of simulation since about 1974 are summarized following a brief review of the foundations of physical modeling and wind‐modeling facilities. Advancements in physical modeling of the following natural wind features are described: (1) Elevated inversions; (2) wind‐water interactions; (3) mountain‐valley winds; and (4) large‐scale atmospheric turbulence. Extensions in the capability to simulate and measure the following wind effects are presented: (1) Diffusion in convective boundary layers; (2) heat transfer by heated jet in wind; and (3) fluctuating wind loads on buildings and structures. Advancements in physical modeling during the last decade have significantly increased the scope of wind‐engineering problems that can be treated quantitatively. However, further advancements are needed. Some challenges for future research and development are identified.

A class of white noise processes defined as the formal derivative of Lévy processes is studied. It is shown that (1) This class consists of two types of processes, the Gauss white noise and the Poisson white noise; (2) there are no other white noise processes of practical interest whose probability law can be specified simply; (3) delta correlated processes used in random vibration analyses to model non‐Gaussian wide band processes seem to be Poisson white noises; and (4) it is not possible to obtain non‐Gaussian white noises from Gaussian white noises by memoryless nonlinear transformations.

An elastica post‐buckling response of a uniform, axially compressed, pinned bar of nonlinearly elastic “soft” material is presented. A stability analysis is performed using two approximate analytical approaches based on a strongly nonlinear bending moment‐curvature relationship. The results are compared with those of an “exact” solution, achieved using the Runge Kutta's technique, showing the reliability, range of applicability, and efficiency of both approaches. Conditions of bifurcational instability, depending on the material nonlinearity, are established. It is found that a critical material nonlinearity exists, depending on the slenderness ratio, for which the mechanism of bifurcational buckling changes from stable to unstable and vice versa. Thus, a bar with nonlinear elastic “soft” material might be imperfection‐sensitive. An extensive variety of numerical results, also allowing the study of the effects of various parameters on the post‐buckling response of the bar, proves the validity and efficiency of the proposed approaches.

A simple mathematical model for predicting the vortex‐excited resonant response of two cylinders in line with the wind direction is presented. For the model, a modified van der Pol equation is employed to account for the effect of fluctuating lift force on the cylinder, and this equation is coupled with the equation for the oscillatory motion of the cylinder. The governing equations are nonlinear in nature, and the solutions of these equations are assumed to be in the form of sinusoidal functions. Results obtained are in good agreement with the experimental data.