Journal of Engineering Mechanics

The compression buckling of mutilayer elastomeric bearings which are widely used as vibration mounts, bridge bearings, and seismic isolators for buildings is well understood and is governed by theoretical analysis and confirmed by extensive experimental work. What is not well known is that the theoretical analysis that predicts the compression buckling behavior also predicts that a bearing could be subject to buckling in tension with a tension buckling load that is of the same order as the compressive buckling load and a buckled shape that is the same as that in compression. The tensile buckling load will not be achievable in practice in most bearings since it will generally be much larger than the load that will induce cavitation in the elastomer, but the analysis can be very valuable in explaining the behavior of seismic isolators when loaded in tension while laterally displaced. This can occur when extreme seismic loading on an isolated building induces global overturning. Isolators at the periphery of the building can be in a state of combined tension and shear. The analysis shows that the elastomer can sustain the tension load without cavitation since rotation of the central portion converts tension to rotated shear.

A mathematical model is developed for calculating liquid sloshing effects such as hydrodynamic pressures and forces in half-full spherical containers under arbitrary external excitation. The velocity potential is expressed in a series form, where each term is the product of a time function and the associated spatial function. Because of the spherical configuration, the problem is not separable and the associated spatial functions are nonorthogonal. Application of the boundary conditions results in a system of coupled nonhomogeneous ordinary linear differential equations. The system is solved numerically, implementing a typical fourth-order Runge-Kutta integration scheme. The proposed simple methodology is capable of predicting sloshing effects in half-full spherical containers under arbitrary external excitation in an accurate manner. Hydrodynamic pressures and horizontal forces on the wall of a spherical container are calculated for real earthquake ground motion data. Dissipation effects are included in the present formulation, and their influence on the response is examined. Finally, it is shown that for the particular case of harmonic excitation, the system of ordinary differential equations results in a system of linear algebraic equations, which yields an elegant semianalytical solution.

This paper examines the important issue of response sensitivities of dynamic models of structural systems to both material and (discrete) loading parameters. Plasticity-based finite-element models of structural systems subjected to base excitation such as earthquake loading are considered. The two methods for computing the response sensitivities, namely, (1) discretizing in time the time continuous-spatially discrete response equations and differentiating the resulting time discrete-spatially discrete response equations with respect to sensitivity parameters, and (2) differentiating the time continuous-spatially discrete response equations with respect to sensitivity parameters and discretizing in time the resulting time continuous-spatially discrete response sensitivity equations, are clearly distinguished. The discontinuities in time of the response sensitivities arising due to material state transitions in the plasticity models, and their propagation from the quadrature point level to the global structural response level are discussed using a specific one-dimensional plasticity model. The procedure to obtain the exact sensitivities of the numerical nonlinear finite-element response, including proper capture of their discontinuities, is formalized. Application examples illustrating the concepts are presented at the end.

Using Schwarz’s alternating method and Muskhelishvili’s complex variable function techniques, this paper presents an iterative algorithm method for the effective and accurate calculation of the stresses in an elastic solid of infinite extent containing multiple elliptic holes and subject to external loading at the infinity. The elliptic holes can have different dimensions and locate at any points while their axis orientations must be orthogonal. The proposed iterative algorithm method is based on the approximation of the resultant force vector on each elliptic hole boundary as a series of complex variable. As a result, exact closed-form analytical stress solutions can then be obtained for the solid with a single elliptic hole whose boundary is subject to the reverse resultant force vector in the forms of complex series. The numerical results presented in the paper show that the iterative solution converges quickly and stably. The proposed convergent criterion ensures the satisfaction of the required accuracy of the stress results. The stress concentration at elliptic holes can then be evaluated with high accuracy.

In this paper, an analytical solution for the four-equation model describing fluid-structure interaction in liquid-filled pipes subjected to impact-induced water hammer is presented. The analytical solution is derived for the case of both Poisson coupling and junction coupling. The results obtained from the analytical solution are in good agreement with experimental measurements and with numerical solutions determined by the method of characteristics. Taking advantage of the analytical solution, some features of coupled wave propagation are presented and discussed.

Methods for stochastic simulation of sample functions have increasingly addressed the preservation of both spectral and probabilistic contents to offer an accurate description of the dynamic behavior of system input for reliability analysis. This study presents an efficient, flexible and easily applied stochastic non-Gaussian simulation method capable of reliably converging to a target power spectral density function and marginal probability density function, or a close relative thereof. Several existing spectral representation-based non-Gaussian simulation algorithms are first summarized. The new algorithm is then presented and compared with these methods to demonstrate its efficacy. The advantages and limitations of the new method are highlighted and shown to complement those of the existing algorithms.

A finite-element method (FEM) is used to simulate water wave propagation with large angle incidence at exterior boundaries. In this paper, the radiation boundary condition is expanded to a second-order approximation and a quadratic shape function is used in the FEM wave model. Cases used for verifications include wave scattering around a vertical cylinder and wave propagation over a submerged circular shoal with concentric contours. Numerical calculations based on this second-order radiation boundary condition are found to be in good agreement with theoretical and experimental results available. The numerical predictions show that this model has made a very good improvement over the first-order radiation boundary conditions for oblique wave incidence in coastal engineering.

The mechanical behavior of the mesostructure of concrete is simulated by a three-dimensional lattice connecting the centers of aggregate particles. The model can describe not only tensile cracking and continuous fracture but also the nonlinear uniaxial, biaxial, and triaxial response in compression, including the postpeak softening and strain localization. The particle centers representing the lattice nodes are generated randomly, according to the given grain size distribution, and Delaunay triangulation is used to determine the lattice connections and their effective cross-section areas. The deformations are characterized by the displacement and rotation vectors at the centers of the particles (lattice nodes). The lattice struts connecting the particles transmit not only axial forces but also shear forces, with the shear stiffness exhibiting friction and cohesion. The connection stiffness in tension and shear also depends on the transversal confining stress. The transmission of shear forces between particles is effected without postulating any flexural resistance of the struts. The shear transmission and the confinement sensitivity of lattice connections are the most distinctive features greatly enhancing the modeling capability. The interfacial transition zone of the matrix (cement mortar or paste) is assumed to act approximately in series coupling with the bulk of the matrix. The formulation of a numerical algorithm, verification by test data, and parameter calibration are postponed for the subsequent companion paper.

The concrete material model developed in the preceding Part I of this study is formulated numerically. The new model is then verified by comparisons with experimental data for compressive and tensile uniaxial tests, biaxial tests, and triaxial tests, as well as notched tests of mode I fracture and size effect.

A quasi-steady duct flow through a parallel plate model for electrorheological (ER) and magnetorheological (MR) fluids under shear-flow mode is investigated mathematically. To do so Herschel-Bulkley power law constitutive model for ER and MR fluid is adopted to account for postyield shear thinning or shear thickening conditions as indicated in recent research. This approach is selected in order to obtain a more flexible representation of ER or MR postyield behavior rather than using the mostly adopted Bingham plastic model. This will lead to developing a theoretical method for prediction of ER or MR force characteristics.

A practical technique to protect structures against the effects of earthquakes is examined and proposed for use in design. The technique involves the bundling of slender steel members to form columns that are stiff and strong vertically, yet stable and quite flexible horizontally, leading to significant deamplifications of the main effects of the earthquake excitation. Because of its lateral deformation capacity, the proposed system can be designed to remain elastic even under severe ground motions. A number of analyses are made to identify the main properties of the proposed column system, and the use of the bundled column concept as a base isolation system is also explored. Example problems representative of realistic earthquake-excited structures are reported, elucidating the main features of the proposed technique and the implications of its implementation. The presentation focuses on the fundamentals, avoiding unnecessary modeling complications, to highlight the main factors involved.

The equation for calculating the normal modes of a uniform beam under transverse free vibration involves the hyperbolic sine and cosine functions. These functions are exponential growing without bound. Tables for the natural frequencies and the corresponding normal modes are available for the numerical evaluation up to the 16th mode. For modes higher than the 16th, the accuracy of the numerical evaluation will be lost due to the round-off errors in the floating-point math imposed by the digital computers. Also, it is found that the functions of beam modes commonly presented in the structural dynamics books are not suitable for numerical evaluation. In this paper, these functions are rearranged and expressed in a different form. With these new equations, one can calculate the normal modes accurately up to at least the 100th mode. Mike’s Arbitrary Precision Math, an arbitrary precision math library, is used in the paper to verify the accuracy.

The objective of this research is to develop a quantitative understanding of the propagation of ultrasonic waves in cement-based materials by examining specimens made of a portland cement-paste matrix and glass bead “aggregate.” The incident ultrasonic waves are broadband and contain wavelengths on the order of the glass bead scatterers. Experimentally measured ultrasonic waves are interpreted using diffusion theory to quantitatively measure dissipation and diffusion coefficients as functions of frequency and microstructure. These results provide a basic understanding of the effect of some features of the microstructure on the propagation of ultrasonic waves, as well as supplying a first step in the characterization of distributed damage using ultrasonic methodologies.

This technical note presents a simplified approach to reproducing historical earthquake records using uniaxial seismic simulators. Although complex, real-time feedback control systems may be utilized to control such simulators, it is shown herein that the application of a simple, off-line correction procedure is adequate for producing reasonable reproductions of historical earthquakes. An analytical model which describes the dynamic properties of a uniaxial seismic simulator is formulated in the frequency domain and calibration of the analytical model is performed via experimental system identification testing. It is shown that the model and identified properties are valid over a practical range of frequencies of motion. The analytical model is subsequently utilized in the implementation of an off-line correction procedure to improve the dynamic tracking performance of the seismic simulator. The effectiveness of the procedure is demonstrated by comparing motion of the simulator using both uncorrected and corrected command signals that correspond to historical earthquake records. The results show that the analytical model developed is adequate for describing the dynamic behavior of the seismic simulator and that the application of a simple, off-line correction procedure improves the dynamic tracking performance of the simulator.

Microscopic and macroscopic characteristics of hyperconcentrated sediment-laden flows are investigated using kinetic theory for differing concentrations of non-cohesive sediment particles. Variations in the microscopic particle velocity distribution function and in derived macroscopic variables such as the particle mean velocity, particle fluctuating velocity, and particle number per unit volume are discussed. Analysis of the microscopic characteristics shows that the peak value of the particle velocity probability density distribution function decreases with increasing vertically averaged volumetric (or mean) particle concentration $\overline{C_v}\text{,}$ particularly when $\overline{C_v}$ exceeds a certain threshold. A case study indicates that the characteristic velocity $u_c$ is hardly influenced by the particle concentration, but the standard deviation σ is significantly affected. For given particle concentrations, both $u_c$ and σ tend to become larger with increasing relative elevation from the bottom. From the derived macroscopic characteristics, apparent changes can be observed in the profiles of particle mean velocity, particle fluctuating velocity, and particle concentration when $\overline{C_v}$ is greater than the threshold value.