Journal of Engineering Mechanics

This paper describes a numerical method to determine the lower-bound solution of limit load of a rigid–perfectly plastic body obeying the von Mises yield criterion. The idea of this method is to construct a smoothed linear stress field that satisfies the yield criterion everywhere in the body. Applying the similar stress recovery techniques as superconvergent patch recovery and recovery by equilibrium in patch in the elastic finite-element analysis, the nodal stresses are obtained from those stresses at the integration points from an iterative process of upper-bound limit analysis. Then, the improved stress fields and lower-bound solutions can be derived by ensuring all the nodal stresses within the yield surface. The convergence of this method is guaranteed. The validity of the proposed method is demonstrated with some numerical examples. The computational results show that more reliable lower-bound solutions can be obtained by using this method, especially for problems with strain singularity.

This paper presents a method for computing the response of a 1D elastic continuum induced by a multi-degree-of-freedom (MDOF) oscillator traveling over it. The continuum and the oscillator are nonconservative systems with proportional damping. Unlike most studies in the field, the solution method does not address a particular type of continuous structure and oscillator. Instead, a rigorous mathematical formulation is presented that can be applied to a broad class of proportionally damped 1D continua and MDOF oscillators, regardless of boundary conditions. The problem is reduced to the integration of a system of linear differential equations with time-dependent coefficients. These coefficients are found to depend on natural frequencies, damping ratios, and eigenfunctions and eigenvectors of the continuum and the oscillator. The method is tested on numerical examples and results are compared to those available in the literature. As a practical application, the method can be used to analyze vehicle-bridge interaction problems.

A mixing of a passive tracer inside a turbulent patch generated by a localized short-time perturbation is studied numerically and analytically. Two kinds of an initial distribution of a tracer are considered: two-layer and continuous with constant gradient. For the turbulent patch shaped as a layer, it is shown that, regardless of details of initial distributions of a turbulent energy and dissipation, a tracer concentration evolves to self-similar regimes as time elapses. Analytical self-similar solutions to turbulent diffusion equations are found for three symmetric shapes of a turbulent patch: layer, cylinder, and sphere. Distributions of the concentration inside a patch are found to be substantially nonuniform, with a typical ratio of a concentration gradient in the middle of a patch to its initial value of about 0.5.

An electrical substation consists of a complex set of equipment items that are interconnected through conductor buses or cables. If the connections are not sufficiently flexible, significant dynamic interaction may occur between the connected equipment items during seismic excitations. This paper investigates the effect of interaction between two equipment items connected by a cable conductor. Analytical as well as large-deformation finite-element analyses are used to determine the nonlinear response of the cable-connected system to selected ground motions. Influences of the cable geometry and its axial extensibility, flexural stiffness, and inertia on the interaction effect are evaluated. It is found that the interaction may significantly amplify the responses of the equipment items relative to their stand-alone responses when the cable lacks sufficient slack. The amplification can be particularly large for the higher frequency equipment item. A parameter for predicting the interaction effect is introduced and evaluated for a large set of example systems.

The behavior of sand is characterized by dilatancy, an increase in overall volume as particles move over each other when the sand assembly is subjected to shear stresses. A stress-dilatancy model for sand in the cyclic loading regime, taking into account microstructural changes, is presented. The model is subsequently integrated into a constitutive model based on hypoplasticity so as to accurately calculate volume changes induced by fabric and dilatancy changes during cyclic loading. Furthermore, it is assumed that fabric evolution is a function of the ratio of deviatoric to mean principal stress. Some numerical examples that capture the effect of fabric changes on the drained cyclic behavior of sand are presented. Among others, it is found that initial fabric can drastically alter both the dilatancy response and net volume change at shakedown conditions even though the initial void ratio and confining pressure are kept unchanged. The void ratio here is defined as the volume of voids to that of solids.

A constrained minimization method is presented for the identification of elastic constants of shear deformable laminated composite plates. Strains and/or displacements obtained from static testing of laminated composite plates are used in the proposed method to identify the elastic constants of the plates. In the identification process, the trial elastic constants of a laminated composite plate are used in a finite-element analysis to predict the strains and displacements of the plate. An error function is established to measure the differences between the experimental and theoretical predictions of strains and/or displacements. A constrained minimization technique is used to minimize the error function and update the trial elastic constants. The best estimates of the elastic constants of the plate are then determined by subsequently reducing the size of the feasible region of the elastic constants and making the error function a global minimum. The accuracy and applications of the proposed method are demonstrated by means of a number of examples. A sensitivity analysis is also performed to study the effects of variations of experimental data on the accuracy of the identified elastic constants.

In this paper, an integrated state-space model of a system with a vector-valued white noise input is presented to describe the dynamic response of bridges under the action of multicorrelated winds. Such a unified model has not been developed before due to a number of innate modeling difficulties. The integrated state-space model is realized based on the state-space models of multicorrelated wind fluctuations, unsteady buffeting and self-excited aerodynamic forces, and the bridge dynamics. Both the equations of motion at the full order in the physical coordinates and at the reduced-order in the generalized modal coordinates are presented. This state-space model allows direct evaluation of the covariance matrix of the response using the Lyapunov equation, which presents higher computational efficiency than the conventional spectral analysis approach. This state-space model also adds time domain simulation of multicorrelated wind fluctuations, the associated unsteady frequency dependent aerodynamic forces, and the attendant motions of the structure. The structural and aerodynamic coupling effects among structural modes can be easily included in the analysis. The model also facilitates consideration of various nonlinearities of both structural and aerodynamic origins in the response analysis. An application of this approach to a long-span cable-stayed bridge illustrates the effectiveness of this scheme for a linear problem. An extension of the proposed analysis framework to include structural and aerodynamic nonlinearities is immediate once the nonlinear structural and aerodynamic characteristics of the bridge are established.

In the case of a circular tower, end-cell-induced vibration (ECIV) occurs at a wind speed a few times higher than the wind speed that induces the vortex-induced vibration. To elucidate the characteristics of the aerodynamic forces due to tip-associated vortices (TAV), which are considered as the cause of ECIV, wind pressures acting on a rigid circular tower were measured in a wind tunnel. The pressure fluctuations due to TAV were detected near the free end of the tower. It is shown that the frequency of fluctuating pressure due to TAV is much lower than that due to the von Kármán vortex sheddings and TAV is generated nonalternately. Also, included in this study are numerical analyses using the measured pressures as fluctuating lift forces; the predicted amplitudes of ECIV for a rocking circular cylinder agree with the amplitudes obtained in the wind tunnel experiments. If a thin circular disk is attached to the model top, the amplitudes of ECIV decrease with the increase of the disk diameter. The reason for this phenomenon is clarified.

Based on the zeroth-order approximation of a two-scale asymptotic expansion, equivalent elastic shear coefficients of periodic structures can be evaluated via the solution of a local function ${\tau }^{{\mathit{kl}}_{\mathit{ij}}(\mathit{y}})$, and the homogenization process reduces to solving the local function ${\tau }^{{\mathit{kl}}_{\mathit{ij}}(\mathit{y}})$ by invoking local periodic boundary conditions. Then, effective transverse shear stiffness properties can be analytically predicted by reducing a local problem of a given unit cell into a 2D problem. In this paper, an analytical approach with a two-scale asymptotic homogenization technique is developed for evaluation of effective transverse shear stiffness of thin-walled honeycomb core structures with general configurations, and the governing 3D partial differential equations are solved with the assumptions of free warping constraints and constant variables through the core wall thickness. The explicit formulas for the effective transverse shear stiffness are presented for a general configuration of honeycomb core. A detailed study is given for three typical honeycomb cores consisting of sinusoidal, tubular, and hexagonal configurations, and their solutions are validated with existing equations and numerical analyses. The developed approach with certain modifications can be extended to other sandwich structures, and a summary of explicit solutions for the transverse shear stiffness of common honeycomb core configurations is provided. The lower bound solution provided in this study is a reliable approximation for engineering design and can be efficiently used for quick evaluation and optimization of general core configurations. The upper bound formula, based on the assumption of uniform shear deformation, is also given for comparison. Further, it is expected that with appropriate construction in the displacement field, the more accurate transverse stiffness can be analytically attained by taking into account the effect due to the face-sheet constraints.

This paper documents the results of an experimental study conducted to demonstrate the capabilities of multiple magnetorheological (MR) devices for seismic control of civil engineering structures. A six-story test structure in the Washington University Structural Control and Earthquake Engineering Lab is considered, and four parallel-plate, shear-mode MR dampers are used to control this test structure. Two control devices are installed in the test structure between the base and first floor, and two are installed between the first floor and second floor. A phenomenological model of the shear mode MR damper is proposed and verified. A nonlinear system identification method, appropriate for multi-input/multi-output systems, is used to develop a model of the integrated structural system. Experimental transfer function data corresponding to one system input are used to update the eigenvalues of an analytical model. Two semiactive control algorithms, including a Lyapunov algorithm and a clipped-optimal algorithm, are considered. An El Centro earthquake example is used to disturb the system at three amplitude levels. The results indicate that high performance levels can be achieved, and the responses of the semiactive system are significantly better than that of comparable passive systems.

A multiple linearization algorithm for the reliability analysis of nonlinear limit states is presented in this paper. This method identifies several hyperplane approximations to the limit state and computes the failure probability through the union or intersection of the failure domains corresponding to each segment. This approach is useful for both component and system level reliability problems. The multiple linearization points are determined through the secant method. Correlation information about the hyperplanes is used to achieve computational efficiency. Numerical examples are presented to show the benefits of the proposed method.

Semirigid connections are usually found in large-scale engineering structures, and the knowledge of the dynamic characteristics of these connections is important to the accurate definition of the dynamic characteristics of the engineering structure. Different models have been presented to define the connection, but most of them are not suitable for model improvement from dynamic measurements of the structure. This paper presents a hybrid finite-element model that consists of a beam element with two semirigid connections at the ends for updating the finite-element model of the jointed structure. The parameter selection strategy of the generic element is adopted, and the stiffnesses of the joint in three dimensions are selected as generic parameters to be updated simultaneously with other structural parameters of the structure. The proposed method is applied to the model updating of a 3D steel truss in the laboratory. Results show that the method could improve significantly not only those vibration modes used in the updating but also the higher modes with a maximum error of 6%.

This paper describes an experimental study on the use of Ritz vectors for damage detection of a grid-type bridge model. A new procedure to extract Ritz vectors from experimental modal analysis is proposed and demonstrated using the test structure. The extracted Ritz vectors are then used for the damage detection of the test structure using a Bayesian probabilistic approach. Using appropriate load patterns, Ritz vectors can be made more sensitive to damage than modal vectors. The results indicate that the use of load-dependent Ritz vectors produce better damage diagnoses than the modal vectors. The Bayesian probabilistic approach is shown to give better diagnostic results than commonly used deterministic methods.

The temperature propagation in a layered structure is of great importance in determining the thermal induced strain in the structure, and in particular the thermal induced stress along the interfaces of the structure due to the different thermal expansion coefficients of the layer media. In this paper, an exact analytical solution is obtained based on the Fourier-Biot heat conduction equation for a two-layer structure with or without a base boundary. Characteristic frequencies or the temperature fluctuation response of two-layer structures are identified. Once the temperature distribution is known, one can compute the stress distribution in the structure. The application of the model to understanding measured temperature data for two-layer structures such as concrete pavements is addressed.