Journal of Engineering Mechanics

A frequency domain approach for nonlinear bridge aerodynamics and aeroelasticity, based on the Volterra series expansion, is introduced in this paper. The Volterra frequency-response functions and the associated linear equations are formulated utilizing a topological assemblage scheme and are identified utilizing an existing full-time-domain nonlinear bridge aerodynamics and aeroelasticity analysis framework. A two-dimensional sectional model of a long-span bridge is used to illustrate this approach. The results show a good comparison between the time-domain simulation and the proposed frequency-domain model. The availability of Volterra frequency-response functions enables gaining a qualitative insight into nonlinear bridge aerodynamics and aeroelasticity.

Track support stiffness (TSS) is used as a quality index of railway tracks to assess their performance and bearing capacity. TSS depends on the elastic stiffness of the elastic materials and the structural characteristics of the track system. The theoretically designed track impact factor (TIF), which is used to design ballasted and slab tracks in the Republic of Korea, is not detailed enough to describe various track types and TSS. In this study, the relationship between the TSS and the TIF for various types of tracks currently employed in Korean urban transit was assessed by performing field tests using actual vehicles running along the service lines. Field tests were performed on ballasted tracks (with good and bad ballast conditions) and three slab track types (i.e., sleeper-embedded track, rail floating track, and sleeper floating track). The theoretically designed TIF and TSS were compared with the corresponding TIF and TSS measured through field tests for the various track types on the service line. The condition of ballast (gravel) and the spring stiffness of the rail support materials directly affected the TSS. Moreover, the TIF for the service line appeared to increase with the TSS; therefore, it was inferred that the TSS directly affected the TIF.

The dissipation occurring below a moving tire in steady-state conditions in contact with a viscoelastic pavement is expressed using two different reference frames: a fixed observer attached to the pavement and a moving observer attached to the pavement–tire contact surface. The first approach is commonly referred to as dissipation-induced pavement–vehicle interaction (PVI), the second as deflection-induced PVI. Based on the principle of frame independence, it is shown that both approaches are strictly equal, from a thermodynamic point of view, and thus predict the same amount of dissipated energy. This equivalence is illustrated through application to two pavement systems: a viscoelastic beam and a viscoelastic plate both resting on an elastic foundation. The amount of dissipated energy in the pavement structure needs to be supplied by the vehicle to maintain constant speed, thus contributing to the rolling resistance, associated excess fuel consumption, and greenhouse gas emissions. The model here proposed can be used to quantify the dissipated energy and contribute to the development of engineering methods for the sustainable design of pavements.

In this research, a new method and numerical procedure for determining the plastic limit load in shell intersections using elastic-plastic finite-element analysis are presented. The proposed method is based on the maximum criterion of the rate of the change of the relative plastic work. For experimental models of cylindrical vessels with radial nozzles under in-plane moment, the results of comparisons with the twice elastic slope method were considered for determining the plastic limit moment. A parametric study of the nonradial cylindrical shell intersections subjected to in-plane moment on the nozzle was performed to examine the influence of an angular parameter on the plastic limit moment on the basis of the proposed criterion.

After a brief review of the problems entailed by the so-called proportional damping matrices, this paper elaborates on a simple technique to construct damping matrices that guarantee the fraction of damping in each mode to be positive and adequate and accomplishes this without solving for either the modes or the natural frequencies. Although the resulting matrices do not generally satisfy the proportionality condition, this fact is irrelevant for the purposes to which such matrices are put.

Stochastic seismic wavelet-based evolutionary response of multispan structures including wave-passage and site-response effects is formulated in this paper. A procedure to estimate site-compatible parameters of surface-to-bedrock frequency response function (FRF) by using finite-element analysis of the supporting soil medium is proposed. The earthquake energy content is represented by a composite power spectrum density function contributed by the surface-to-bedrock FRF and bedrock power spectra. A long span multisupport structure is subjected to spatially varying differential support motions where the spatial-variability is represented by bedrock parametric coherency models and time-lags. In addition to the time-lags from wave-passage effects, the site-response effects from different soil conditions at the supports are characterized by frequency-dependent time-lags. In an illustrative case study, a three-span, two-dimensional hangar frame is analyzed using the proposed formulations. The time-lags resulting from site-response effects and computed by different FRFs show different variation in trends and frequency content. The site-response effect is found to introduce additional frequency nonstationarity and leads to an increase in the frame responses but with slower attenuation in time.

Conveyor pulleys are typical axisymmetric structures subjected to nonaxisymmetric loading. Taking full advantage of the characteristics of the pulley structure, this paper presents a precise finite-element formulation for pulley stress analysis based on the Hamiltonian form of elasticity. In the model, the solution is expanded into a set of Fourier series; a paired set of state variables are selected from the Fourier coefficients; and the governing equations are reorganized in Hamiltonian form with the use of the paired state variables. The general solutions to the Hamiltonian system can be obtained numerically and formulated into a finite-element model, from which the final stress solution for a pulley can be found. Numerical examples show that this method is much more efficient than the conventional FEM with comparable accuracy.

The present investigation deals with the nonlinear stability behavior of cross-ply laminated composite circular cylindrical shells subjected to partial and complete edge loading along with uniform external pressure. The shell is modeled using Donnell’s shell theory including the first-order shear deformation theory (FSDT). The analysis uses the simply supported boundary condition (at $x=0$, $L\hspace{0.17em}{N}_{\mathit{xx}}={\overline{N}}_{\mathit{xx}}$, $w=M_{\mathit{xx}}=v={\varphi }_{\theta }=0$). The equations governing the nonlinear stability behavior of cylindrical shells are derived in terms of displacements ($u\text{-}v\text{-}w$) and rotations (${\varphi }_x$, ${\varphi }_{\theta }$). The applied partial edge loading is expressed in terms of Fourier series, and stress distributions within the cylindrical shell are determined by prebuckling analysis. The study uses multiterm Galerkin’s method along with the Newton-Raphson method to solve the governing partial differential equations of the shell nonlinear stability. With the help of numerical investigations, the authors present the number of modes required for the postbuckling analysis and the influence of initial geometric imperfections on the equilibrium path in the presence of partial edge loading. They have developed a simple algorithm based on potential theory to locate the exact location of bifurcation and limit points on the equilibrium path using the bisection method.

This study develops a semi-implicit characteristic-based-split (SI-CBS) finite-element algorithm under the framework of the fractional step method to cope with the vortex-induced vibration (VIV) problem. The authors present a modified linear spring analogy algorithm for successful updating of the grid deformation. They verify the computational code against two benchmark problems. One is the VIV of an elastically mounted cylinder with transverse oscillation at $\mathsf{R}=150$. The other is the transversely wake-induced vibration (WIV) of a circular cylinder by a stationary one. The authors conduct a two-dimensional (2D) numerical investigation on the problem of laminar flow over a two-cylinder system, which consists of a front stationary square cylinder and a rear two-degree-of-freedom (2-DOF) circular cylinder in a tandem arrangement. They find that the Reynolds number and reduced velocities play key roles in the WIVs of the circular cylinder. In addition to the wake patterns 2S, 2P, and $\text{P}+\text{S}$, the authors observe a steady-state wake pattern. They observe performances of dual-resonance, which means synchronization in both the in-line and transverse directions. For the $X\text{-}Y$ trajectories of the circular cylinder, they obtain figures in the shape of an egg, a figure-8, and a point.

While several procedures or guidelines for predicting pullback loads in pipe installation using the horizontal directional drilling (HDD) technique have been developed, they are based on static assumptions and are approximate analytical or empirical methods. Because of the nature of HDD, determination of the pipe pullback loads is a complex dynamic problem. This paper presents a new dynamic model to simulate the pipe pullback process and numerically calculate the pipe pullback loads in HDD installation, where the pipes are modeled by three-dimensional Euler-Bernoulli flexible beam elements based on an absolute nodal coordinate formulation and the interaction between the pipes and the borehole/ground surface is described by a local contact model using the nonlinear Hertz contact theory. To evaluate the method presented, a typical case of HDD installation is examined. The analytical solution of the case in the steady state is derived to validate the method presented. Numerical results for such useful details as the pulling force, the transient and steady-state axial forces at different locations of the pipes, and the axial stresses in the pipes during and after installation are provided.

This paper develops a generalized strain-energy density (GSED)–based method to predict the failure loads of laterally loaded masonry wall panels. The method reveals the relationship between the failure loads of the base/test and the new masonry wall panels in the sense of GSED and directly uses the existing testing data in the predicting task. First, the GSED values of the base panel are extracted from its finite-element analysis (FEA) result. Second, similar zones between the base and the new wall panels are matched through the criterion for matching zone similarity. Then, the GSED values on the base wall panel are projected into similar zones on the new wall panel. Finally, the GSED-based parameter is proposed to relate the failure load of the new wall panel. The case studies validate the GSED-based method by comparing the existing yield line method and the FEA method. The GSED-based method explores an innovative way of structural analysis by combining the FEA and cellular automata methods and directly applying testing data.

In this paper, the problem of longitudinal free vibration of nonuniform rods is investigated for the first time by using the discrete singular convolution (DSC). This method is a relatively novel and powerful numerical approach especially in analyzing vibration problems. The governing equation of this problem is nonlinear and has analytical solutions only in a few cases, so the analysis uses DSC as a numerical method. The regularized Shannon delta kernel is used in the present algorithm. The nondimensional natural frequencies of rods with various-area cross sections have been studied in this paper. Results show good agreement with the previous analytical solutions. This study indicates the efficiency of the DSC in solving nonuniform rod problems.

This study aimed to find a simplified micromechanical formulation of Helmholtz free energy for quasi-brittle materials by making use of a system of microelements, and to provide a thermodynamic foundation for the development of multiscale constitutive theories. The microscopic incompatible strain field and residual stress field in an uncracked matrix between frictional microcracks were reproduced with microsprings, faults, and sliders by taking the microscopic fracture strain as a random variable. The locked microscopic additional strain energy—plastic free energy—was represented in an abstract way by the locked deformation energy within the microelement system. Straightforward free-energy functions dependent on the probability distribution of microscopic fracture strain were derived, which can be used in both deterministic and stochastic constitutive modeling.