Journal of Engineering Mechanics

In comparison with atmospheric boundary-layer winds, which are generally regarded as stationary, windstorms such as hurricanes and thunderstorms/downbursts have strong nonstationary features characterized by rapid changes in wind speed and direction. The averaging interval associated with turbulent wind characteristics in boundary-layer winds is typically varied between 10 min and 1 h. A fixed averaging interval (FAI), which uses a constant mean to isolate the fluctuating wind component, has been effective in characterizing boundary-layer winds; however, the question remains as to whether the user-defined interval is appropriate for nonstationary winds. To address this concern, a variable averaging interval (VAI) scheme is proposed. For better understanding of the characteristics of nonstationary winds, traditional FAI methods are compared with alternative FAI approaches that use time-varying means and the proposed VAI approaches. In addition, the definitions for gust factor, turbulence intensity, and turbulence integral length scale are revised to ensure compatibility with the proposed schemes. Nonstationary data measured during the passage of Hurricane Lili and transient data measured during a rear-flank downdraft obtained from the 2002 thunderstorm outflow field experiment are used to examine the efficacy of FAI and VAI schemes and the associated turbulent wind characteristics.

This paper presents the development and application of a simplified analytical model to analyze the energy response of an idealized composite sandwich panel under blast loads. The model is used to gain insight into optimizing the energy absorption capabilities, and thus blast resistance, of the core of these structures. The analytical predictions calculate spatial and time variations in blast pressure as a result of charge size and location as well as the corresponding structural response based on velocity transfer among the sandwich panel components and discretization of the sandwich panel into a system of single degree of freedom mass-spring systems. The energy absorption mechanisms considered include absorbed strain energy as a result of inelastic deformation of the core and energy dissipation through progressive failure of the core, where the failure criterion is the failure strain where the composite material loses strength. The results demonstrate that energy absorption is maximized when failure of the core is prevented. The accuracy of the program as a result of the simplifying assumptions made in the derivation of the analytical approach is also reviewed.

The free vibration of two-dimensional (2D) functionally graded annular sector plates is analyzed based on the three-dimensional (3D) theory of elasticity, using the 2D differential quadrature method. The plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. This paper presents a novel 2D power-law distribution for ceramic volume fraction of 2D functionally graded material that gives designers a powerful tool for flexible designing of structures under multifunctional requirements. Various material profiles along the thickness and radial direction are illustrated using the 2D power-law distribution. The effective material properties at a point are determined in terms of the local volume fractions and the material properties by the Mori-Tanaka scheme. A semianalytical approach composed of the differential quadrature method and series solution is adopted to solve the equations of motion. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The interesting results indicate that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional one-dimensional functionally graded material. The multidirectional graded material can likely be designed according to the actual requirement and it is a potential alternative to the unidirectional functionally graded material.

It is now well known that a variety of instability modes can appear before the conventional plastic limit condition is met. In this note, both flutter and divergence instability modes are investigated. First, the criterion for detecting their occurrence is established, and the case of kinematically constrained discrete systems is investigated. Based on an illustrative example, the competition between the occurrences of each of these instability modes is analyzed, showing that the prevalence of a given mode is strongly related to both the loading conditions and the stiffness properties of the material system at hand.

Titanium-nickel (Ti-Ni)–based bulk metallic glass (BMG) alloys were prepared by centrifugal casting into a copper mold. The effect of five rolled temperatures, namely, room temperature and 200, 300, 400, and 500°C, on the behavior of amorphous BMG, the microstructural features, and the mechanical properties were investigated. High-resolution scanning electron microscopy (HRSEM) reveals the formation of nanoparticles in the amorphous alloys. The ultimate compressive stress of the rods rolled at 300°C was found to be the highest, whereas that of the rods rolled at 500°C was the lowest. The fracture strain for the rods rolled at 500°C was found to be the highest, which reflects the roughness of the fracture surface and the strength and integrity of the internal structure.

This paper presents a computationally efficient method for the conditional simulation of nonstationary fluctuating wind speeds for the buffeting analysis of long-span bridges. The fluctuating wind speeds, with part of their time histories measured at some points, are regarded as a zero-mean nonstationary Gaussian vector process characterized by an evolutionary power spectral density (EPSD) matrix. The Kriging method is then applied to the random vector of the Fourier coefficients of the evolutionary vector process for conditional simulation. A mathematical proof of this conditional simulation is provided. A fast algorithm of the conditional simulation is further derived, by converting the Cholesky decomposition of a large size covariance matrix of the Fourier coefficients into the Cholesky decomposition of a series of small-size coherence matrices with much less computational time. The procedure for implementing the fast algorithm-based conditional simulation method is detailed. Finally, this method is applied for the conditional simulation of typhoon-induced nonstationary wind speed time histories for the buffeting analysis of Stonecutters Bridge in Hong Kong. The time domain buffeting responses of the bridge obtained using the conditionally simulated wind speed time histories indicate that the proposed simulation method is feasible and applicable.

A linear thermoelastic isotropic material is considered. A complete solution in terms of three scalar potential functions for the coupled displacement-temperature equations of motion and heat equation is presented, where the governing equations for the potential functions are the wave, heat, or a repeated wave-heat equation. The completeness theorem is proven based on a retarded Newtonian potential function, existence of solutions for the repeated wave equation and heat equation, and perturbation theory. A connection is also made between a complete solution already existing in the literature and the solution introduced in this paper, which in itself is another method to prove the completeness. If no heat source exists, the number of potential functions is reduced to two. In some circumstances, the number of potential functions is reduced to only one, and the required conditions for this case are discussed. As a special case, the torsionless and rotationally symmetric configuration with respect to an arbitrary axis is carefully assessed. The degenerated case to elastodynamics is obtained, and it is shown that the solutions given here are identical to a complete solution, which already exists in the literature for the equations of motion. The potential functions may be used for elastostatics, if the time dependence of the displacement vector and the temperature, and also the potential functions, are suppressed. In analogy with the deformation theory of a fluid saturated poroelastic material, the results given here may be used in the theory related to steady-state water flow.

Drilling fluids injected into geothermal, oil, and gas borehole create a temperature gradient in rock near the bottom hole. This temperature gradient is more pronounced in underbalanced drilling (UBD) with gaseous fluids because of the Joule–Thomason cooling effect at the drill bit. The effect of the temperature gradient on rock failure was investigated experimentally and interpreted by an analytical model in this study. The result indicates that the temperature gradient can significantly promote rock failure during drilling. The rate of penetration (ROP) increased by 22.4% on average as the temperature differential increased from 30 to 180°C in the Chagan Sandstone from the Tamuchage Basin, Mongolia. This explains high ROP, hole enlargement, and hole deviation in gas UBD operations. The analytical model developed in this work can be used for optimizing drill bit and fluid injection rate in geothermal, oil, and gas well drilling.

A modified bounding surface hypoplasticity model is developed to capture distinct dilatancy behaviors of loose and dense sandy soils during various phases of undrained cyclic loading. Based on observations from laboratory tests, new modulus formulations are proposed to improve the simulation of cyclic mobility and postliquefaction behaviors of both loose and dense sands. The state-dependent dilatancy and effects of accumulated plastic strains on the plastic moduli are also incorporated in this model. The model demonstrates excellent capabilities through systematic comparison between the model predictions and a series of undrained cyclic simple shear tests on Fraser River sand.

For a single pile subjected to compressive load, a softening model and a hyperbolic model are adopted in this work to simulate the relationship between pile-soil relative displacement and unit skin friction developed along the pile-soil interface, whereas a bilinear model is used to describe the unit end resistance–displacement response developed at the pile tip soil. Based on the proposed three models, two simple analytical approaches for nonlinear analysis of the load-displacement response of a single pile are presented. One method uses a softening model of skin friction and a bilinear model of end resistance to capture the pile response, and the other approach is based on a hyperbolic model of skin friction and a bilinear model of end resistance to describe the pile load-displacement response. As for the analysis of the response of a single pile subjected to a compression load, a highly effective iterative computer program is developed using the two proposed approaches and the load-transfer curve method. To demonstrate the effectiveness and accuracy of the proposed analytical methods, comparisons of the results derived from the present methods, other analytical methods, and well-documented field experimental pile loading cases are made. Further study is conducted to clarify the influence of the parameters related to the proposed softening model and hyperbolic model of unit skin friction on the load-displacement response of a single pile.

Structural vulnerability theory is a theory of structural form and connectivity. Its purpose is to identify particular failure scenarios by analyzing the connectivity of the structural form. In this paper, the displacement resulting from a unit force is taken as the evaluation index of the well-formedness of a structure. Load and structural form are studied in a unified theoretical framework to identify the potential weaknesses in such a structure under loading. A vulnerability analysis is then performed on three shake table test models of a single-layer reticulated dome built at a scale of 1:10 to determine its vulnerable failure scenarios. The results show that the collapse modes and the identified weaknesses of the structure predicted by the suggested method are consistent with the test results. This study verifies the effectiveness of the suggested method in determining the weaknesses and damage locations of the structure under load.

An analysis of the supercritical spreading of radial flow in a horizontal basin indicates that the variation of depth, velocity, and Froude number normalized by corresponding inlet values becomes independent of the inlet Froude number ${\mathsf{F}}_0$ when ${\mathsf{F}}_0>5$, both for inviscid and viscous flows. Assuming a linear variation of the hydrostatic pressure force along the hydraulic jump, a generalized equation for the sequent depth ratio is developed, which is valid for the free and submerged jumps both in radial and rectangular basins. This is simpler than existing equations and is verified with experimental data available in the literature. A new scale is proposed such that the sequent depth ratio for different ${\mathsf{F}}_0$ and the radius ratio collapse into a single line. A procedure to approximately locate the position of a free radial jump and determine the type of the jump is also described.

In this paper, buckling delamination around interface inner cracks contained within the simply supported elastic and viscoelastic rectangular sandwich plate under biaxial loading is studied. It is assumed that the materials of the face layers are viscoelastic and the material of the core layer is pure elastic. Moreover, it is assumed that the material of the core layer is stiffer than the materials of the face layers. Within these assumptions it is supposed that between the face and core layers there are rectangular inner cracks, the locations of which are symmetric with respect to the plate geometry. The edge surfaces of the cracks have insignificant initial imperfections before the loading. The evolution of these initial imperfections with the flow of time is investigated within the scope of the three-dimensional (3D) geometrically nonlinear field equations of the theory of viscoelasticity. For determination of the values of the critical parameters (buckling force, time, and buckling mode), the initial imperfection criterion (i.e., the case where the size of the initial imperfection starts to increase and grows indefinitely) is used. Mathematical modeling of the corresponding boundary value problem is formulated within the framework of the piecewise homogeneous body model. To solve the corresponding boundary-value problems, boundary form perturbation techniques, the Laplace transform, 3D FEM modeling and the Schapery method are used. The numerical results related to the influence of the materials or geometrical parameters of the plate on the critical parameters and critical time are presented and analyzed.

A planar rigid-body dynamics formulation describing the seismic behavior of a squat rectangular rigid body initially resting on an inclined rigid plane is presented. The downslope motion of the body is limited by a rigid boundary perpendicular to the inclined plane. This type of problem appears in several practical applications. Coulomb and hysteretic friction with velocity- and pressure-dependent properties are considered at the body-to-ground interface. The weaknesses of hysteretic friction models incorporating static and kinetic velocity-dependent components are identified and remedied. Impact models for collision of the body with the rigid boundary and the inclined plane are also derived. The formulation is embodied in a numerical model through a dedicated computer code. A comparative study is conducted to demonstrate the effects on the body response of major model characteristics, including the rigid boundary; inclination angle; Coulomb, hysteretic, and combined Coulomb-hysteretic friction; and velocity dependence of the frictional properties. It is shown that the presence of the rigid boundary considerably affects the body response, and that small inclination angles can significantly limit the outward body displacement.

Close-in explosive charges, such as improvised explosive devices, produce localized blast loadings that can potentially cause damage to property in military and civil structures and/or loss of life. Because the localized short-duration blast pulse affects most severely a small area of a plated structure, the plate’s boundary effects are not as influential as they would be when quasi-static or even a global blast loading is applied, and thus full plate action may not be used. Many common structural forms are composed of individual plated elements, and thus the investigation of localized blast loading effects on plates is an important aspect that leads to understanding the integral behavior. Typically, plates are made of ductile metallic materials, such as steel, which exhibit considerable postyield deformation capacity when subjected to such extreme dynamic loads. An analytical study of the dynamic plastic response of rigid plastic plated structures is the aim of the current study. A circular plate is studied in the present work, and a general form of a localized blast loading function with a spatial variation having a central radial zone with constant pressure and exponentially decaying profile outside the zone is assumed. Assuming that steel exhibits perfectly plastic behavior and considering transverse shear and rotatory inertia effects, using the approach developed previously, results for the permanent transverse displacements and response durations are found in terms of an applied impulsive velocity, which is a function of the applied localized blast load. It is found that the influence of transverse shear is only relevant for small values of $\nu$, or plate radius-to-thickness ratio, which do not correspond to typical plate geometries found in plated structures subjected to blast loading. Both midpoint and support displacement are only significantly affected by transverse shear effects for $\nu \le 5$. The same argument is extended to inclusion of rotatory inertia. It is also seen that, for close-in blasts, the effects of transverse shear and rotatory inertia are irrelevant, even for small values of $\nu$.

The dynamic instability of thin, clamped, flat isotropic elastic panels of superelliptical planform set on a two-parameter Winkler-Pasternak foundation and subjected to uniformly distributed pulsating in-plane loads is theoretically investigated. The plate perimeter is described by a superelliptic function with a power corresponding to shapes ranging from a circle (ellipse) to a square (rectangle). The classical Galerkin procedure is used to reduce the problem into a set of nondimensional coupled Mathieu-Hill equations, and the regions of parametric instability for principal and combination resonant frequencies are determined by applying Hsu’s technique. The effects of the superellipticity parameter, plate aspect ratio, and foundation stiffness on the dynamic stability behavior (onset and width of the instability regions) are examined. Moreover, the transient flexural response of the panel under static in-plane load and subjected to a transverse uniform step force is obtained. The validity of the results is established by comparison with the available data as well as with the aid of a commercial finite-element package. The proposed model is believed to be the first rigorous attempt in dynamic stability and/or flexural dynamic response analysis of superelliptical plates.

Magnetic levitation (maglev)-based high-speed trains are one of the most promising means of transport for the near future. To optimize the relatively high investment cost of these networks, engineers need to develop accurate dynamical simulations of the whole, complex maglev system. This involves proper consideration of the interactions between the cars of the train, the levitation frames, and the guideway. In this paper a coupled model for the train-bridge interaction is introduced, which describes the vibrations of the vehicle and the guideway by using deformable Bernoulli-Euler beams continuously connected by springs and viscous dampers. The case of a train arriving on a simply supported guideway is simulated and the results are discussed in detail.

A geometrically linear slender system subjected to an active and passive specific load is discussed. The boundary conditions, which take into account the specific load, were derived on the basis of the boundary conditions for the general load (the load present at the ends of the column induced by a longitudinal and transversal force, as well as by the concentrated moment). The boundary value problem of the basic system (the system subjected to a generalized load) was formulated using Hamilton’s principle. With regard to the specific load, the column was investigated for two types of active load: a generalized load by a force directed toward the positive pole, and a load by the follower force with a circular contour directed toward the positive pole. Heads consisting of linear elements were used to realize the active load, whereas heads consisting of circular elements were used to realize the passive load by the follower force directed toward the positive pole. Numerical research concerning the critical load and characteristic curves was carried out for different values of the parameters of the considered columns. The accuracy of the assumed mathematical model is confirmed by experimental research.

The present paper proposes a general framework for the description of short- and long-term behavior of cement-based materials subjected to mechanical loading and chemical degradation. The framework can take into account two different damage mechanisms, mechanical damage and chemical damage, and their interaction also can be considered. A special model is presented for the modeling of leaching-mechanical coupling behavior of fiber-reinforced concrete. The elastic modulus, Drucker-Prager–type criterion, and empirical evolution law of creep strain are related to mechanical damage and chemical damage variables. The evolution kinetic of mechanical damage caused by compression and tensile stress are defined, respectively. The chemical damage is defined with respect to the actual concentration of calcium in the solid skeleton, which is calculated from the mass balance equation of calcium ions. The diffusion coefficient is written as a positive function of mechanical damage variable. The proposed model is implemented into COMSOL Multiphysics and validated from decoupling experiments to fully coupling experiments to progressively determine the model parameters. The proposed model offers an adaptable framework to facilitate description of the chemomechanical coupling behavior of cement-based materials.

Mixed-mode fracture parameters were determined numerically for a cracked straight-through flattened Brazilian disk (CSTFBD) specimen containing an angled center crack and subjected to diametral-distributed uniform compressive loading. The stress-intensity factors ($K_{\mathrm{I}}$ and $K_{\text{II}}$) and the $T$ -stress were calculated from finite-element analysis for different values of the crack angle, crack length, and specimen height. The fracture parameters ($K_{\mathrm{I}}$, $K_{\text{II}}$, and $T$) decreased by reducing the height of the CSTFBD specimen. Furthermore, the pure Mode II crack inclination angle decreased in the CSTFBD specimen for larger crack lengths and smaller specimen heights. The $T$-stress was always negative for all mode mixities. Also, the influence of the specimen height on the fracture parameters was more pronounced than the other affecting parameters, such as crack length.

Based on the methods of variable separation and matching eigenfunction expansion for the velocity potential, an analytical solution is developed for a wave diffraction problem on a submerged vertical cylinder in finite water depth. It is validated by comparison with the results from a higher-order boundary-element method and convergent examinations on the number of expanding models. Numerical examinations are carried out to investigate the influences of submerged depth, cylinder length, and water depth. The wave forces on the submerged cylinder are decreased with the increase of submerged depth. Compared with a floated cylinder, the surge force is always small, whereas the heave force and pitch moment may be larger than those on the floated cylinder at some frequencies. The influence of the cylinder length is also analyzed for surge, heave, and pitch results.

A simple explicit formula is presented here to approximate the dispersion relationship of linear water waves, which allows direct and accurate calculation of wavenumber $k$ for a given frequency $\omega$. This formula is valid for all water depths, having an accuracy of the maximum error being 0.33% compared with the true solution (which is typically obtained by iterations or other root-finding numerical algorithms). It can easily be realized on a simple hand calculator (e.g., approved calculators for the Fundamentals of Engineering and the Principles and Practice of Engineering exams), and does not need any iteration, appealing in particular for practical engineering and pedagogical purposes. Another explicit formula, with still higher accuracy but slightly less simple form, is also discussed.

When a dynamic point load is applied laterally to a beam, the deflection gradually spreads over time until the entire beam length is affected. The determination of the early stages of response presents substantial mathematical difficulties. The normal-mode superposition is made awkward by the fact that the number of modal components necessary to get a reasonably accurate answer increases as the time interval of interest decreases. This paper presents a different solution based on a dominating flexural wave, which allows one to formulate compact and transparent expressions.