Journal of Engineering Mechanics

In multistoried RC wall-frame buildings, properly designed and detailed RC slender structural walls significantly improve earthquake resistance. In walls on isolated spread footings with marginal taper, severe stress concentration is observed at the wall-footing junction during earthquake shaking. In this paper, new tapered configurations are proposed in the bottom portion of walls with and without enlarged boundary elements. Analytical correlations are derived among salient structural and soil parameters of the tapered wall-footing. An extensive parametric study is carried out through linear-elastic finite-element analysis of an isolated wall-footing system under estimated actual vertical and lateral forces. Under the estimated forces, significant loss of contact is observed at the bottom of the wall-footing; thus, soil or rock anchors need to be provided to ensure stability of the wall-footings during strong shaking. Force flow from wall to footing improves significantly in the proposed integrated wall-footing system. In the wall, the region of the inelastic response and possible seismic damage is expected to occur above the tapered region and away from the footing level. Permissible parametric limits are also proposed through the observed stress-deformation response.

In a companion paper, new tapered configurations are proposed of slender RC structural walls with and without enlarged boundary elements at the wall-footing junction region. On the basis of identified parametric limits and the wall response in linear-elastic finite-element analyses, a stepwise seismic design procedure is proposed of tapered integrated wall-footing systems with soil or rock anchors at the bottom. This incorporates a capacity design of the plastic hinge region above the tapered portion and an elastic design of the tapered portion. The location of the region of seismic damage and energy dissipation in the wall is controlled by proportioning of the tapered wall-footing as per the new design procedure.

Two elementary response features of bridge aerodynamics, namely unit-step (indicial) and unit-impulse response functions, as the fundamental building blocks for the convolution integral, are reviewed systematically. The comparison of these elementary response functions was carried out from theoretical, experimental, and numerical perspectives. Theoretically, their new interpretation is given in the context of bridge aerodynamics. Experimentally, the underlying mechanism concerning these elementary response functions as applied to bridge aerodynamics was investigated, e.g., the overshooting feature and the applications to the simulation of gust- and motion-induced forces. Numerically, a comparison of the indicial and rational function approximations, often utilized in the indirect identification of the effective unit-step and unit-impulse response functions, respectively, is highlighted by underscoring the underlying physics in the associated mathematical derivation. A numerical example of a long-span bridge is presented to demonstrate the fidelity of simulation based on these numerical approximations.

Recent research has shown the viability of using nonlinear energy-sink (NES) devices for vibration mitigation in mechanical and structural systems. When attached to a primary structure, these lightweight passive devices can effectively reduce the structural vibration response through their nonlinear stiffness properties. In this research, a two-degree-of-freedom NES device is designed using innovative elastomeric bumpers as the critical components providing nonlinear restoring forces. A number of elastomeric bumper configurations are evaluated experimentally, and the effect of geometric bumper parameters is investigated with a focus on their influence on the stiffness properties of the bumper. A NES device employing different bumpers is then implemented on a 6-story model building and tested using impulse-like base motion. Nonlinear system identification of the NES device shows that nonlinear stiffness properties are achieved using the elastomeric bumpers. Shake-table testing of the building equipped with the NES device demonstrates that the device is capable of dissipating and redistributing the induced vibration energy in a rapid, effective, and robust fashion.

Many engineering and biological media can be described as the combination of several heterogeneous constituent phases. For instance, a tumor-containing organ can be approximated as two phases: tumor and tissue media. A nonlinear elastography method is developed in this paper to identify the distribution of mechanical properties in two-phase media, based solely on the measurement of displacements and forces on the external boundary. The two-phase distribution is approximated with a general continuous material parameter field, for which a designed grouping technique is applied to reduce the number of unknowns. The numerical efficiency of the minimization-based reconstruction is further enhanced by user-supplied gradients of the objective function, which are computed with minimal cost using a nonlinear adjoint method. Sample reconstruction is performed to identify two irregular inclusions in a two-dimensional nonlinear medium.

Engineering structures are often designed to have complex geometries, which could introduce stress singularities that are weaker than the conventional $-1/2$ crack-tip singularity. Extrapolating the results of small-scale laboratory tests to predict the response of a full-scale structure comprised of quasi-brittle materials requires an understanding of how the weak stress singularities modify the classical energetic and statistical scaling theories of quasi-brittle fracture. Through a theoretical and numerical study, a new scaling law for quasi-brittle fracture is derived, which explicitly relates the nominal structural strength to the structure size and the magnitude of the stress singularity. The theoretical analysis is based on a generalized weakest-link model that combines the energetic scaling of fracture with the finite weakest-link model. The model captures the transition from the energetic scaling to statistical scaling as the strength of the stress singularity diminishes. The new scaling law is in close agreement, for the entire range of stress singularities, with the size effect curves predicted through finite-element simulations of concrete beams containing an arbitrary-angle V-notch under Mode-I fracture.

Large deflection analysis of functionally graded annular sector plates subjected to thermomechanical loads is presented. Based on the first-order shear deformation theory in conjunction with nonlinear von Kármán assumptions, the governing system of equations is derived. A polynomial-based generalized differential quadrature (GDQ) method is used to discretize the nonlinear governing equations. The Newton-Raphson algorithm is then employed to solve the system of nonlinear algebraic equations. Material properties of the plates are assumed to depend on temperature and are graded in the thickness direction based on a simple power-law distribution. Based on a comparison of results obtained for plates with temperature-dependent material properties versus plates with temperature-independent material properties, it is found that the effects of temperature dependency cannot be neglected. Furthermore, the effects of temperature rise, material index, thickness-to-radius ratio, and temperature dependency of material are studied in detail.

A hybrid real-time structural health monitoring and control system for building structures is presented in this study. A model-reference adaptive control algorithm for the designed substructures was developed and integrated with a previously developed interstory drift–based acceleration feedback method for health monitoring. A virtual healthy model, installed with health monitors, is used to generate proper control forces to obtain the desired response for the controlled substructure during a disastrous event such as an earthquake. An adaptive controller and an adaptation mechanism are designed using the Lyapunov theory to calculate the real-time adaptive control force. The local feedback control actuates the actual substructures to track the desired response signals. The results obtained by numerical simulations for the illustrative example in this study are further validated by experimental investigations using a 3-story aluminum frame structure. The asymptotical tracking of the state of the substructure and convergence of the time-varying parameters in the adaptive controller are found to be in agreement with the experimental data obtained for this example. Several representative experimental data sets are compared with the corresponding numerical simulation results for this example with favorable correlations.

A crack in a steel structure will cause a local change in its stiffness. The change in stiffness will lead to a change in buckling loads and a discontinuity in the associated buckling modes. The changes in the buckling characteristics of columns cause a change in the buckling stability of the structure. The effect of cracks on the buckling load of structural systems can be investigated through numerical methods. The FEM is a well-known method for this work. In this paper, a new and innovative finite-element (FE) formulation for the buckling analysis of cracked columns is presented. The method presented is simpler and, at the same time, more accurate and practical than those available in the literature. The proposed FE formulation for cracked columns has the same format as that for intact columns. The formulation is used successfully in efficient and accurate buckling analysis of cracked frames.

Based on the theoretical solution for vibrations of simply supported bridges under moving train loads, resonance and cancellation conditions are derived. The results reveal two types of vibration cancellations for simply supported bridges under moving train loads: the first is related to a single moving load, which is independent of the number and the composition of the train, while the second is related to the interval between a pair of moving loads. When cancellation occurs, the free vibrations induced by the moving loads cancel to null, and the bridge response is determined by the loads still on it. A resonance disappearance effect occurs when train speed meets both the resonance and cancellation conditions, while the cancellation plays a predominant role. Bridge damping has an influence on the cancellation effect: the higher the damping and the longer the interval between the loads, the lower is the cancellation efficiency. In a case study, dynamic responses of a bridge under high-speed train loads are analyzed and the mechanisms of resonance and cancellation are explained to support the theoretical solution.

Rigid structures, such as groins or spur dikes, are constructed along riverbanks for various purposes, which pose computational challenges for unsteady flow in engineering mechanics. This paper presents a study of turbulent flow past a series of groins in a shallow, open channel by large-eddy simulation (LES). A direct-forcing immersed boundary method (IBM) was implemented to approximate complex boundaries around groins with round heads. The time-averaged velocities and turbulence intensities at the water surface obtained by an experiment using particle image velocimetry (PIV) were employed to validate the LES model, finding a satisfactory agreement between laboratory data and model results. Subsequently, the numerical model was employed to investigate the impact of groin parameters (i.e., head shape, aspect ratio $L/D$, and length $L$) on the flow properties. Model results showed that a rectangular-headed groin generates higher turbulence intensities and larger vortices than a round-headed groin. On the other hand, the groin aspect ratio ($L\text{/}D$) affects the strength of turbulence intensities, vorticity in the mixing layer, and flow patterns in the groin field. Consistent with previous studies, the groin length ($L$) significantly affected the turbulent intensities and the vorticity but had little influence on the streamline in the recirculation zone. Eddies were produced at the groin tips and transported downstream. The shape of the vortex group varied as the vortices were transported downstream by the flow. Coherent structures were visualized by $Q$-criterion around the groin tips.

This paper presents the exact relation between the real and imaginary parts of aerodynamic transfer functions for deriving impulse response functions that satisfy the causality condition. A truncated Fourier series is used to express the aerodynamic transfer functions, and the causality condition is defined in terms of the coefficients of a Fourier cosine and sine series, which represent the real and imaginary parts of the aerodynamic transfer functions, respectively. The impulse response functions that satisfy the causality condition are obtained through the inverse Fourier transform of the aerodynamic transfer functions that conform to the exact relation. The coefficients of the Fourier series are determined by minimizing the error between the transfer functions formed by measured flutter derivatives and by the Fourier series. Because the impulse response functions become a series of Dirac delta functions in the proposed method, the aerodynamic forces are easily evaluated as the sum of current and past displacements with the same number of the terms in the Fourier series. The validity of the proposed method is demonstrated for two types of bluff sections: a rectangular section with a width-to-depth ratio of 5 and an H-type section. Time-domain aeroelastic analyses are performed for an elastically supported system with each section. The proposed method yields stable and accurate solutions for the examples efficiently.

This study analyzes wave propagation in a Timoshenko beam model of a high-rise building excited by base motion. This model accounts for wave dispersion caused by bending and is more realistic for analysis of wave propagation in high-rise buildings than shear beam and other discrete nondispersive models. The model transfer functions and impulse response functions are obtained from the analytical solution for a forced vibration response of the beam excited by base motion. The impulse response functions represent the model response to a virtual input pulse; a set of such functions at different levels is used to study pulse propagation in the beam. A parametric study of dispersion and its effects on the model transfer functions and impulse response functions is presented in terms of dimensionless parameters and in ranges corresponding to buildings. The model is validated for a 9-story full-scale RC building and smaller earthquake excitation. The results provide insight into dispersive wave propagation in buildings caused by bending, which is useful for the interpretation of impulse responses of buildings obtained from earthquake records and for the development and testing of wave methods for structural health monitoring. The results can also be used for testing numerical models for pulse propagation in buildings.

A precise iterative strategy to compute the polar decomposition of the three-dimensional deformation gradient tensor is presented for nonlinear solid mechanics analysis software. By exploiting relationships between various stretch tensors, polar decomposition is transformed into the solution of six nonlinear (quadratic) simultaneous equations, via Newton-Raphson (N-R), and a subsequent $3\times 3$ matrix inversion and multiplication. The approach is easy to program and is versatile in its applicability to statics or dynamics. With only modest computational increases, the approximations and potential numerical drift of incremental decomposition schemes is avoided. Convergence can be accelerated using stretch histories, which, coupled with a modified N-R approach, can reduce computer times. Using an explicit central difference time integration scheme, convergence is shown to be attained in only a few iterations with very tight tolerances for severe deformations. Numerical examples compare different method variations that are demonstrated to be robust and efficient. The results also demonstrate its effectiveness for large time increments (the entire analysis), which can be especially useful for static and implicit solvers.

The flow in a submerged hydraulic jump with three-dimensional (3D) baffle blocks was experimentally studied. An incoming jet with varying supercritical Froude numbers was deflected with one or two rows of 3D baffle blocks for different downstream water depths. Depending on the submergence factor, two flow regimes were observed for which the time-averaged 3D velocity field was measured with an acoustic Doppler velocimeter (ADV). Measurements were conducted at different stations located both upstream and downstream of the blocks and above the crest of the blocks. Velocity measurements were made in a plane located at the center of the middle block (i.e., the centerplane of the flume) and, also, in a plane located at the midpoint between the blocks (off-centerplane). The mean flow pattern was found to be significantly different for the two flow regimes. In the deflected surface jet (DSJ) regime, which occurred at low submergence factors, the major flow features were a small surface roller upstream of the blocks and a larger recirculating flow region located downstream of the blocks. The reattaching wall jet (RWJ) regime, which was formed at large submergence factors, could be characterized by a large surface roller and a small standing eddy just behind the blocks in the centerplane. In both flow regimes, the maximum longitudinal velocity component was observed to decrease rapidly at the blocks and the jet half-width was found to increase quickly. The DSJ regime was found to have a smaller streamwise dimension and to be more effective in reducing the streamwise velocity and increasing the jet half-width. These features can be considered an advantage of the DSJ regime over the RWJ regime; that is, hydraulic structures should be designed such that the DSJ regime occurs over the entire range of tailwater depths that are likely to occur.

In this paper, the results of numerical studies on linear and nonlinear transverse vibrations and instability of a geometrically nonlinear column with an internal crack subjected to Euler’s load are presented. The investigated column is composed of two members. The internal member consists of two rods connected by a pin and strengthened by a rotational spring of stiffness $C$. The stiffness $C$ of the rotational spring reflects the size of the internal crack. The Hamilton principle was used to formulate the boundary problem. Because of the geometric nonlinearity, the solution to the problem was achieved by means of the perturbation method. The natural vibration frequencies (the linear problem) were computed after obtaining the equations from the first power of the small parameter $\epsilon$. The orthogonality condition was applied to find and calculate the first correction of vibration frequency. The nonlinear vibration frequency of a column is derived as dependent on vibration amplitude. The results of the numerical calculation are based on vibration frequency, critical loading, and the amplitude–vibration frequency relation.

The governing dynamic equilibrium equation of $N$-story periodic shear structure with arbitrary top-story mass, arbitrary base-story stiffness, and that is subjected to base excitation is given in the form of a constant coefficient second-order finite-difference equation. The first integration of the governing difference equation for the eigenanalysis results in the Volterra difference equation of convolution type and yields the first boundary condition. The $z$-transform method is applied to the equation to obtain the general solution for displacement mode shapes. Applying the second boundary condition to the general solution results in the characteristic equation in which the frequencies are obtained by solving it. The general form of the characteristic equation for eigenfrequencies is presented, and analytical solutions for some special cases are derived. Displacement and drift mode shape functions are obtained. All the modal parameters, including modal mass, excitation factor, participation factor, and effective modal mass, are derived using the sum and the sum of the square modal displacements and are presented as closed-form solutions.

Based on the methods of variable separation and matching eigenfunction expansions for velocity potential, analytical solutions are developed for a water wave radiation problem by a submerged vertical cylinder in finite water depth. They are validated by comparison with results from the higher order boundary element method and convergent examinations on the number of expansion models. Numerical analysis is carried out to investigate the influence submerged depth, cylinder length, and water depth on added mass and radiation damping. When the submerged depth is large, the added mass approaches a stable value, and radiation damping tends to zero. At high frequency range, the heave and pitch of the added mass of the submerged cylinder is about twice that of the floating cylinder. The influence of cylinder length for hydrodynamic coefficients is quite complex and shows the various properties at different frequency ranges. Added mass can be increased with the decrease of water depth, whereas the effect of water depth on radiation damping is quite small.