Journal of Engineering Mechanics

This paper proposes an expectation-maximization (EM) algorithm embedded statistical damage prognosis paradigm for in-service civil structures against natural hazards. Being within the scope of structural health monitoring, damage prognosis examines the future safety performance of existing structures given relevant damage diagnosis results that reveal the current health condition of the structures under investigation. The damage diagnosis results, which constitute a prerequisite for a reasonably accurate damage prognosis, may in reality turn out to be incomplete owing to various on-site or off-site operation issues. Instead of working on measures to help preclude any data missingness event, this study focuses on exploring an innovative approach, namely for the purpose of damage prognosis striving to make the most of the damage diagnosis results that have become incomplete. The proposed EM algorithm embedded damage prognosis paradigm comprises two sets of procedures, i.e., prognosis validation and prognosis implementation, and each set of the procedures takes into account both the time invariant and time variant damage prognoses. The paradigm is first illustrated by using some meticulously constructed generic performance functions and then applied to some typical situations where existing civil structures are subjected to natural hazards.

Rolling isolation systems (RISs) have been used extensively to protect bridges, buildings, and equipment from earthquake-induced ground and floor motions. RISs are attractive in a performance-based design context because horizontal acceleration design requirements may easily be met by adjusting the slope of the rolling surface. However, in the process of reducing horizontal accelerations, the isolator transmits vertical accelerations due to the pendulumlike motion. These vertical accelerations may exceed tolerable limits if left unchecked. In this study, the influence of the rolling surface profile on peak vertical accelerations is assessed through experiments and simulations. RISs with different radii of curvature are fabricated and then tested for a wide range of ground-motion frequencies and amplitudes. The experiments and simulations show that vertical accelerations are not negligible and should not be ignored in the design of RISs.

Creep functions are often represented by “rheological models” consisting of springs and dashpots, while the actual microscopic origins of creep, such as micro-sliding along interfaces, has only recently been explicitly considered in a continuum mechanics framework. The question arises whether formal analogies between the former and the latter can be derived: This question is answered here for the rheological models of the Kelvin-Voigt and Maxwell type. Thereby, it appears a full analogy between shear stresses and strains acting on the rheological models, and those acting on a micromechanical representative volume element consisting of an elastic solid matrix with embedded viscous interfaces, whereby the respective viscosity arises from layered polar fluids absorbed at these interfaces. The corresponding Kelvin-Voigt parameters are much simpler and more intuitively related to the micromechanical quantities, when compared to the Maxwell parameters. More specifically, rheological spring parameters are always related to the shear stiffness of the elastic solid matrix, while they may additionally depend on the Poisson’s ratio of the elastic solid matrix, and on the interface density. On the other hand, dashpot viscosities are always related to interface viscosities, interface radii, and interface densities; and they may even depend on the Poisson’s ratio of the elastic solid matrix.

Whereas the companion paper provided a micromechanical explanation of the spring and dashpot parameters occurring in the rheological models of the Kelvin-Voigt and Maxwell type, we here extend this discussion toward rheological chain models. Therefore, the considered micromechanical system is extended from one interface phase to $N$ interface phases differing in size and viscosity. Elimination schemes allow for deriving differential equations with only overall stresses and strains and their derivatives as unknowns, rather than microstresses and microstrains in case of micromechanics, or spring/dashpot-related stresses and strains in case of the rheological chain models. Comparison of corresponding coefficients reveals a full analogy between the two different types of chain models, and also between the latter and the micromechanics model. For the Kelvin-Voigt chain, this analogy is even identical to the one of the Zener model of companion paper Part I. The Maxwell chain-related analogy is much more complex, and analytical solutions only exist in the case of very few chain units.

The response of structural dynamical systems excited by multiple random excitations is considered. Two new procedures for evaluating global response sensitivity measures with respect to the excitation components are proposed. The first procedure is valid for stationary response of linear systems under stationary random excitations and is based on the notion of Hellinger’s metric of distance between two power spectral density functions. The second procedure is more generally valid and is based on the $l_2$ norm based distance measure between two probability density functions. Specific cases which admit exact solutions are presented, and solution procedures based on Monte Carlo simulations for more general class of problems are outlined. Illustrations include studies on a parametrically excited linear system and a nonlinear random vibration problem involving moving oscillator-beam system that considers excitations attributable to random support motions and guide-way unevenness.

This paper focuses on calculating the load level and the ultimate state of steel plane frames consisting of straight slender nonprismatic rods. The plastic behavior is modeled in the theory of second order with a step-by-step method that only considers the bending moment effect and leads to the formulation of sudden concentrated plastic hinge. The plastic process results in the loss of stiffness, leading to lower strength of the section of the structure as a whole. Therefore, it also affects the stability of the whole, which is checked during the loading process each time a new plastic hinge is formed by the equations of stability. Thus, it is well known that it is necessary to suggest the static equilibrium in the deformed or actual configuration. The plastic design allows saving materials as well as ensuring the safety, functionality, and durability of the structure. In addition to the static analysis, the ability to evaluate the frequencies and the associated vibration modes is included. All this enables a tracking process of the structure response for each load state until the collapse.

Three-point bending tests of fiber-reinforced polymer (FRP) plated notched concrete beams have great potential to become a standard test method for evaluating the shear bond performance of FRP-to-concrete interfaces. This paper presents an analytical approach to predict the full-range response of FRP-plated notched concrete beams. The focus of the analysis is to simulate the interactions between Mode II debonding of the FRP-to-concrete interface and Mode I fracture at the crack tip of the concrete beam. In analyzing the FRP-to-concrete interface, the slip is selected as the unknown function to derive a second-order ordinary differential equation, and the analytical relationship between the pull force of the FRP laminate and the interfacial slip at its loaded end is formulated. Crack propagation in concrete is modeled using the weight function method. The stress intensity factors induced by various external loads and internal forces are all given in an analytical manner. Finally, a global equation with one single unknown is established. The equation can be solved easily and good convergence is assured. The derived analytical solutions are verified with experimental results obtained from the literature. Further parametric studies reveal quantitatively the effects of various factors on the load-crack mouth opening displacement (CMOD) curve of the FRP-plated concrete beam, which is found to be characterized by two peak loads. The first and second peak loads increase with the increase in the strength of concrete, the thickness of the FRP laminate, and the interfacial bond strength. It is also found that increasing the initial crack length decreases the first peak load but exerts no effect on the second peak load.

This article presents an analytical method to draw influence lines and diagrams of variations for deflection, rotation, bending moment, and shearing force for a generally restrained Euler-Bernoulli beam. To do so, Green’s function method is used. The Green’s functions of the parameters are first derived and then used to obtain the influence lines and diagrams for variations in deflection, rotation, bending moment, and shearing force for different beams with different boundary conditions. Examples provide an indication of the accuracy of the proposed exact solution.

The first-order reliability method (FORM) is a powerful tool for structural reliability analysis, providing a good trade-off between computational accuracy and efficiency. Nevertheless, it has two main drawbacks: (1) its approximation is not necessarily adequate for limit state surfaces which depart significantly from linearity, and (2) it does not give information about the degree of accuracy achieved. In this paper, the secant hyperplane method (SHM) is proposed, which is a new linear approximation of the limit state surface based on the support vector method (SVM). The key idea is to treat structural reliability as a classification problem and to seek a suitable secant hyperplane to the limit state that gives improved approximation over the use of a tangent hyperplane. The two drawbacks of FORM are thereby resolved, while keeping the geometrical simplicity and ease of implementation of FORM. The implication of very high-dimensional geometry is examined, demonstrating that FORM can give good approximations if reinterpreted as a linear classifier, and SHM has the potential of scalability to spaces of high dimensionality. Two numerical examples, including stochastic dynamic analysis, show the accuracy and effectiveness of SHM.

This paper presents dynamic stability analysis of beams with shear deformation and rotary inertia subjected to periodic axial forces by employing a discrete singular convolution (DSC) algorithm with regularized Shannon kernel. The shear effect has been taken into account based on Engesser’s and Haringx’s theories, respectively. A modified algorithm is proposed to solve the governing equations of beam motion. The influence of rotary inertia, shear deformation, and damping on dynamic instability regions has been investigated. The obtained numerical results are compared with those of the existing method. Numerical results indicate that the modified algorithm is a reliable approach for the solutions of this kind of problem in this investigation. The differences between dynamic instability regions of beams based on Engesser’s and Haringx’s theories are also presented.

This paper extends the Tail-Equivalent Linearization Method (TELM) to the case of a nonlinear mechanical system subjected to multiple stochastic excitations. Following the original formulation, the method employs a discrete representation of the stochastic inputs and the first-order reliability method (FORM). Each component of the Gaussian excitation is expressed as a linear function of standard normal random variables. For a specified response threshold of the nonlinear system, the Tail-Equivalent Linear System (TELS) is defined in the standard normal space by matching the design points of the equivalent linear and nonlinear systems. This leads to the identification of the TELS in terms of a frequency-response function or, equivalently, an impulse-response function relative to each component of the input excitation. The method is demonstrated through its application to an asymmetric, one-story building with hysteretic behavior and subjected to bi-component ground motion. The degree of asymmetry is controlled by the eccentricity of the center of stiffness with respect to the center of mass. The correlation between the probability of failure and the degree of asymmetry is studied in detail. The statistics of the response for stationary excitation obtained by TELM are in close agreement with Monte Carlo simulation results.

Floating offshore wind turbines are recently being considered widely for adoption in the wind power industry, attracting interest of several researchers and calling for the development of appropriate computational models and techniques. In the present work, a nonlinear finite-element formulation is proposed and applied to the static and dynamic analysis of mooring cables. Numerical examples are presented, and in particular, a mooring cable typically used for floating offshore wind turbines is analyzed. Hydrodynamic effects on the cable are accounted for using the Morison approach. A key enabling development here is an algorithmic tangent stiffness operator including hydrodynamic coupling. Numerical results also suggest that previous empirical hydrodynamic coefficients could be obtained by fully coupled fluid–structure interaction. Convergence-rate and energy-balance calculations have been used to demonstrate the accuracy of computed solutions. The introduction of the developed cable model in a framework for the study of the global behavior of floating offshore wind turbines is the subject of the current work. Source code developed for this work is available as online supplemental material with the paper.

The present paper deals with the study of peristaltic motion, with heat and mass transfer of a coupled stress fluid through a porous medium in a channel with compliant walls. The motion is induced by sinusoidal waves traveling along the channel walls. A system of nonlinear partial differential equations, which controlled this motion, is solved analytically by using the perturbation technique. The velocity, temperature, and concentration distributions are obtained as functions of the problem parameters. The effects of the permeability parameter of the medium, coupled stress parameter, and spring stiffness of the wall on these distributions are discussed and illustrated graphically through a set of figures.

The transient dynamic response of the substructures above a removed column is the most direct and realistic to demonstrate the structural performance against progressive collapse. To efficiently obtain the transient dynamic response, a nonlinear single degree-of-freedom (SDOF) model is proposed with a tri-linear resistance function that is capable of describing various forms of structural resistance, including catenary action and softening resistance and a loading function consisting of a linear ascending part and an ensuing constant force that considers the effect of column removal time. Moreover, the model accounts for nonzero initial conditions, which are very likely to occur under blast loading. The closed-form analytical solutions of the model are derived with Laplace transform techniques and verified with dynamic experimental results of steel and reinforced concrete assemblies subjected to column removal scenarios. The verification indicates the generality and the accuracy of the SDOF model in predicting displacement responses of substructures. Then, the model is used for parametric studies. The results show that sudden column removal scenarios, which are used for progressive collapse design, provide an upper bound of structural deformation in cases that take a relatively long time to destroy a column but underestimates the structural deformation in cases that have upward displacement and nonzero velocity at the start of the progressive collapse stage.

A computational procedure for robust-to-modeling and robust-to-change design of structural systems is proposed with application to planar rigid frames. A structure is considered robust when it is least sensitive to changes that alter its system coefficients (stiffness matrix for static loading). The upper limits of change from perturbations in the stiffness matrix are available from linear algebra; however, what is not clear is an ideal pattern of material allocation throughout the structure, or a preferred preliminary model from a set of viable models, such that it results in a final design that has low error bounds while satisfying the limit states of performance and safety. Because gradient-based optimization is not feasible, the authors rely on statistical simulation techniques to study the variation of error upper bounds in structural response when the system is subjected to changes in its components (elasticity, cross-sectional dimensions, member lengths). Application of the methodology to lateral design of a set of multistory rigid frames shows that initial models with uniform material distribution over their height produce more tolerant designs. Along the way, the authors analytically present the necessary condition for making multiobjective design (also known as performance-based design) of multistory frames with a single objective. The procedures have the potential of saving time and resources during the lengthy design projects and creating structures that are more tolerant to change, hence improving their resiliency and lifespan.

Nonlinear features concerning self-excited drag forces induced by the vertical and torsional motions for typical deck sections are investigated comprehensively in this study. The self-excited drag forces are calculated using computational fluid dynamics (CFD)-based numerical simulations. In a conventional analysis framework, the self-excited drag force is modeled as a linear function of the structural motions. However, the simulation results from CFD indicate that in many instances, the second-order (nonlinear) component of the self-excited drag force is more significant than the first-order (linear) component. To enhance the modeling fidelity of a conventional aeroelastic analysis framework on the basis of the semiempirical flutter derivative concept, a nonlinear mathematical model for characterizing both the first- and second-order components is developed to better quantify the self-excited forces and more accurately extract the flutter derivatives. Its efficacy and superiority compared with the traditional linear model is verified using different deck sections. For asymmetric bluff sections, the first-order self-excited drag force components are more significant than the higher-order ones. However, for streamlined plate-like sections and symmetric deck sections, i.e., streamlined and bluff, the second-order self-excited drag force components are predominant. For such cases, the proposed nonlinear model is more appropriate. The proposed nonlinear mathematical model can help to serve as a building block for developing an overall nonlinear analysis framework for accurately simulating nonlinear aerodynamics and the aeroelasticity of long-span bridges.