Journal of Engineering Mechanics

The paper deals with interface behavior of bimaterial ceramic-metal composites under dynamic time-harmonic load. The first plate is precracked with a normal crack touching the interface between the plates. It is assumed that the respective restriction for the ratio of energy release rates of the plates allowing the occurrence of an interface single delamination before the initiation of the normal crack in the second plate is satisfied. The growth of interface delamination is not considered. The used approximate shear-lag dynamic approach gives a possibility to obtain solutions in a closed form for axial and shear stresses of the structure. At an elastic-brittle interface behavior theoretical predictions for single debond length of two bimaterial structures are calculated. The parametric analysis reveals the sensitivity of the interface single debond length and shear stress to the type of bimaterial structure and to the characteristics of the dynamic load—in particular its frequency and amplitude. All results are illustrated in figures and tables and are discussed.

Fiber-reinforced polymer (FRP) composite materials have been widely used in the field of retrofitting. Theoretical analysis of FRP plate- or sheet-strengthened cracked concrete beams is necessary for estimating service reliability of the structural members. In previous studies, the effect of a perfectly bonded FRP plate or sheet was equivalent to a cohesive force acting at the bottom of crack to delay the crack propagation in concrete and reduce the crack width. However, delamination between FRP and cracked beam is inevitable due to interfacial shear stress concentration at the bottom of crack. The intention of this paper is to present an analytical solution for fracture analysis of carbon FRP (CFRP) sheet–strengthened cracked concrete beams by considering both vertical crack propagation in concrete and interfacial debonding at CFRP-concrete interface. The interfacial debonding is modeled as the interfacial shear crack propagation in this paper. Four different stages are discussed after initial cracking state of the concrete. At the first stage, only fictitious crack propagation occurs in the concrete. At the second stage, macrocrack propagates in the concrete without interfacial debonding. At the third stage, both vertical macrocrack propagation in the concrete and horizontal shear crack propagation at the CFRP-concrete interface occur in the strengthened beam. The tensile stress in the CFRP sheet and interfacial shear stress along the span are formulated based on the deformation compatibility condition at the CFRP-concrete interface at this stage. Finally, macroshear crack propagates at the interface until the CFRP sheet is completely peeled out from the beam, and then the member is fractured. The applied load is determined as a function of the referred two crack lengths at different stages. At the beginning, the applied load increases to one peak value with the full propagation of fictitious crack at the first stage. At the third stage, the applied load is improved to another peak value due to the relatively high cohesive effect of the CFRP sheet. Then the two peak values are determined by the Lagrange multiplier method. The validity of the proposed analytical solution is verified with the experimental results and numerical simulations. It can be concluded that the proposed analytical solution can predict the load-bearing capacity of CFRP sheet-strengthened cracked concrete beams with reasonable accuracy.

This study addresses the complexity of slope reliability problems based on limit equilibrium methods (LEMs). The main focus is on the existence of multiple failure modes that poses difficulty to many LEM-based slope reliability methods. In particular, when weak seams are present, the failure modes associated with those seams may be difficult to detect. A systematic way of searching the failure modes is proposed, and its robustness over slopes with or without weak seams is demonstrated. It is found that in the presence of weak seams, assuming circular slip surfaces may cause underestimation of slope failure probability. The conclusion of the study promotes the use of finite elements as the stability method for reliability evaluation because it is not necessary to search for failure surfaces in finite-element stability analysis.

The present work deals with the dynamic response of structures that are irregular in height, consisting of two parts, a lower part made of concrete and an upper part made of steel. Irregularity is due to different dynamic responses of the two parts, here expressed by their different damping ratios and inelastic material laws. The seismic design of such structures is not satisfactorily covered by current design codes, especially if a decoupled procedure is chosen for the analysis, where the lower part is excited first and its response is used as excitation for the upper part. The present paper aims at contributing toward better understanding of the interaction between the two parts and at proposing improved decoupling criteria for the seismic analysis of inelastic primary-secondary systems. Toward that goal, each part is modeled as a one-degree-of-freedom system, and the maximum responses of coupled and decoupled inelastic time history analyses are compared over a wide range of dynamic characteristics and strength levels of the two parts. The results are presented in the form of error levels between the two alternative analysis procedures.

We combine Bayesian networks (BNs) and structural reliability methods (SRMs) to create a new computational framework, termed enhanced BN (eBN), for reliability and risk analysis of engineering structures and infrastructure. BNs are efficient in representing and evaluating complex probabilistic dependence structures, as present in infrastructure and structural systems, and they facilitate Bayesian updating of the model when new information becomes available. On the other hand, SRMs enable accurate assessment of probabilities of rare events represented by computationally demanding physically based models. By combining the two methods, the eBN framework provides a unified and powerful tool for efficiently computing probabilities of rare events in complex structural and infrastructure systems in which information evolves in time. Strategies for modeling and efficiently analyzing the eBN are described by way of several conceptual examples. The companion paper applies the eBN methodology to example structural and infrastructure systems.

The enhanced Bayesian network (eBN) methodology described in the companion paper facilitates the assessment of reliability and risk of engineering systems when information about the system evolves in time. We present the application of the eBN: (1) to the assessment of the life-cycle reliability of a structural system; (2) to the optimization of a decision on performing measurements in that structural system; and (3) to the risk assessment of an infrastructure system subject to natural hazards and deterioration of constituent structures. In all applications, observations of system performances or the hazards are made at various points in time and the eBN efficiently includes these observations in the analysis to provide an updated probabilistic model of the system at all times.

In this investigation, a two-dimensional time-domain closed-form mathematical model for the hydrodynamic forces on the upstream vertical face of a given rigid dam subjected to a specified horizontal ground motion accelerogram was developed. The model includes the absorption of energy at the elastic reservoir bottom, characterized by the impedance ratio of the sub-bottom materials with respect to water $\left(\alpha \right)$ . The formulated boundary-value problem is solved in Laplace’s domain and subsequently transformed back to the time domain. Response spectra for the hydrodynamic base shear force and overturning moment are constructed for extreme values of the parameter $\alpha$ . It is found that, frequently, including the solid-foundation elasticity in the reservoir model attenuates the resultant hydrodynamic forces on a rigid barrier, as compared to the results for the case of a rigid reservoir foundation. In this case, the elasticity of the sub-bottom materials constitutes an effective energy dissipating mechanism (radiation damping). By contrast, for sub-bottom materials with less-than-water impedance, amplification of the effective earthquake forces is obtained, as compared to the results for the case of a rigid reservoir foundation.

Toroidal shells are widely used in structural engineering. The governing equations of toroidal shells are very complicated because of its variable coefficients with singularity. To find their analytical solution, traditionally, the complex form governing equations were proposed and some useful solutions were obtained. Unfortunately, no any closed-form solution has even been obtained for either general or slender toroidal shells. This paper focus on a special case of toroidal shells, i.e., slender symmetrical toroidal shells. For the first time, the closed-form solution of this kind of shell has been successfully obtained from displacement form governing equations. The closed-form solution is demonstrated for the example of thermal compensation devices. The correction of well-known Dahl formula for slender toroidal shell has been proposed based on the solution obtained in this paper.

A concept for the modeling of a laminated and curvilinear shell that is deformed in a geometrically nonlinear elastic manner is reported in this technical note. The shell is assumed to be sufficiently thin and all the laminate materials sufficiently stiff to facilitate a degenerated approximation. The model equations are derived to be valid for problems involving large strains and rotations and to take into account transverse shear deformations. This is accomplished by combining an unrestricted displacement form of the strain tensor with the Touratier kinematic model and then expressing the resulting equations in terms absolute nodal coordinates instead of displacement vector components. It is anticipated that the theory documented here can be used to develop a specialized degenerate finite-element type.

The analytical strip method is presented in this paper for the analysis of the bending-extension coupling problem of antisymmetric thin laminates. A system of three equations of equilibrium, governing the general response of antisymmetric laminates, is reduced to a single eighth-order partial differential equation (PDE) in terms of a displacement function. The PDE is then solved in a single series form to determine the displacement response of antisymmetric cross-ply and angle-ply laminates. The solution is applicable to rectangular laminates with two opposite edges simply supported and the other edges being simply supported, clamped, or free. The laminate can be subjected to any combination of concentrated, uniform, line, and patch loads. This method overcomes the limitations of other analytical methods (e.g., Navier’s and Levy’s) and provides an alternative to numerical, seminumerical, and approximate methods for rectangular plates with two parallel edges simply supported. The results obtained from this method compare very well with the ones derived using the finite-element program ANSYS and, where applicable, the existing classical laminated plate theory.

Two analytical perturbation methods which give approximate solutions of postbuckling behavior of orthotropic simply supported plates are considered in this work: the method of Chandra and Raju and the method of Shen and Zhang. The reproduction of the algebraic developments of these methods by the Mathematica symbolic manipulator program has revealed that there are errors in the formulas included in the original paper by Chandra and Raju. After a revision and correction of these errors, the analytical results of both methods for a set of 23 orthotropic plates are compared, an excellent agreement being found for a wide range of values of geometrical and mechanical parameters in which many actual plates lie. A numerical simulation performed on a reduced sample of six plates using finite-element code ABAQUS has validated analytical results. The present work is intended as a first step in the investigation of the possibility of using reliable analytical formulas in the design of composite plates.

Using the Hankel Transform Technique, an analytical solution is derived for two-dimensional solute transport in a homogeneous isotropic aquifer. The aquifer is subjected to time-dependent point source contamination. The solution is derived under two conditions: (1) the flow velocity in the aquifer is a sinusoidally varying function and (2) the flow velocity is an exponentially decreasing function. Initially the aquifer is assumed solute free. The analytical solution is illustrated using an example.