Journal of Engineering Mechanics

Exact solutions for stresses, strains, displacements, and the stress concentration factors of a perforated rectangular plate by a circular hole subjected to in-plane bending moment on two opposite edges are investigated by two-dimensional theory of elasticity using the Airy stress function. The hoop stresses, strains, and displacements occurring at the edge of the circular hole are computed and plotted. Comparisons are made for the hoop stresses and the stress concentration factors from the current study and rectangular plates with a circular hole under uniaxial and biaxial uniform tensions and pure shear loading.

The rocking response of rigid, free-standing bodies to earthquake pulses is revisited. A two-dimensional rectangular block resting on a rigid base is considered, subjected to an idealized ground acceleration pulse composed of two constant half-cycles of equal amplitude, equal duration, and opposite sign. Closed-form expressions are obtained for the dynamic response, whereas rigorous overturning criteria are established for conditions with and without impact. The solutions are expressed in terms of three dimensionless parameters, namely, pulse duration, uplift strength, and restitution coefficient. Despite the apparent simplicity of the problem, the response can exhibit complex—even counterintuitive—patterns, a trait attributed to the possibility of overturning in two distinct modes (forward and backward), the nonlinear nature of the impact, the real-valued (positive) pole of the differential operator, and the presence of multiple immobility points in a particular response branch. The bifurcation behavior associated with the existence of two overturning modes is highlighted. Comparisons against idealized pulses of other shapes and actual near-fault recorded ground motions are presented and commented.

A new numerical analysis procedure is presented for the nonlinear analysis of structures. The proposed methodology is developed within the framework of the direct stiffness method and the hysteretic formulation of finite elements. The derived numerical scheme relies on the natural evolution of localized inelastic quantities within the element, that is, the plastic deformation evaluated at properly defined collocation points rather than the evaluation of global and varying state matrices. This is accomplished by considering the additive decomposition of the total strain rate into elastic and plastic parts. Using the principle of virtual work, an equilibrium expression is derived in which the total applied load is equilibrated by an elastic internal force vector and an additional term acting as a nonlinear correction to the elastic component. The evolution of the plastic components is based on a smooth multiaxial hysteretic law that is derived within the framework of classical plasticity. Examples are presented that demonstrate the validity of the proposed method and its computational advantages with respect to existing methods of inelastic analysis.

The confinement effect has been of significant importance for improving the resilience against extreme compression loadings such as seismic excitations. Notwithstanding the accuracy of previous confinement models, some challenges remain regarding their applicability. The previous approaches often build on structure-dependent parameters necessitating intractable calibrations, and their formulations are defined on an integration point or a small portion of the structure, thereby precluding general applicability to complicated real-scale RC structures. Here a general confinement model is proposed in a novel way that it can harness physical information inside the real-scale system. The information is denoted nonlocal information, since it is processed by the nonlocal formulation for assuring the mesh-objectivity. Physically, the nonlocal information provides the proximity to adjacent stiff materials and boundaries through the information index suggested herein. Numerical issues regarding the parallel computing and the optimal selection of the length parameter for the nonlocal formulation are also addressed. The unprecedentedly broad applications include a solid column, a hollow column, a rectangular wall, a T-shaped wall, and even a wall with opening, which strongly bear out the promising potential and universality of the novel confinement model.

Corrugated shell structures are widely used in civil, naval, automotive, and aerospace engineering because of their superior properties. In this paper, the nonlinear dynamic deformation of a class of longitudinally corrugated shell with a second-order differentiable wave under a uniform load was investigated. On the basis of their previous research result—that the corrugated shell undergoes large deformation but small strains—the authors proposed an assumption that the dynamic configuration of the corrugated shell is the same as the static configuration with a different load. Then the governing equations of the dynamic deformation of the corrugated shell were derived using Lagrange’s equation, and an efficient numerical method without element discretization to solve those nonlinear differential equations was formulated. The accuracy of the present simplification was proved by comparing it with results obtained from a widely used nonlinear finite-element program, and the assumption on the dynamic configuration was shown to be applicable for most engineering applications. Furthermore, the developed method was adopted to perform parametric studies and it is found that the loading rates, the depth of wave, and the number of wave can greatly change the expansion velocity of the corrugated ring. And most importantly, the authors revealed that different corrugation types with the same ratio of the radius of the median surface to the depth of wave $R_0/L_w$, the number of waves $N$, and the circumference $C_T$ can yield similar dynamic expansion responses, which should be useful for future design of corrugated shell.

The previously developed cyclic void growth model (CVGM) has been demonstrated to accurately simulate ductile fracture initiation under monotonic and ultralow cycle fatigue loading for a variety of steel materials and geometric configurations. Prediction of ductile fracture initiation involves significant uncertainty, particularly where there is high variability in the material (e.g., welded connections) subjected to irregular cyclic loading. The reliability of the model predictions is improved through a probabilistic formulation based on maximum likelihood parameter estimation. The probabilistic formulation, which incorporates information from both the failure and nonfailure loading cycles, has the following features: (1) the calibration of model parameters provides the maximum likelihood of agreement for a given set of cyclic fracture observations, and (2) fracture predictions are provided in a probabilistic sense by generating a distribution of the expected instant of fracture. The benefit of the approach is twofold. First, it eliminates an inconsistency that is inherent in the deterministic calibration procedure, as proposed in the original development of the CVGM. Second, the degree of certainty of fracture predictions is quantified. In combination, these features significantly enhance the robustness of the framework within which the model is implemented. Although this paper applies this approach in the specific context of the CVGM, the method can be generalized to other models that share similar characteristics.

In reliability analysis, the first-order reliability method (FORM) and various optimization algorithms are widely used to locate the most probable point (MPP) and calculate the reliability index. These algorithms generally require first-order response sensitivities or gradients of the limit-state function. However, in engineering, the reliability analysis is often merged with finite-element (FE) analysis or other structural/mechanical analyses, and the limit-state function is implicit. The sensitivity analysis may be computationally intensive or cumbersome, and several techniques were developed to deal with this problem. In the present paper, a general iterative algorithm that does not need gradients is proposed. This algorithm produces $n$ series of sequence points iteratively in the $n\text{-dimension}$ standard normal space. It is proven that the $n$ series of points will converge to the same point, which is just the MPP, and its distance to the origin is the reliability index. The proposed algorithm also introduces new step lengths to control the convergence of the sequence. These step lengths are new because they may be constant during the iteration or varied using the interim evaluations of the reliability index, which means a self-adjust process in essence. Eighteen examples are given to verify the effectiveness of the proposed algorithm. It is indicated that the proposed algorithm is effective and robust.

This study presents the mechanical properties of the Al-12Si matrix composite reinforced by various amounts of titanium carbide (TiC) and titanium nitride (TiN) particles. The wear behavior was investigated using a pin-on-disk wear testing machine with varying parameters such as normal load, reinforcement percentage, and track velocity. The results show that the wear of the Al-12Si matrix reinforced by 5, 10, and 15% TiC particles at 150 rpm with 15-N loads was $73\times {10}^{-3},61\times {10}^{-3},\text{and}\hspace{0.17em}50.5\times {10}^{-3}\hspace{0.17em}{\text{mm}}^3$, respectively, which is less than the wear for the same composites at 225 rpm with a 15-N load. This is because of the length of rubbing is more in the case of a higher speed. The results also show that the wear of the samples was decreased with an increasing percentage of reinforcement of TiN at both sliding speeds (150 and 225 rpm). The hardness of the $\text{Al-}12\text{Si}/\text{TiC}$ composites with 5% TiC particles was found to be 50, and the hardness of same composites with 15% TiC reinforcements was 67, which is less than the hardness of $\text{Al-}12\text{Si}/\text{TiN}$ composites with 15% TiN reinforcements. The composites before the wear test showed a uniform distribution of TiC and TiN particles through the cross section of the specimens and finer surfaces compared with matrix composite after the wear test. The mechanical properties such as hardness and wear resistance are observed to be increased considerably compared with the matrix composite.

During mudflows, geomaterials evolve in a very specific manner, because initially they behave as solids, and then they turn to flow as viscous fluids. This paper proposes an original approach to simulate, within a single numerical framework, such a transition between a solid-like and a fluid-like behavior. The model used is based on the association of an elastoplastic and a viscous constitutive relation to describe both phases of the behavior. The transition between the two is assumed to correspond to a failure state, and the transition criterion considered is thus based on the general second-order work stability criterion. The Plasol elastoplastic model and the Bingham viscous model are used because they are suitable to describe soils and granular suspensions, respectively. In this preliminary study, the global model is tested for two homogeneous loading paths with drained and undrained conditions. For these cases, the radical transformation of the material behavior at failure is captured, and both the solid-to-fluid and the fluid-to-solid transitions are consistently enabled, making possible future applications of this approach for gravitational flow modeling.

Asphalt mixtures exhibit primary, secondary, and tertiary stages in sequence during a rutting deterioration. Many field asphalt pavements are still in service even when the asphalt layer is in the tertiary stage, and rehabilitation is not performed until a significant amount of rutting accompanied by numerous macrocracks is observed. The objective of this study was to provide a mechanistic method to model the anisotropic cracking of the asphalt mixtures in compression during the tertiary stage of rutting. Laboratory tests including nondestructive and destructive tests were performed to obtain the viscoelastic and viscofracture properties of the asphalt mixtures. Each of the measured axial and radial total strains in the destructive tests were decomposed into elastic, plastic, viscoelastic, viscoplastic, and viscofracture strains using the pseudostrain method in an extended elastic-viscoelastic correspondence principle. The viscofracture strains are caused by the crack growth, which is primarily signaled by the increase of phase angle in the tertiary flow. The viscofracture properties are characterized using the anisotropic damage densities (i.e., the ratio of the lost area caused by cracks to the original total area in orthogonal directions). Using the decomposed axial and radial viscofracture strains, the axial and radial damage densities were determined by using a dissipated pseudostrain energy balance principle and a geometric analysis of the cracks, respectively. Anisotropic pseudo J-integral Paris’ laws in terms of damage densities were used to characterize the evolution of the cracks in compression. The material constants in the Paris’ law are determined and found to be highly correlated. These tests, analysis, and modeling were performed on different asphalt mixtures with two binders, two air void contents, and three aging periods. Consistent results were obtained; for instance, a stiffer asphalt mixture is demonstrated to have a higher modulus, a lower phase angle, a greater flow number, and a larger $n_1$ value (exponent of Paris’ law). The calculation of the orientation of cracks demonstrates that the asphalt mixture with 4% air voids has a brittle fracture and a splitting crack mode, whereas the asphalt mixture with 7% air voids tends to have a ductile fracture and a diagonal sliding crack mode. Cracks of the asphalt mixtures in compression are inclined to propagate along the direction of the external compressive load.

For elastic-plastic materials, the plastic core region around a crack tip generally has a limited dimension, and therefore, the corresponding radius $r_p$ from the crack tip to the elastic-plastic boundary can be considered as a critical parameter. However, neither the critical radius $r_{p\text{I}c}$ for mode I nor the critical radius $r_{p\text{II}c}$ for mode II can be applied solely as the critical parameter to predict mixed-mode fractures well. In current work, a new parameter combining $r_{p\text{I}c}$ with $r_{p\text{II}c}$ has been proposed, and accordingly, the preexisting $R$-criterion has been improved. The improved $R$-criterion not only can predict crack initiation angle but also can predict the critical load, which is more significant in predicting material fractures. A series of fracture tests using the semicircular bend specimens with different mode mixities were conducted on polycarbonate (PCBA), and the test results were compared with the predictions of several criteria. This comparison shows that the test results agree well with the improved $R$-criterion. Finally, the advantage of using a combination of mode I and mode II fracture toughness in a criterion is analyzed.

Ship-generated waves and return currents are capable of resuspending significant quantities of bottom and bank sediments. However, most of the previous studies done on the subject do not show how and where sediment is resuspended by the wakes and the directions of net transport. In this paper, a three-dimensional (3D) numerical model based on hydrosedimentary coupling is presented to search the relationship between the sediment movement and the pattern of ship-generated waves around and far away from the vessel and the return currents around the ships. The hydrodynamic model is based on 3D Navier-Stokes equations, including the standard $k\text{-}\epsilon$ model for turbulence processes, and the sediment transport model is based on a 3D equation for the resuspended sediment transport. The computation results show that the areas of sediment concentration and transport (whether by resuspension or by the bedload) depend mainly on the position, the speed of the ship in the waterways, the kinematics of ship-generated waves, and the return flows. Thus, a map of sediment distribution and the modes of sediment transport generated by the passage of the ship are presented.

The equations of motion and corresponding boundary conditions for the vibration of a single-edge cracked RC beam strengthened with fiber-reinforced polymer (FRP) have been developed by applying the Hamilton principle, where the stress concentration near the crack is taken into account by introducing a crack disturbance function into the beam’s compatibility relations. The solution employs the Galerkin method. A parametric study is carried out to investigate the influence of the crack geometry parameter, in which the steel bar’s restraints, as well as FRP reinforcement on the dynamic behavior of the RC beam, are considered. It is shown that calculating the dynamic characteristics of a single-edge cracked RC beam strengthened with FRP must take into account the effect of the steel bar’s restraints and FRP reinforcement, simultaneously, whereas the crack geometry parameter has very little influence on the dynamic characteristics of the cracked beam. The crack position has little effect on the frequency of the RC beam and concrete beam.

Seismic isolation using multilayer elastomeric isolators has been used in the United States for more than 20 years. The isolators are constructed of many layers of elastomer (usually natural rubber) reinforced with steel plates, and they are very stiff in the vertical direction but soft in the horizontal direction, which enables them to carry the weight of a building but cause the building to have a fundamental natural frequency that is both lower than that of the same building if conventionally founded and the dominant frequencies of strong ground motion. They appear to be very stable, but the low shear stiffness causes a buckling phenomenon. However, it is straightforward to design them to have a large factor of safety against buckling when used. The study of the buckling under compression load is based on a linearly elastic theory and, although the elastomer is not really linearly elastic, the deformation is predominantly one of shear, and the typical elastomers used in bearings are very linear over a large range of strain. The linear theory, although approximate, is relatively accurate and is adequate for most design purposes. What is not known is the large deformation response of a bearing when buckling occurs. The question of the stability of the postbuckled state remains unresolved. In the analysis of dynamic response of structures on these isolators, it is also necessary to understand the interactions between horizontal stiffness and vertical load and between vertical stiffness and horizontal displacement and both the postbuckling compressive and tensile behaviors. All these effects can be derived by a simple two-spring model described in this paper.

This paper presents a numerical model for evaluating internal fracture and delamination at the interface of fire insulation and steel surface in structural members. A cohesive zone model in combination with contact condition is employed in a 3D finite-element model to simulate the fire-insulation damage throughout the loading range, from initial loading stage until failure through fracture. The numerical model is validated by comparing model predictions, namely internal fracture and interfacial delamination of insulation, against test data generated at both material and structural levels. The validated model was applied to quantify the effect of critical factors on the extent of delamination between steel and fire insulation. Results from the parametric studies indicate that critical fracture energy at steel–insulation interface, insulation thickness, modulus of elasticity, and internal cohesion of insulation material have significant influence on the spread of delamination at steel–insulation interface. Further, delamination of insulation from steel surface occurs mostly in the plastic hinge zone and specifically in the tensile flange.

A novel method to compute the bounds of the response of structures to dynamic loads, including earthquakes, is presented. This method, based on reachability analysis, deterministically predicts the sets of states an elastic structural system can reach under uncertain dynamic excitation starting from uncertain initial conditions, where deterministic uncertainty ranges describe uncertainties. Ellipsoidal approximations of these reachable sets for three canonical dynamic problems are presented to demonstrate the applicability of this method to single-degree-of-freedom (SDOF) systems. The principle of superposition is formulated as a concatenation of ellipsoidal reachable sets using their semigroup properties. Using this extension, computation of the external (worst-case) ellipsoidal approximation of reachable sets for a SDOF system under earthquake excitation is presented. Possible applications of this method for software validation and hybrid simulation are discussed.

A numerical formulation has been proposed for solving an axisymmetric stability problem in geomechanics with upper bound limit analysis, finite elements, and linear optimization. The Drucker-Prager yield criterion is linearized by simulating a sphere with a circumscribed truncated icosahedron. The analysis considers only the velocities and plastic multiplier rates, not the stresses, as the basic unknowns. The formulation is simple to implement, and it has been employed for finding the collapse loads of a circular footing placed over the surface of a cohesive-frictional material. The formulation can be used to solve any general axisymmetric geomechanics stability problem.

A new family of structure-dependent methods is presented. Although the numerical properties of this family method are similar to those of the previously published family method developed by Chang, their difference equations are essentially different. In fact, for the proposed family method, both the difference equations are structure dependent, whereas for the previously published family method, only the difference equation for the displacement increment is structure dependent. In general, the two family methods can have unconditional stability and second-order accuracy, and they both do not involve nonlinear iterations for nonlinear systems. However, some differences are found. In fact, the major differences are overshooting behaviors and implementation details, which are addressed. It is confirmed that the proposed family method is computationally more efficient than the previously published family method.