Journal of Engineering Mechanics

This paper presents a global-local (GL) method to simulate the interaction of ultrasonic guided waves with structural defects in isotropic and multilayered composite platelike structures. The GL method uses a full finite-element (FE) discretization of the defected region to properly represent wave diffraction phenomena and a suitable set of wave functions to simulate regions away from the joint. Displacement and stress continuity conditions are imposed at the boundary between the global and the local regions. The radiated wave field can be then calculated by using standard techniques (least-squares method). The novelty of the proposed approach over previous GL techniques is the use of semianalytical FE (SAFE) modeling for the “global” simulation. The SAFE method, which only requires the discretization of the waveguide’s cross section, allows handling complex structures (multilayered composites, arbitrary cross sections, etc.) in a computationally efficient manner. Applications of the GL method to damage quantification will be shown for the cases of notches in aluminum plates and delaminationlike defects in aircraft composite panels.

This paper presents the derivation of a mechanical model to estimate the effects of damage on the response of ropes. Damage can be represented through a degradation of the properties of individual rope elements, and it can also include the complete rupture of one or more elements. The general assumptions made to estimate the length over which damage propagates along the length of a rope and how this length is considered in modeling damaged rope behavior are explained. Consistent with tests on damaged polyester (PET) mooring ropes, numerical simulations demonstrate the existence of strain localization around the failure region and, due to degradation of rope element properties, damage localization as well. This damage localization causes the premature failure of rope elements, reducing the maximum load capacity and maximum failure strain that a damaged rope is capable of resisting relative to that of an intact rope. The proposed model suggests that some of the variables that affect damaged rope behavior are the degree of damage present at a given cross-section, the location of broken rope elements, and the length over which damage propagates along the rope length. Experimental data are used to validate the model.

This paper presents a nonlinear thermal buckling analysis of circular shallow pin-ended arches that are subjected to a linear temperature gradient field in the plane of curvature of the arch. The linear temperature gradient produces axial expansion and curvature changes in the arch. The bending action produced by the curvature change and the axial compressive action produced by the restrained axial expansion may lead the arch to buckle suddenly in the plane of its curvature. The end reactions resulting from the restrained axial expansion also produce bending actions that are opposite to that produced by the temperature differential and tend to produce deflections on the convex side of the arch. A geometrically nonlinear analysis for thermoelastic buckling has been carried out based on a virtual work technique, and analytical solutions for the critical temperature gradients for the in-plane limit instability and bifurcation buckling are obtained. It is found that antisymmetric bifurcation is the dominant buckling mode for most shallow arches that are subjected to a linear temperature gradient. The limit instability is possible only for slender and shallow arches. It is also found that a characteristic value of the arch geometric parameter exists and that arches whose geometric parameter is less than this characteristic value show no typical buckling behavior. The formula for this characteristic value of the arch geometric parameter is derived.

The increased deformation and shear fragilities of corroding RC bridge columns subject to seismic excitations are modeled as functions of time using fragility increment functions. These functions can be applied to various environmental and material conditions by means of controlling parameters that correspond to the specific condition. For each mode of failure, the fragility of a deteriorated column at any given time is obtained by simply multiplying the initial fragility of the pristine/nondeteriorated column by the corresponding function developed in this paper. The developed increment functions account for the effects of the time-dependent uncertainties that are present in the corrosion model as well as in the structural capacity models. The proposed formulation is a useful tool for engineering practice because the fragility of deteriorated columns is obtained without any extra reliability analysis once the fragility of the pristine column is known. The fragility increment functions are expressed as functions of time $t$ and a given deformation or shear demand. Unknown parameters involved in the models are estimated using a Bayesian updating framework. A model selection is conducted during the assessment of the unknown parameters using the Akaike information criterion and the Bayesian information criterion. For the estimation of the parameters, a set of data are obtained by first-order reliability method analysis using existing probabilistic capacity models for corroding RC bridge columns. Example fragilities of a deteriorated bridge column typical of current California’s practice are presented to demonstrate the developed methodology. The increment functions suggested in this paper can be used to assess the time-variant fragility for application to life cycle cost analysis and risk analysis.

Previous research has shown many advantages of the mixed Lagrangian formulation (MLF) for the solution of dynamic problems. In particular, it has shown a very stable and robust behavior with respect to the time step size required for convergence, even in cases where plasticity and fracture were considered. This paper presents another step toward enabling the prediction of progressive collapse of structures using MLF. A new gap element is added to the framework by formulating an additional component in the Lagrangian function. It is shown that by carefully formulating the new component, the optimization problem to be solved in each time step of the MLF algorithm retains its form which is quadratic in the cases considered. Hence, a unified formulation is attained for all stages of the analysis whether contact forces are present or not. After presenting details of the formulation, the proposed method is used for the solution of two examples. These examples illustrate that relatively large time steps can be considered even for contact problems. Furthermore, the reasons for this capability of the algorithm are discussed in the paper.

In this paper, we study the progressive collapse of three-dimensional framed structures made of reinforced concrete after the sudden loss of a column. The structures are represented by elastoplastic Euler-Bernoulli beams with elongation-rotation failure threshold. We performed simulations using the discrete element method considering inelastic collisions between the structural elements. The results show what collapse initiation and impact-driven propagation mechanisms are activated in structures with different geometric and mechanical features. Namely, we investigate the influence of the cross sectional size and reinforcement $\alpha$ and of the plastic capacity $\beta$ of the structural elements. We also study the final collapse extent and the fragment size distribution and their relation to $\alpha$ , $\beta$ , and to the observed collapse mechanisms. Finally, we compare the damage response of structures with symmetric and asymmetric reinforcement in the beams.

The nonlinear behavior of masonry arches strengthened with externally bonded composite materials is investigated. A finite-element (FE) formulation that is specially tailored for the nonlinear analysis of the strengthened arch is developed. The FE formulation takes into account material nonlinearity of the masonry construction and high-order kinematic relations for the layered element. Implementation of the above concept in the FE framework reduces the general problem to a one-dimensional nonlinear formulation in polar coordinates with a closed-form representation of the elemental Jacobian matrix (tangent stiffness). A numerical study that examines the capabilities of the model and highlights various aspects of the nonlinear behavior of the strengthened masonry arch is presented. Emphasis is placed on the unique effects near irregular points and the nonlinear evolution of these effects through the loading process. A comparison with experimental results and a discussion of the correlating aspects and the ones that designate needs of further study are also presented.

A truss-based simulation of reinforced concrete columns under compression is presented in this study. The concrete truss elements are modeled based on advanced constitutive equations that take into consideration confinement dependent hardening followed by softening. The computational advantages, as well as the challenges of this approach, are discussed. The effects of confining steel content and spacing on the failure mechanisms of concrete columns under compression are examined using a parametric analysis. This analysis verifies the well-established trends that strength and ductility increase with increasing transverse steel content and decreasing tie spacing. It is also found that improvements on strength and ductility have limits. Finally, it is found that the amount and spacing of transverse reinforcement influences the type of failure, which can be one of shear or concrete crushing.

A family of interaction expressions are developed for steel elliptical hollow sections (EHSs) subjected to combinations of axial force, biaxial bending moments, torsion, and bimoments. The formulation is based on kinematically admissible strain fields within the context of the upper bound theorem of plasticity. The interaction relations derived successfully capture the effect of confining radial strains present at welded end sections, as well as sections that are free to deform in the radial direction away from end welded sections. The interaction expressions developed consist of a set of elliptical integrals which are cast in a dimensionless form applicable for EHS of general geometries. An iterative solution technique is developed to solve the resulting nonlinear relations. The applicability of the resulting interaction relations for conducting the cross-sectional check is illustrated through examples. A comparison with shell finite-element analysis results illustrates the validity of the interaction relations derived.

An experimental investigation on the axial load capacity of fixed-end pretwisted steel bars of rectangular solid cross sections is described in this paper. The fixed-end bar test conducted in this study includes bars with both ends griped and embedded in cylindrical slips. More than 200 specimens are considered in this study containing bars with four different cross sections, widths of 20 mm or 30 mm and thicknesses of 3 mm or 6 mm, and three different lengths of 300, 400, and 500 mm. The samples are twisted beyond their elastic limit using torque machine and then subjected to axial load using a compression MTS machine. A set of twisting angles ranges between 0 and 225° is considered for each length. Three samples are tested for each angle then the average of the results is calculated. It is proven experimentally that the permanent twists have influenced the axial strength and the static performance of the pretwisted bars. This improvement is supported by the considerable increase in the critical buckling loads of the bars for certain angles of twists. Multiple regression analysis (MRA) is also conducted using the experimental results to develop mathematical models capable of predicting the critical loads of the tested bars. Results indicate that, with a minimal processing of data, MRA could predict well the critical loads of the pretwisted bars within 99% confidence interval.

In computational mechanics, strain softening generates ill-posed boundary value problems, which cannot be solved without being regularized, e.g., through the introduction of an internal length scale. This paper investigates how the internal length scale that is introduced by regularization may interact with the external length scale arising from boundary conditions in the particular case of a strain-softening bar of varying cross section and a nonlocal averaging regularization. The interaction of internal and external length scales is examined using an analytical closed-form solution for overnonlocal softening plasticity that derives from a Fredholm equation of the second kind. In the absence of external length (bars of constant section), the analysis shows that the overnonlocal averaging confines and smoothly distributes plastic strain into a localized band. The localization width, plastic strain distribution inside the band, and load-displacement response are controlled by the internal length of the averaging function and the overnonlocal weighting factor. In the presence of external length (bar of varying section), the analytical solution shows that the localization width is controlled by the interaction of external and internal length scales. This interaction is significant when the external and internal lengths are of comparable magnitude, and decreases when the external length becomes large compared to the internal length. The bandwidth is found to depend on the internal and external lengths and stress level while strain localizes, and to relate only to the internal length when the bar collapses.

The analysis of microheterogeneous materials exhibiting eigenstressed and/or eigenstrained phases requires an estimation of eigenstrain influence tensors. Within the framework of continuum micromechanics, we here derive these tensors from extended Eshelby-Laws matrix-inclusion problems, considering, as a new feature, an auxiliary matrix eigenstress. The auxiliary matrix eigenstress is a function of all phase eigenstresses and, hence, accounts for eigenstress interaction. If all material phases are associated with one and the same Hill tensor, the proposed method degenerates to the well-accepted transformation field analysis. Hence, the proposed concept can be interpreted as an extension of the transformation field analysis toward consideration of arbitrarily many Hill tensors, i.e., as an extension toward heterogeneous elastic media comprising inclusion phases with an arbitrary ellipsoidal shape and with arbitrary spatial orientation. This is of particular interest when studying heterogeneous media consisting of constituents with nonspherical phase shapes, e.g., cement-based materials including concrete, or bone. As for polycrystals studied by means of the self-consistent scheme, the auxiliary matrix eigenstress turns out to be equal to the eigenstresses homogenized over the representative volume element (RVE), which is analogous to the self-consistent assumption that the auxiliary stiffness is the average stiffness of the RVE. The proposed method opens the door for micromechanics-based modeling of a great variety of composite phase behaviors characterized by eigenstresses or eigenstrains, e.g., thermoelasticity, poroelasticity, drying-shrinkage, as well as general forms of inelastic behavior, damage, fatigue, and fracture.

This paper presents an investigation on the dynamic instability of cantilevered nanorods/nanotubes subjected to an end follower force. Eringen’s nonlocal elasticity theory is employed to allow for the small length scale effect in the considered dynamic instability problem. The general solution for the governing differential equation is obtained and the dynamic instability characteristic equation is derived by applying the boundary conditions. Exact critical load factors are obtained. These nonlocal solutions are compared with the classical local solutions to assess the sensitivity of the small length scale effect on the critical load factors and flutter mode shapes. It is found that the small length scale effect decreases the critical load and the corresponding frequency parameters as well as reduces the severity of the double-curvature flutter mode shape.

Linear consolidation analyses are usually treated either by means of Terzaghi-Rendulic uncoupled theory or Biot’s consolidation theory. In this note, the problem of consolidation displacements around an axially loaded sphere was considered. It is demonstrated that both the uncoupled analysis and the coupled analysis give the same governing equation for pore fluid pressure dissipation with time. A simplified procedure for deriving transient strain components is illustrated. A general solution for time-dependent displacements is obtained using uncoupled consolidation analysis. Close agreement is evident between the new approximate uncoupled analysis solution and the existing coupled analysis solution with a maximum error of less than 0.5%.