Journal of Engineering Mechanics

Local delamination buckling formulas for laminated composite beams are derived based on the rigid, semirigid, and flexible joint models with respect to three bilayer beam (i.e., conventional composite, shear-deformable bilayer, and interface-deformable bilayer, respectively) theories. Two local delamination buckling modes (i.e., sublayer delamination buckling and symmetrical delamination buckling) are analyzed and their critical buckling loads based on the three joint models are obtained. A numerical finite-element simulation is carried out to validate the accuracy of the formulas, and parametric studies of delamination length ratio, the transverse shear effect, and the influence of interface compliance are conducted to demonstrate the improvement of the flexible joint model compared to the rigid and semirigid joint models. The explicit local delamination buckling solutions developed in this study facilitate the design analysis and optimization of laminated composite structures and provide simplified and improved practical design equations and guidelines for buckling analyses.

This paper reports the dynamic instability behavior of functionally graded (FG) shells subjected to in-plane periodic load and temperature field using a higher-order shear deformation theory in conjunction with the finite-element approach. Properties of FG materials are assumed to be temperature dependent and graded in the thickness direction according to the power-law distribution in terms of volume fraction of the constituents. Five forms of shells considered in this investigation are singly curved cylindrical, doubly curved spherical, and hyperbolic paraboloid having two principal curvatures, doubly curved hypar having twist curvature only, and doubly curved conoid having one curvature and twist curvature. The boundaries of dynamic instability regions are obtained using Bolotin’s approach. The structural system is considered to be undamped. The correctness of the formulation is established by comparing the writers’ results with those of problems available in the published literature. Effects of material composition and geometrical parameters are studied on the dynamic instability characteristics of the aforementioned five forms of shells having practical applications in many engineering disciplines.

The hybrid nonlocal Euler-Bernoulli beam model is applied for the bending, buckling, and vibration analyzes of micro/nanobeams. In the hybrid nonlocal model, the strain energy functional combines the local and nonlocal curvatures so as to ensure the presence of small length-scale parameters in the deflection expressions. Unlike Eringen’s nonlocal beam model that has only one small length-scale parameter, the hybrid nonlocal model has two independent small length-scale parameters, thereby allowing for a more flexible and accurate modeling of micro/nanobeamlike structures. The equations of motion of the hybrid nonlocal beam and the boundary conditions are derived using the principle of virtual work. These beam equations are solved analytically for the bending, buckling, and vibration responses. It will be shown herein that the hybrid nonlocal beam theory could overcome the paradoxes produced by Eringen’s nonlocal beam theory such as vanishing of the small length-scale effect in the deflection expression or the surprisingly stiffening effect against deflection for some classes of beam bending problems.

The influence of three loading paths on the collapse of loose sand is analyzed with a particular attention paid to the onset of collapse and the mode of failure exhibited. Experimental results on conventional undrained triaxial compression tests, constant shear drained tests, as well as quasi-constant shear undrained path are presented, compared, and analyzed. It is now recognized that some collapses can occur before the Mohr-Coulomb plastic limit criterion is reached, and our recent results obtained with the new arrangement built up highlight that these collapses occur under a diffuse mode of failure. An extensive experimental series of tests shows that the first negative value of the second-order work computed using experimental data corresponds to the loss of controllability. Moreover, it is shown that the stress ratios at collapse and the corresponding mobilized angles of friction are very close for all types of tests. For similar void ratios, the onset of collapse is thus largely independent of the loading path under drained and undrained conditions but depends on a stress state to bring the material inside the unstable domain and also on the current direction of the stress increment. Indeed, it appears that the orientations of the stress increments at collapse for all tests are the same, what explains, according to the second-order work criterion, that collapse occurs at the same stress ratio. A potentially unstable domain, depending on the stress increment direction, can thus be defined.

The paper presents micromechanical formulations of stress dilatancy and their connection to a flow rule in classical elastoplasticity. Dilatancy is inarguably the manifestation of an internal kinematic constraint involving both particle shape and connectivity (texture or fabric) with operative interparticle friction against applied stresses. However, this notion of microstructural dependence is nonexistent in most stress-dilatancy formulations in the literature. We present two different micromechanical approaches that arrive at stress-dilatancy expressions with embedded micromechanical information in the form of a second-order fabric tensor. In connection to stress dilatancy, the underlying nature of the flow rule is next discussed with respect to the dependence of the plastic strain increment vector on the direction of loading (stress increment). It is demonstrated analytically that the flow rule is singular in three-dimensional stress and strain conditions. Finally, the dependencies of dilatancy on fabric are illustrated through various numerical simulations using the micromechanically enriched stress-dilatancy models and a discrete element method.

An explicit pseudodynamic algorithm with an improved stability property is proposed herein. This algorithm is shown to be unconditionally stable for any linear elastic systems and any instantaneous stiffness softening systems. The most attracting stability property is that it can have unconditional stability for the instantaneous hardening systems with the instantaneous degree of nonlinearity less than or equal to 2. This property has never been found among the currently available explicit algorithms. Hence, it may be applied to perform a general pseudodynamic test without considering the stability problem since it is rare for a civil engineering structure whose instantaneous degree of nonlinearity is greater than 2. This explicit algorithm can be implemented as a common explicit pseudodynamic algorithm, such as the use of the Newmark explicit method, since it does not involve any iteration procedure. In addition, it possesses comparable accuracy as that of a general second-order accurate integration method such as the Newmark explicit method. Both numerical and error propagation properties are analytically studied and numerical experiments are used to confirm these properties. Actual pseudodynamic tests attested to the feasibility of this proposed explicit pseudodynamic algorithm.

Mesoscale homogenization provides a computationally efficient way of capturing some degree of local variation in the behavior of a composite microstructure. In this work, techniques are explored in which the local two-phase microstructure is homogenized using the moving-window generalized method of cells (GMC) technique. Both elastic and plastic material behavior is investigated using GMC-generated anisotropic stress-strain curves. An optimization procedure is used to define Hill’s yield criterion parameters which best fit the GMC-generated data. Two perfectly plastic models are developed based on the GMC results; these are called the subcell initial yield model and the matrix average yield model. A technique is also developed which incorporates hardening behavior. Different windowing techniques are investigated: an overlapping windowing technique which requires more computational time, and a nonoverlapping technique which requires less computational time. It is found that the matrix average model using small nonoverlapping windows is the best technique in the cases studied, combining accuracy and computational efficiency.

This paper presents a new Boussinesq-type model equations for describing nonlinear surface wave motions in porous media. The mathematical model based on perturbation approach reported by Hsiao et al. is derived. The drag force and turbulence effect suggested by Sollitt and Cross are incorporated for observing the flow behaviors within porous media. Additionally, the approach of Chen for eliminating the depth-dependent terms in the momentum equations is also adopted. The model capability on an applicable water depth range is satisfactorily validated against the linear wave theory. The nonlinear properties of model equations are numerically confirmed by the weakly nonlinear theory of Liu and Wen. Numerical experiments of regular waves propagating in porous media over an impermeable submerged breakwater are performed and the nonlinear behaviors of wave energy transfer between different harmonics are also examined.

This paper addresses the use of complex frequencies in problems of wave propagation and structural vibrations. The most common form of application is as artificial damping that is extracted after the response in the time domain has been obtained. Then again a rather unorthodox application is in the simulation of systems of infinite spatial extent by means of finite systems modeled with discrete methods such as finite elements, a task that can be accomplished even when no transmitting or absorbing boundaries are used. This latter application of complex frequencies, which goes by the name damping-solvent extraction method or its acronym DSE, is assessed herein by means of exact solutions to canonical problems that are used to establish the conditions that must be met by the finite models to work as intended, especially the size of the models, the magnitude of the imaginary component of frequency, and the limitations of the method.

A finite-element procedure was used to simulate the dynamic behavior of four full-scale reinforced soil retaining walls subjected to earthquake loading. The experiments were conducted at a maximum horizontal acceleration of over 0.8 g, with two walls subjected to only horizontal accelerations and two other walls under simultaneous horizontal and vertical accelerations. The analyzes were conducted using advanced soil and geosynthetic models that were capable of simulating behavior under both monotonic and cyclic loadings. The soil behavior was modeled using a unified general plasticity model, which was developed based on the critical state concept and that considered the stress level effects over a wide range of densities using a single set of parameters. The geosynthetic model was based on the bounding surface concept and it considered the S-shape load-strain behavior of polymeric geogrids. In this paper, the calibrations of the models and details of finite-element analysis are presented. The time response of horizontal and vertical accelerations obtained from the analyses, as well as wall deformations and tensile force in geogrids, were compared with the experimental results. The comparisons showed that the finite-element results rendered satisfactory agreement with the shake table test results.

A decentralized control method with improved robustness and design flexibility is proposed for reducing vibrations of seismically excited building structures. In a previous study, a control scheme was developed for multistory building models using nonlinear, decentralized control theory. This control method has now been improved in this study in that less information about material properties and geometrical parameters of the building is needed and the selection of control design parameters is more flexible. The nonlinear behavior of the proposed control system is studied and its stability property is proven mathematically. To evaluate the effectiveness and robustness of the proposed method, three illustrative structural models, i.e., an eight-story elastic shear beam model, a two-story nonlinear elastic shear beam model, and a 20-story elastic benchmark model are studied. The 1940 El Centro and the 1995 Kobe earthquakes are used in these examples. The performance of the current control design, as applied to these examples, has shown to be more effective in reducing structural responses and improving robustness.

In this work, closed-form expressions for the buckling loads of a weakened column with different boundary conditions are presented. The cracked-column model is based on the well-known method consisting of dividing the column into two segments connected by a rotational linear spring whose flexibility is related to the crack size and the geometry of the cross section. For the formulation of closed-form expressions, the perturbation method is used and the results are compared with those found by directly solving the eigenvalue problem.

The Sandler and Rubin cap model is the most popular cap model that is able to take account on geomaterial dilation and compaction effects. However, its nonsmooth yielding surface often results in a slow convergent rate or even nonconvergent solution in some numerical simulations. More often, analysts with the Sandler and Rubin model have to switch to a smooth cap model, for example, the Pelessone model, in order to obtain a convergent solution. For cases of original experimental data available direct fitting is the best way for obtaining the required smooth model parameters. For cases of only derived nonsmooth model parameters available, a transformation from nonsmooth models to smooth models is necessary. However, such a transformation is nontrivial. In this paper, we propose two simple and robust methods for transferring the Sandler and Rubin nonsmooth model to the Pelessone smooth model through making a few reasonable assumptions and solving only one nonlinear equation for one primary unknown. Two model examples are presented to demonstrate the good performance of our proposed methods.