Journal of Engineering Mechanics

Although many numerical techniques such as approximate Riemann solvers can be used to analyze subcritical and supercritical flows modeled by hyperbolic-type shallow-water equations, there are some difficulties in practical applications due to the numerical unbalance between source and flux terms. In this study, a revised surface gradient method is proposed that balances source and flux terms. The new numerical model employs the MUSCL–Hancock scheme and the HLLC approximate Riemann solver. Several verifications are conducted, including analyses of transcritical steady-state flows, unsteady dam break flows on a wet and dry bed, and flows over an irregular bathymetry. The model consistently returns accurate and reasonable results comparable to those obtained through analytical methods and laboratory experiments. The revised surface gradient method may be a simple but robust numerical scheme appropriate for solving hyperbolic-type shallow-water equations over an irregular bathymetry.

A reliability-based structural control design approach is presented that optimizes a control system explicitly to minimize the probability of structural failure. Failure is interpreted as the system’s state trajectory exiting a safe region within a given time duration. This safe region is bounded by hyperplanes in the system state space, each of them corresponding to an important response quantity. An efficient approximation is discussed for the analytical evaluation of this probability, and for its optimization through feedback control. This analytical approximation facilitates theoretical discussions regarding the characteristics of reliability-optimal controllers. Versions of the controller design are described for the case using a nominal model of the system, as well as for the case with uncertain model parameters. For the latter case, knowledge about the relative plausibility of the different possible values of the uncertain parameters is quantified through the use of probability distributions on the uncertain parameter space. The influence of the excitation time duration on feedback control design is discussed and a probabilistic treatment of this time duration is suggested. The relationship to ${\mathcal{H}}_2$ (i.e., minimum variance) controller synthesis is also examined.

To understand and model damage generated during impact by a penetrator of ultrahigh strength concrete targets, edge-on impact tests are performed with Ductal concrete, which is unreinforced or reinforced with short fibers. Two edge-on impact configurations are designed with a dynamic confinement system. The first configuration uses aluminum projectiles and allows us to study the dynamic fragmentation that spreads out within the tile without any confined damage close to the impact point. The fragmentation process is composed of numerous oriented millimetric cracks. In the second configuration, steel projectiles are used with a higher impact velocity. Damaged zones are visualized by using an ultrahigh speed camera and a sarcophagus configuration designed to prevent the fragments from moving. Postmortem studies of impacted tiles enabled us to observe an intense fragmentation of the targets and confined damage close to the impact point when steel projectiles were used. Simulations are performed with an anisotropic damage model coupled with a concrete plasticity model. Orientation and crack density are compared with postmortem observations.

Exact analytical solutions, based on the Hamilton principle, are obtained for the response of supported partial ring segments subjected to concentrated loads. Loading may be applied in the lateral direction, perpendicular to the plane of the ring, or radially, in the plane of the ring. Results of a number of experimental tests are included. Very good agreement between theory and experiment was obtained. It is shown that the theoretical model is easy to apply. There are a number of industrial applications for this solution technique, some of which are discussed.

Accurate prediction of shear band formation in geomaterials is crucial in the solution of various stability problems in geotechnical engineering. The initiation of shear band is strongly dependent on the constitutive description of the prelocalization homogeneous deformation. Conventional plasticity models assume that coaxiality exists between the directions of principal stresses and the directions of plastic strain increments. Accumulating evidence has however shown that this assumption is not appropriate. In this paper, a noncoaxial constitutive modeling platform is presented in a general three-dimensional stress space. It is shown that the classical vertex-like structure, which has been widely adopted to describe the noncoaxial constitutive response, only represents the two-dimensional condition. Examples are presented to demonstrate the capability of the modeling platform in capturing the initiation and orientation of shear band in a granular soil. The significance of the noncoaxiality effects is illustrated by comparisons of the predictions produced by coaxial and noncoaxial (both two-dimensional and three-dimensional) plasticity models.

Temperature rise may lead to strength degradation and stiffness deterioration of structures under fire conditions. The purpose of this paper is to theoretically study the thermal effect on the postbuckling behavior of an elastic or elastoplastic two-member truss, based on large-deformation elasticity considerations. Two kinds of loadings are considered, i.e., trusses under constant temperature but increasing loads, and trusses under constant loads but rising temperature. For the case with constant temperature, the critical load of an elastic truss will be greatly reduced if the effect of yielding is taken into account. Moreover, yielding of material can cause the truss to bifurcate from the original elastic path. For the case with constant loads, a critical temperature that occurs as the limit point of the temperature–deflection curve can always be found. Besides, the presence of yielding can drastically reduce the critical temperature of an elastic truss, causing it to collapse in an abrupt manner. The solutions presented herein can be used as benchmarks for calibration of the accuracy of general finite-element procedures in analyzing structures under fire conditions.

Semidefinite programming (SDP) provides a convenient framework for the solution of optimization problems involving the eigenvalues of symmetric matrices. The classical Mohr–Coulomb yield criterion for an isotropic cohesive-frictional continuum is most naturally expressed in terms of principal stresses (eigenvalues of the symmetric stress tensor), while the associated flow rule and plastic dissipation function can both be expressed in terms of principal strains (eigenvalues of the symmetric strain tensor). This suggests that SDP could be suitable for performing limit analysis of three-dimensional (3D) structures obeying the Mohr–Coulomb criterion, where the yield and flow rule constraints are difficult to enforce using other methods of optimization. In this paper it is demonstrated that SDP can indeed be used to obtain both lower and upper bounds on the exact collapse load for a Mohr–Coulomb continuum in 3D, though a novel derivation is needed to arrive at an efficient SDP formulation of the upper bound in terms of kinematic quantities only. Two numerical examples are studied, using finite-element discretizations of the stress and displacement fields that preserve the strictness of the lower and upper bound solutions. The arising optimization problems are solved using the general-purpose SDP solver SeDuMi, with no attempt to modify or tailor the code for this specific application. Even so, 3D analyses of moderate size (several thousand tetrahedral elements) are handled with encouraging efficiency.

The results from experiments conducted in a $2\mathrm{m}$ high flow compartment at large Reynolds numbers are reported in this paper. Flow entered the compartment through an opening at the base on one side of the compartment and exited from an opening at the bottom of the opposite wall of the compartment. A shear layer is formed at the boundary between the incoming flow and the ambient fluid in the compartment. The impingement of the shear layer on the opposite wall of the compartment gives rise to periodic vortex formation and highly organized oscillations in the shear layer. When a density interface is present inside the compartment, resonance conditions were set up when the oscillations of the internal standing waves were “locked in” with the shear layer oscillations. Under resonance conditions, internal standing waves with amplitudes of up to $0.1\mathrm{m}$ were observed. The formation of the internal standing waves is linked to the shear layer oscillations. Resonance conditions result when the shear layer is oscillating close to the natural frequency of the stratified fluid system in the compartment. The results of this investigation are applicable for fresh water storage in floating bottom-opened tanks in the sea, where under resonance conditions, entrainment rates could be significantly increased.