Journal of Engineering Mechanics

A plasticity model using a strain‐rate formulation is presented to describe the uniaxial response of concrete when subjected to combined thermal and mechanical actions. The total strain rate is resolved into three individual components: mechanical strain, thermal strain, and transient creep strain. Each component is formulated individually. The mechanical strain rate is assumed to consist of an elastic strain rate and a plastic strain rate, which itself is taken as temperature‐dependent. In describing the plastic strain rate, the nonlinear part of the uniaxial stress‐strain curves is assumed to be a quarter of ellipse, defined for a given temperature in the range 20°C–800°C. The model was first used to analyze uniaxial (experimental) data under variable load but isothermal conditions, and then to investigate the effect of a sustained load on the deformational response of a concrete specimen under heating. Thirdly, a set of experimental relaxation tests was studied, in which temperature and stress vary continuously under a zero total strain condition. Here, the importance of a variable temperature and stress, and the significance of the history, is demonstrated.

The paper presents the numerical prediction of turbulent wind pressures on the surfaces of L‐shaped buildings (either in plan view or in cross section) for different wind directions. The computer program developed for this purpose solves the time‐averaged Navier‐Stokes equations by using the $k‐\epsilon$ turbulence model for closure. A zonal treatment methodology has been applied for the formulation of boundary conditions of turbulence properties ($k$ and $\epsilon$). The computational procedure is applicable to any arbitrarily shaped building composed of two rectangular blocks and wind blowing from any direction. A nonuniform grid‐generation routine applicable to these building configurations was developed. Naturally, only mean values of wind‐induced pressures on the building envelope can be evaluated by the present numerical approach. Computed pressures have been compared with experimentally obtained values for a stepped‐roof building (L‐shaped in cross section). Good agreement is found for normal wind directions, and differences exist in oblique wind cases.

The dynamic stability behavior of a single‐degree‐of‐freedom system with piecewise linear stiffness is considered. The analytical expression representing the divergence of perturbed trajectories is derived. The mechanism triggering dynamic instability of trajectories and the cause of chaotic behavior are then studied. Liapunov exponents are used as a quantitative measure of system stability. Numerical results including bifurcation diagrams and largest Liapunov exponents of a system with symmetric bilinear stiffness are presented. Several different types of bifurcation and nonlinear phenomena are identified, including pitchfork, fold, flip, boundary crisis, and intermittency of type 3. To illustrate the initial‐condition dependent nature of the problem, basins of attraction of multiple steady‐state responses are determined on the phase plane using the simple cell mapping method.

A theory for flow in a saturated compressible porous medium is developed to simulate the solid‐liquid separation operations known as expression in practice. A mathematical model that consists of the mass‐conservation equation, quasistate equilibrium equation, stress‐strain relation for an elastic matrix, and a variable total stress expression was employed to obtain numerical solutions for pore pressure and compaction variations due to time‐dependent and constant displacement conditions at the upper boundary of saturated porous columns. Results were obtained for five problems of practical importance. Cases studied include the compression of a porous column with a specified time‐dependent displacement of the upper boundary, compression with instantaneous displacement of the pervious upper boundary of a saturated porous column, compression with time‐dependent displacement at the impervious upper boundary, compaction with an upper boundary moving at a constant velocity, and dynamic compression of a saturated porous column with variable permeability and porosity. The effects of piston (upper boundary) and membrane (lower boundary) resistances on pore pressure variation and compaction distribution have been investigated, and the implications of constant porosity and permeability assumptions were demonstrated. It was shown that lower and upper boundary resistance factors have critical influence on the operation.

This paper investigates the free vibration of thick sector plates with different supporting edge conditions. The Rayleigh‐Ritz procedure is used in the energy functional, which includes the effect of shear deformation and rotatory inertia in deriving the governing eigenvalue equation. Sets of mathematically complete two‐dimensional polynomials (P‐2) are used as the admissible displacement and rotational functions. A basic function (B) is introduced to satisfy the prescribed free, simply supported and clamped supporting edge conditions. This resulting PB‐2 Rayleigh‐Ritz method is applied to obtain solutions for thick sector plates of different radii (cutout ratios), sector angles, relative thickness ratios and with various end conditions along the radial and circumferential edges. The present results, wherever possible, are compared with existing published values from the open literature.

A vertical porous wave maker sitting in an infinitely long channel of constant depth is studied. The wave maker performs horizontal oscillatory motion. A simplified analytical approach for thin porous wave maker and an approach of boundary integral method valid for a porous‐wave maker of any thickness are presented in this study. The fundamental assumption for an analytical approach of a thin porous wave maker is that the vertical velocity profiles are identical throughout the porous wave maker. The validity of the assumption for the thin porous‐wave‐maker approach is verified by the numerical solution of the boundary integral method. However, the numerical solution also shows very different results between thin and thick porous wave makers. The effect of inertial reactance on a porous medium compared with viscous resistance is also discussed in this study. When the flow‐efficiency parameter R defined in this study is greater than or equal to O(1), the inertial reactance can no longer be ignored as previous investigations did.

An explicit time‐domain transmitting boundary is presented for far‐field modeling in the three‐dimensional (3D) analysis of dam‐reservoir interactions. This transmitting boundary is a semianalytical solution of the governing wave equation of the far field with the assumption that the ground motion is uniform along the upstream direction. By using this transmitting boundary, radiation condition and water compressibility can readily be incorporated in the analysis. Therefore, the finite‐element method (FEM) can be used to accurately analyze a dam‐reservoir system while maintaining its efficiency in time‐domain analysis. The transmitting boundary includes vertical and cross‐stream ground motions in the far field. Hence, the near field size can be as small as geometry and nonlinearity allow. This transmitting boundary is more efficient that the implicit one presented by Tsai and Lee in 1990, also because only a few eigenmodes are employed. Numerical results have excellent agreement with the analytical solutions available.

A spatially semidiscrete finite‐element technique is developed for the linear analysis of wave propagation in layered, fluid‐filled poroelastic media. The wave motion is expressed as a combination of modes that are discrete in the vertical direction but continuous in any horizontal direction. Algebraic eigenvalue problems are derived for the wave numbers and shapes of these modes. Plane‐strain and antiplane‐shear motions are considered, while arbitrary motions in axisymmetric regions are expanded in Fourier series with respect to the azimuthal coordinate. Consistent transmitting boundaries are constructed for both plane and axisymmetric regions. In problems of dynamics of foundations, these boundaries provide an accurate and convenient representation of the far field and can be coupled directly with conventional finite elements modeling the near field. In the companion paper, results of an application of the present technique to the calculation of the dynamic stiffness of rigid strip and circular foundations are reported and analyzed.

The finite‐element technique presented in the companion paper is applied to the calculation of the static and dynamic stiffnesses of rigid strip and circular foundations on a fluid‐filled poroelastic stratum. A simplified approximate method is also proposed for the estimation of the dynamic stiffnesses. In this approximation, the two‐phase medium is replaced by a single‐phase solid. The shear‐wave velocity of the equivalent solid is set equal to that of the solid skeleton. In the case of vertical excitation, the pressure‐wave velocity is taken equal to the velocity of the slow dilatational wave of the mixture, while the average of the velocities of the fast and slow dilatational waves of the mixture is used in the cases of horizontal excitation and rocking. Stiffness and damping coefficients are computed and compared with those obtained by the approximate method. The effects of seepage forces on the dynamic stiffnesses are examined.

A general boundary‐element formulation is presented for the prediction of the dynamic response of fluids with viscoelastic behavior. The fluid is modeled by a generalized constitutive relation that contains either complex‐valued parameters and complex‐order derivatives or real‐valued parameters and fractional‐order derivatives. These models are consistent with basic theories and are not arbitrary constructions. The models are valid for linear viscoelastic fluid behavior and are limited to fluid motions with infinitesimally small displacement gradients. The governing equations are transformed into the Laplace domain and the infinite space fundamental solution is derived. The resulting integral equations are then solved by numerical procedures. The method is applied in the prediction of the dynamic mechanical properties of a viscous damper containing a viscoelastic fluid in the form of silicon gel. The fluid is modeled by a fractional derivative Maxwell model. The predicted mechanical properties of the device are found to be in excellent agreement with experimental results.

A finite element formulation combined with stochastic linearization and normal mode methods developed earlier for the study of geometrically non‐linear random vibration responses of beam and frame structures subjected to simultaneously spatial and temporal Gaussian stationary nonwhite and nonzero mean random excitations is now extended to treat the plate and shell structures in the same fashion. Examples include dynamic random responses of simply supported square plate, cylindrical panel with all edges supported by rigid diaphragms, clamped spherical cap, and double‐curved square panel under different random loadings. To validate the present formulation and solutions, results are compared with alternative analytical solutions whenever available. The Monte Carlo simulation method is also used to generate solutions to compare with some of the present results when alternative solutions are not available.

The recently developed turbulence model, which provides a rate‐dependent algebraic expression for the Reynolds stress tensor, is briefly reviewed. The modified TEACH code, which incorporates the new rate‐dependent model, is described. The turbulent flow fields in a two‐stream mixing layer is predicted and the results are compared with the available experimental data and those obtained from the earlier model and discussed. It is shown that the new model is in reasonable agreement with the experimental data and is somewhat superior to the earlier $k‐\epsilon$ and algebraic stress models.