Journal of Engineering Mechanics

A study is made of the effect of strain rate on the strength of St 52‐3N mild steel, commonly used as deck plating in offshore structures. Stress‐strain curves are obtained in both tension and torsional shear at room temperature at strain rates from ${10}^{-4}{s}^{-1}$ to ${10}^3{s}^{-1}$ and compared with previous work on mild steel. The tensile data show that the lower yield stress is approximately twice as strain rate sensitive as stresses in the hardening region and that the ultimate tensile strain is approximately unaffected by strain rate effects up to a strain rate of $20s^{-1}\text{.}$ The torsion data extends to large strains (300%) and shows adiabatic thermal softening at the higher strain rates. The tension and torsion data show that the von Mises yield criterion overestimates the flow stress in pure shear. The material data have been used in determining the penetration resistance of deck structure to dropped objects such as drill collars and it has been found that strain rate effects are of minor importance for the structural response and can be neglected in design.

Discrete cracks have been modeled with interface elements in which the tractions are related to the relative displacements of the crack sides. Three stages in the cracking process can be distinguished: (1) The linear‐elastic state; (2) the development state in which a tension‐softening model is used; and (3) the open‐crack state. For the open‐crack state five different crack‐dilatancy models have been implemented. Explicit relations have been derived for the tangential stiffness matrices of these models. The tangential stiffness relations turn out to be nonsymmetrical; this has major consequences for the stability of the discretized mechanical system. The stability has been analyzed via eigenvalue analyses of the tangential‐stiffness matrix. Here, marked differences appear between the various models. This observation may have broad implications for the convergence behavior of assemblies of continuous and discrete elements in which these material models are utilized.

Discrete cracks have been modeled with interface elements in which the tractions are related to the relative displacements of the crack sides. Three stages in the cracking process can be distinguished: (1) The linear‐elastic state; (2) the development state in which a tension‐softening model is used; and (3) the open‐crack state, for which five different crack‐dilatancy models have been implemented. The predictions of these crack‐dilatancy models have been compared mutually as well as with available experimental data. The discrete‐crack elements have subsequently been used in an analysis of an experiment on crack dilatancy. Again, the results for the various crack‐dilatancy models are compared. Finally, a nonlinear analysis of a moderately deep shear‐critical beam is presented including aggregate‐interlock effects.

The free‐vibration analysis of a column‐supported cooling tower with ring stiffeners has been undertaken using the finite element method. The tower has been modeled using anisoparametric quadrilateral shell of revolution element, and the rings and columns have been modeled using an isoparametric three‐dimensional curved beam element. The kinematic assumptions used in these elements to describe the displacement field correspond to the recently proposed high‐order shear deformation theories. Numerical results illustrate the advantages of providing the stiffening rings on the vibrational response of the cooling tower. These numerial results reveal that the provision of ring stiffeners significantly alters the modal characteristics of the higher modes with circumferential waves greater than 3. Also, it is concluded that under seismic excitation of the cooling tower the stiffening rings may not help increase the resistance of the structure because these rings have no influence on the modal characteristics of structures under such excitations and whereas the stiffening rings help increase the load‐carrying capacity of towers under wind excitations.

The analysis of axisymmetric circular tank foundations has been made in the past using the classical Winkler model, where the properties of the elastic foundation are modeled by one parameter, k, called modulus of subgrade reaction. Even though many recommendations have been made for the value of k, the model yields erroneous results, because the value of k depends on the depth of the soil stratum with respect to the size of the slab as well as to the distribution of the loading. Also, the elastic properties of the soil can vary within the soil stratum. Assuming that the elastic properties of the soil stratum are constant or linearly varying in the vertical direction, and that the stratum rests on a rigid surface, a simple, more accurate mathematical model is developed here. Two parameters are used to represent the elastic foundation, and an iterative technique is introduced to obtain a consistent energy solution. The finite difference method is employed to get the solutions. The loading can be either uniform or axisymmetric lateral pressure, axisymmetric live load, or moments at the edge. The slab or plate at the bottom of the tank should be flexible enough to satisfy the assumptions of the linear plate theory. The results of an example tank problem with different types of loadings are compared with more exact finite element solutions.

A finite element model is developed for the numerical simulation of the start‐up of a deep‐well wet oxidation reactor using steam. The model is capable of handling different cases of start‐up, using saturated steam of arbitrary quality including hot water. The transient temperature field in the well‐earth system is studied. The governing equation for the earth is the conductive heat equation. For the reactor, the analysis involves solving the energy balance equations describing the convective and intertube heat transfer, mass balance equations, and thermodynamic relations for the fluid in the tubes. The equations for the reactor and the earth are coupled by the continuity of the temperature and heat flux at the interface between them. A Galerkin finite element formulation is used for the spatial discretization of the heat equation in the earth; a Petrov‐Galerkin finite element formulation is employed for the energy balance equations in the reactor tubes. The resulting set of ordinary differential equations is discretized in time and solved by a predictor‐multicorrector algorithm. The model is tested on a typical deep‐well reactor to study its start‐up dynamics. The results can be used to estimate the start‐up time and the amount of steam or water required to obtain the necessary initiation temperature for the process.

In the variationally coupled finite element‐boundary element method, the terms involving tractions on the interface are eliminated. A single variational principle is obtained for both the finite element and boundary element subdomains. However, the domain integrals that appear in this principle involve the singular fundamental solution. A new technique is proposed wherein these singular domain integrals are transformed to boundary integrals. Numerical examples show that the present method improves the accuracy of the results remarkably and decreases computation time compared with the domain integral method. In the “coupled patch test,” consisting of a constant strain field in an arbitrarily skewed patch of zones, the maximum errors for the variationally coupled method is 0.03%, whereas in the stiffness coupling and traction‐matching coupling methods, the maximum errors are 16% and 5%, respectively. Excellent results are also obtained for the variationally coupled solution of single‐edged notched specimens.

Two aseismic hybrid control systems are proposed for protecting building structures against strong earthquakes. The hybrid control system consists of a base‐isolation system connected to either a passive or active mass damper. The base‐isolation system, such as elastomeric bearings, is used to decouple horizontal ground motions from the building; whereas the mass damper, either active or passive, is used to protect the safety and integrity of the base‐isolation system. The performance of the proposed hybrid control systems is investigated, evaluated, and compared with that of an active control system. It is shown from the theoretical/numerical results that the proposed hybrid control systems are very effective in reducing the response of tall buildings under strong earthquakes. Likewise, the practical implementation of such hybrid control systems is easier than that of an active control system alone.

The influence of the location of the downstream boundary on unsteady incompressible flow solutions is investigated in a series of numerical experiments performed for flow past a circular cylinder at Reynolds number 100. The governing equations are the velocity‐pressure formulation of the Navier‐Stokes equations, and at the downstream boundary the traction‐free condition is imposed. Temporally periodic flow fields obtained by using computational domains with various lengths are compared. It is observed that as far as the near‐field solution, the Strouhal number, and the lift and drag coefficients are concerned, the downstream boundary can be placed as close as 14.5 diameters from the center of the cylinder with virtually no difference in the solution. Furthermore, only third‐digit variations in the Strouhal number and the lift and drag coefficients and very minor changes in the near‐field solution are observed when the downstream boundary is brought as close as 6.5 diameters from the center of the cylinder. Bringing the downstream boundary closer than this seems to result in more significant changes in the solution. In particular, if the distance is 2.6 diameters or closer, the solution becomes symmetric and steady.

A numerical model is presented for analyzing the combined transient dynamic response of floor systems with occupants. Structural analysis of a floor is based on a finite‐strip formulation that takes account of the various complexities common to its construction: orthotropic plate cover, variability in individual stiffener properties, and semirigid plate‐to‐stiffener connections. Occupants on the floor are idealized as lumped parameter assemblages comprised of discrete masses, springs, and viscous dashpots. Two vibratory human models are compared: one having just 2 degrees of freedom (DOF) and the other more detailed, with 11 DOF. The applicability of the numerical model is demonstrated with two example floors: a lightweight residential wooden floor and a longer spanning, heavier composite steelbeam concrete slab floor. With each example the floor is excited dynamically by, and interacts with, an occupant or occupants situated on the floor. The motivation for this work is towards providing a realistic means for evaluating floor systems under occupancy‐induced loading, which is required for the establishment of vibrational‐based serviceability design criteria.

The Ritz method, which is widely used for the free‐vibration analysis of isotropic plates and shells, is employed here to determine the displacements and stresses in cantilevered shallow shells that are statically loaded. The shallow shells are made of composite materials such as filamentary laminates or reinforced concrete. Displacements are assumed in the form of algebraic polynomials. Convergence for the membrane stress and bending moment resultants is demonstrated to be less rapid than for the displacements. Numerical results are presented for three‐layer cross‐ply and angle‐ply laminates made of graphite/epoxy materials. Displacements and stresses for shallow shells of spherical, circular cylindrical and hyperbolic paraboloidal curvature and square planform subjected to gravity loading are compared with those of flat plates.

The fluid‐saturated medium is viewed as a two‐phase continuum consisting of a solid porous skeleton with interconnected voids that are filled with a perfect fluid, and the formulation based on the theory of mixtures. Conditions for dynamic strain localization to occur in the rate‐independent elastic‐plastic saturated porous solid are first discussed. In particular, it is shown that the existence of a stationary discontinuity is only dependent upon the material properties of the underlying drained porous solid skeleton. Viscoplasticity is then introduced as a general procedure to regularize the elastic‐plastic porous solid, especially for those situations in which the underlying inviscid drained material exhibits instabilities that preclude meaningful analysis of the initial‐value problem. Rate‐dependency naturally introduces a length scale that sets the width of the shear bands in which the deformations localize and high strain gradients prevail. Then, provided that the element size is appropriate for an adequate description of the shear band geometry, the numerical solutions are shown to be pertinent. Stable and convergent solutions with mesh refinements are obtained that are shown to be devoid of spurious mesh length‐scale effects. Also, the effects of permeability on shear band development are studied and discussed. It is shown that low permeabilities delay considerably the growth of the shear band instabilities in agreement with Rice's (1975) predictions. Finally, the effect of the specimen geometry on the pattern of shear banding is illustrated.

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