Journal of Engineering Mechanics

A family of variationally consistent, linear, shear‐deformation theories is developed for thin, shallow, elastic, homogeneous, anisotropic shells. The infinitely many members of the family share the same mathematical form but differ in their generalized displacements and shear factors. For maximum accuracy, which is uniform throughout the family, the theories are regarded as two‐step iterative theories, with one predictor phase and one correction. The Reissner‐Naghdi theory belongs to the family as its generic, simplest, noniterative member. The iterative members offer through their diverse generalized displacements a variety of models for geometric edge conditions. A refined Kirchhoff‐Love‐type theory is discovered as a mathematically degenerate but no less accurate member of the family. The generalized displacements in this refined theory are associated with the top and bottom bounding surfaces rather than the middle surface, normally used with the Kirchhoff‐Love theory. Adequate families of three‐dimensional displacement and stress fields are constructed from the family of shell theories and used to determine the accuracy of the theories and their admissible generalized displacements.

Three‐point bending fatigue tests are performed on two types of concrete using two different R ratios. The maximum strain is recorded during the tests. A damage mechanics model for the fatigue of concrete is proposed. It is based on a damage parameter proportional to the irreversible increment per cycle of the largest principal positive strain. This model predicts both the evolution of the strain as a function of the number of cycles and the fatigue life based on the initial strain and the strain increments. Comparisons of our experimental results are made with the model. Results reported by Holmen for compression fatigue tests are also used for comparison.

A relatively simple approach is first presented for the approximate analysis of the collapse of circular rings under external pressure. It accounts for geometrical and material nonlinearities, and is able to approximate the precollapse and postcollapse behaviors of rings. Applications of the approach to selected rings are made, and the resulting solutions are shown to be in good agreement with those of accurate finite element analyses. An examination is then made of the relationship between the ring‐collapse problem and the buckle‐propagation phenomenon in submarine pipelines, leading to an improved understanding of the phenomenon and to the development of a simple expression for the associated buckle‐propagation pressure. Relevant information and concepts of structural behavior are also reported, which are useful for practical applications. Predictions of the developed expression for the buckle‐propagation pressure are shown to be in good agreement with available experimental data, and it is proposed that the expression be used for design purposes.

A random‐vibration approach for uniaxial and biaxial nonlinear structures is presented based on the stochastic equivalent‐linearization method. By modifying and combining existing modeling techniques, a unified hysteretic modeling scheme is proposed. The method is applicable both to conventional uniaxial systems and general orthotropic systems, i.e., structural systems having different nonlinear characteristics in different directions. A significant attention is directed to the numerical errors associated with the equivalent‐linearization approximation. Numerical errors are classified as stationary and nonstationary errors. The mechanism of each error is carefully studied and quantitatively evaluated through a series of parametric studies. The postyield stiffness ratio, a, has been singled out as a key parameter in the error analysis. A practical error‐correction scheme is presented based on a large number of simulations.

Optimal control algorithms usually involve a state feedback including displacements and velocities. For control of building structures subjected to strong earthquake ground motions, it is much easier to measure the acceleration response than the displacement response. In this paper, a version of the instantaneous optimal algorithm, using velocity and acceleration feedbacks, for nonlinear or hysteretic structural systems is presented. Stable controllers are obtained using the Lyapunov direct method. The Lyapunov function for the controlled nonlinear structure is obtained through an appropriate transformation. The optimal algorithm is applied to control of a hysteretic building structure equipped with an aseismic hybrid control system. It is demonstrated numerically that for the particular hybrid control system considered, the performance of the present control algorithm is as good as the previous algorithm, which uses the displacement response of the structure for the determination of the control vector.

This paper analyzes the pseudostrain‐hardening phenomenon of brittle matrix composites reinforced with discontinuous flexible and randomly distributed fibers, based on a cohesive crack‐mechanics approach. The first crack strength and strain are derived in terms of fiber, matrix, and interface micromechanical properties. Conditions for steady‐state cracking and multiple cracking are found to depend on two nondimensionalized parameters that embody all relevant material micromechanical parameters. The results are therefore quite general and applicable to a variety of composite‐material systems. Phrased in terms of a failure‐mechanism map, various uniaxial load‐deformation behaviors for discontinuous fiber composites can be predicted. The influence of a snubbing effect due to local fiber/matrix interaction for randomly oriented crack‐bridging fibers on the composite properties is also studied.

Momentum equations expressed in the boundary‐fitted curvilinear coordinate systems have been used in the multidimensional modeling of estuaries and lakes. These equations are analyzed and reviewed with focus on the nonlinear advection terms. Imposing the conservation law of momentum on a differential volume in the curvilinear plane, one can derive the momentum equations with components specified in contravariant directions. Geometric information of the curvilinear grid is represented by the transformation coefficients associated with the transformed equations. These mathematical coefficients are defined here with new physical meanings and comparisons made among equations having different forms for the advection terms. Analyses of these comparisons indicate the non‐conservativity of the advection terms in existing equations is caused, not by orthogonality, but curvilinearity of the grid in which the velocities are expressed. We demonstrate that conservative forms of the advection terms cannot exist when momentum is expressed in contravariant directions in a curvilinear, orthogonal or nonorthogonal, grid system.

A numerical prediction of turbulent shear flow over a two‐ and three‐dimensional obstacle is obtained by solving weakly compressible flow equations, along with Smagorinsky's subgrid‐scale turbulent model. The numerical scheme is based on MacCormack's predictor‐corrector explicit finite volume method. First, computations were made for the case of flow over a two‐dimensional obstacle having different input boundary‐layer thickness, then for a cubical bluff body in one fourth‐power boundary layer. The computed results are in good agreement with the available experimental data. The effect of input boundary layer on the flow field in the two‐dimensional case was analyzed. The time‐averaged pressure around the cubical bluff body, wake pattern behind the body, horseshoe vortex, and a pair of axial vortices in the far wake region were well predicted.

The mechanical performance of brittle and quasi‐brittle materials can be significantly improved by the introduction of fibers. Fiber debonding, which results in the formation of bridging ligaments at the wake of cracks, is the major mechanism accounting for performance improvement. A strength‐based two‐way debonding theory, which accounts for fiber debonding at both the pulled and embedded ends, has recently been developed. In this paper, two‐way debonding based on a fracture criterion is considered. With the fracture‐based debonding theory, expressions for fiber stress and displacement, and thus the general de‐bonding features, are found to be similar to those given by the strength‐based theory. However, interpreting the same interfacial measurement (such as a pull‐out test record) with the strength and fracture approaches will lead to predictions of different debonding behavior in composites with practical volume fractions. To determine whether debonding is governed by strength or fracture, interfacial properties should be measured from a number of specimens with different fiber sizes or fiber volume fractions.

A vertical column possessing two different flexural rigidities is clamped at the bottom end and is free at the top. Both piecewise uniformly distributed axial loads (self-weights) and a concentrated load at the top are applied to the column. For the buckling load, the governing differential equation is a second-order nonlinear with variable coefficients. Even upon linearization, its solution involves linear combinations of the special functions. The equation for the eigenvalue problem is exact but tedious to solve numerically. Since the physical problem is fundamental in structural mechanics, this note develops some useful approximate formulas for the stability criterion. For the first mode, which is the most important one, elastic stability criterion is determined by a quadratic equation with variable coefficients via the Rayleigh-Ritz energy approach. The effects of ratios among various loads and between flexural rigidities on buckling loads are found. The comparison with the exact results available shows the formula giving satisfactory approximation.