Journal of Engineering Mechanics

A brittle aggregate composite such as portland cement concrete or mortar is modeled in two dimensions as a system of perfectly rigid particles of various sizes separated by interface layers that are characterized by a given force‐displacement relation for the normal and tangential components. The force‐displacement relation exhibits for the normal component a tensile strength limit followed by a sudden drop of force to zero. The system of rigid particles is generated randomly. The particles are not allowed to overlap and are generally not in contact; however, when the distance between the particles is less than a certain limit, a deformable interface layer is introduced. Numerical simulation of a fracture specimen with a notch shows that the fracture front consists of an irregular band of interparticle cracks the width of which is about three maximum particle sizes. The interparticle cracks remain continuous and do not coalesce into a continuous line fracture until the deformation is very large. The load‐displacement relation exhibits gradual softening after the peak force, with a rapid force decrease followed by a long tail of slowly decreasing force. These features qualitatively agree with observations of concrete.

A constitutive relation is formulated for coated fabrics that exhibit both elastic and inelastic, but time‐independent, responses. The nonlinear orthotropic response is represented by an elastic portion related to yarn stretch and coating shear, and an inelastic part related to crimp interchange. A method is proposed to compute the path‐dependent inelastic strain and the elastic strain for any loading once material parameters are evaluated from uniaxial tests in the principal directions of elasticity.

A theoretical study is made of the inelastic hysteretic behavior of an axially loaded bar member. Variable repeated loading is applied by axial load, axial displacement, change in temperature, or a combination of these actions. Elastic‐perfectly plastic constitutive relations in the use of stress resultants lead to a closed‐form solution to determine the planar deformation characteristics of the bar. This formulation allows for the reduction of yield stress due to a rise in temperature and is done in a form convenient to take viscous effect into consideration. Both lateral deflection and elongation or shortening cause the axial displacement of one bar end relative to the other; the two causes are additive. The concept of an extensible yield hinge is used. It is pointed out that the plastic axial deformation at a yield hinge plays an important role in the hysteretic behavior of bars of moderate length. This governs the behavioral deterioration, and stabilization or convergence of hysteretic loops for cyclic loading.

This investigation explores a method for predicting deformation in the vicinity of interfaces of dissimilar materials. Instead of using a slide‐line algorithm or interface elements, a new nonlocal approach for simulating the response near soil‐concrete interfaces is proposed. It is assumed that the stress field is a function of both strain and strain gradients, and that no slip occurs at the contact surface between soil and concrete. Different response features for the region of localized shear strain adjacent to the interface can be obtained by adjusting material parameters. Numerical results for static and dynamic cases show that softening and localization are handled in a stable manner independent of mesh size.

An Improved interface smeared crack method for finite element modeling of cracks in concrete is developed into a usable procedure and applied to the seismic analysis of concrete gravity dams. The method pushes back displacements in elements bordering an open‐crack interface to eliminate strains normal to the crack face. The amount of pushing back is found by dividing the normal strain by the appropriate strain interpolation function derivative. Pushing‐back algorithms are described for interfaces at angles to the global coordinates and for skewed elements. A biaxial tensile strain failure criterion is employed. The method is combined with a cyclic ultimate strength equivalent uniaxial strain material model to analyze the behavior of Koyna Dam in the December, 1967 earthquake.

This paper shows how to design the parameters of a passive control mechanism in order to keep bridges safe at all possible resonant frequencies caused by nonlinear effects due to midplane stretching. The control mechanism is a king‐post truss tendon mechanism. It is basically chosen to shift the natural frequencies of the bridge away from possible resonances. However, the structural parameters of this mechanism can be designed to eliminate or reduce the nonlinear effects on the primary‐resonant responses of bridges. The design has been made using a perturbation technique for a hinged‐hinged single‐span bridge.

This paper shows the time‐delay effect on the distributed parameters structures controlled using direct velocity feedback. It is shown how the stability of the structure could be lost due to time delay. Two ways of time‐delay compensation are suggested. The first way is to redesign the gain matrix considering the presence of the time delay. In this case, however, the structure could remain unstable when using control moments as control actions. The other way is to use low‐pass filters to filter the velocity measurements from the frequency components of the high order modes. In this case, one can control and compensate for time delay a number of vibrational modes equivalent to the number of control actions. However, the higher order modes remain uncontrolled.

A solution is derived for stresses in an orthotropic quarter plane loaded by (1) A tangential concentrated line load at distance a from the edge; (2) a uniform normal load over length a and at distance a from the edge; and (3) a uniform normal load over length a at the edge. The results may find application in reinforced‐earth and geotextile retaining walls, vertical slopes of horizontally jointed rock, and unsupported excavations of anisotropic soil.

A smeared crack model that covers tensile softening in mode I and shear softening in mode II fracture is described. In addition, the model provides for unloading and reloading and for multiple crack formation. Particular forms of tension and shear softening functions and relations with more conventional models are discussed. Two examples involving mixed‐mode fracture in notched, unreinforced concrete beams have been included to demonstrate the versatility of the model. The results indicate that the addition of shear softening is essential to obtain realistic results in the post‐peak regime since the classical approach based on a constant shear retention factor then results in a too stiff behavior. The results furthermore demonstrate that snap‐back behavior may occur in strain‐softening concrete under quasistatic loading conditions. Attention is also given to the possibility of hour‐glass formation when constitutive laws involving softening are deployed in a finite element model.

The optimal finite‐difference (FD) method for two‐dimensional potential flows is studied. The nine‐point FD coefficients for Laplace equations are derived for rectangular cells with an arbitrary length‐to‐width ratio r. The accuracy and performance of the present optimal FD formula are compared with the finite‐analytic (FA) formulas. It is found that the present FD formula gives better results than those given by the FA formulas, and that it produces more stable results than those in other studies for large values of r. An example of potential flow in a channel with an abrupt change in its width is also given.

A comprehensive analysis is made of the dynamic response of liquid containing, upright circular cylindrical tanks to a rocking base motion of arbitrary temporal variation. Both rigid and flexible tanks are examined. Critical response quantities for rigid tanks are evaluated over wide ranges of the parameters involved and the results presented in a form convenient for use in practical applications. The interrelationship of the responses of the system to rocking and lateral base motions of the same temporal variation is established, and it is shown that some of the effects of base rocking may be determined from available data concerning the response of laterally excited tanks. Additionally, the well‐known mechanical model for a laterally excited tank is generalized to permit consideration of the effects of base rocking. The influence of tank flexibility is evaluated by an extension of a simple approximate technique proposed previously for laterally excited tanks.

The study of rotating fluid is important for many problems in cosmical fluid dynamics, meteorology, etc. The large scale and moderate motions of the atmosphere are greatly affected by the vorticity of the Earth's rotation. In the case of infinite fluid rotating about an axis as a solid body rotation, the amount of energy possessed by the fluid is infinite, and it is of great interest to know how small disturbances propagate in such a fluid when the bounding lower naturally permeable plate of finite thickness is given a sudden translatory motion. This paper gives the results for fluid motion of a rotating Newtonian fluid over an infinite naturally permeable wall (which is also rotating), when the wall is given a sudden translatory motion.