Journal of Engineering Mechanics

The fracture of rock is assumed to arise from propagation of a blunt crack band with continuously distributed (smeared) microcracks or continuous cracks. This approach, justified by material heterogeneity, is convenient for finite element analysis, and allows analyzing fracture on the basis of triaxial stress‐strain relations which cover the strain‐softening behavior. A simple compliance formulation is derived for this purpose. The practical form of the theory involves two independent material parameters, the fracture energy and the tensile strength. The width of the crack band front is considered as a fixed material property and can be taken as roughly five‐times the grain size of rock. The theory is shown to be capable of satisfactorily representing the test data available in the literature. In particular, good fits are demonstrated for the measured maximum loads, as well as for the measured resistance curves (R‐curves). Statistical analysis of the deviations from the test data is also presented.

A differential equation model for hysteretic systems is analyzed under nonzero mean random excitation. Under certain conditions, a closed form linearization of the equations of motion is possible. Resulting mean and zero time lag covariance responses agree well with Monte Carlo response simulations. Generalization to degrading systems is straightforward. Skewness coefficients computed from simulation results indicate significantly asymmetric response. Stationary response statistics are found to relate closely to the zero mean case.

Flow with increasing discharge in trapezoidal cross sectional channels is studied using the classic equation of “momentum.” Such equation is normalized utilizing the coordinates of the singular point. In this way it is possible to completely analyze different flow regimes that may occur in the channel and also the curves representing the free surface may be classified. The cases in which the slope of the channel is zero and non‐zero is investigated.

A 10‐ft square, one‐story model structure was subjected to horizontally incident SH‐waves to determine the effect of foundation embedment on the response. Structural and foundation‐soil impedances were calculated from the fundamental resonant frequency and mode shape. The resulting impedance values and embedment factors were then compared to theoretical values. The translatory and rocking impedances for the unembedded case were found to be in agreement with values obtained from analytical formulations. However, the experimentally obtained embedment factors were generally much larger than predicted by theory.

A 10‐ft square, one‐story model structure was subjected to horizontally incident SH‐waves to determine the effect of foundation embedment on the response. Structural and foundation‐soil impedances were calculated from the fundamental resonant frequency and mode shape. The resulting impedance values and embedment factors were then compared to theoretical values. The translatory and rocking impedances for the unembedded case were found to be in agreement with values obtained from analytical formulations. However, the experimentally obtained embedment factors were generally much larger than predicted by theory.

In this investigation the boundary integral equation (BIE) method with numerical evaluation of the boundary integral equations is applied to the analysis of simply supported plates of any shape, resting on an elastic foundation. The numerical results are compared with those available from analytical solutions. Moreover, the efficiency of the BIE method is demonstrated and examined.

In this paper the dynamic characteristics of oval cylindrical panels, with simply supported curved edges and various boundary conditions along the straight edges, are established on the basis of the Flügge or Donnell type theories using the procedure presented by the writers (5). Numerical results are presented and the effect of the ovality as well as other geometric parameters of the panels are investigated. Moreover, the results obtained on the basis of the aforementioned theories are compared.

Investigated in this paper is the dynamics of structures with their foundation mat supported only through gravity and thus permitted to uplift from the supporting system. In its fixed base condition the structure is idealized as a single‐degree‐of‐freedom system attached to a rigid foundation mat, which is supported at each edge by a spring‐damper element. Analytical expressions are presented for the free vibration response of the system and the effects of foundation uplift are examined. An effective numerical procedure, based on expressions of the Rayleigh‐Ritz concept, to evaluate the structural response to earthquakes is presented. Based on the response spectra presented it is shown that foundation mat uplift has the effect of reducing the base shear for shortperiod structures, with these reductions being especially significant for the more slender structures.

Complex variable methods have been devised to investigate the effect of geometric irregularities on the dynamic characteristics of inviscid liquids in circular basins. The fundamental frequency of the slosh mode has been determined by the stationary property of Schwarz quotients. Lower and upper bounds for the frequency have been obtained by a comparison theorem. Results show that frequencies are decreased with the increase of out of roundness parameters.