Journal of Engineering Mechanics

Tests were carried out in Resolute NWT, Canada, (74°43′N, 95°04′W) on first‐year sea ice to determine for the first time the notch sensitivity of first‐year sea ice. A displacement feedback control was used on a soft portable testing frame to apply a calculated strain rate of 10⁻³ s⁻¹ at the extreme tensile fiber of the beam. An ice beam $0.1m\times 0.1m$ in cross section, 1.0 m long was loaded in four‐point bending, the constant moment region was 0.5 m long. In this region three identical cracks were prepared with lengths of 0 to 50% of the thickness of the beam. Beams with prepared cracks 1.5 mm long fractured at sites other than a prepared crack in nine out of 16 samples. In the 81 other beams, the crack initiated in the first prepared crack 29 times, in the second 32, and in the crack last sharpened, 20 times. The nominal failure strength was calculated using the unbroken ligament as the thickness, and it dropped to one‐half the tensile strength at $a/w=0.25$, but the fracture toughness did not drop from 190 kNm^−3/2 to 124 kNm^−3/2 until $a/w=0.5$.

A complete closed‐form solution in terms of elementary functions is given for the first time to the title problem. Explicit expressions are derived for the fields of stresses and displacements in both transversely isotropic and isotropic space weakened by a penny‐shaped crack and subjected to a shear loading with a magnitude being a linear function of coordinates $x$ and $y$. The stress intensity factors for mixed mode II and III loading have been evaluated. The method is based on the new results in potential theory obtained recently.

Many materials of interest contain initial crack‐like defects. Often these cracks are oriented more or less regularly and hence, they contribute to an anisotropic material behavior. We have applied a second‐order tensorial representation of damage, and treat the cracks as a continuum phenomenon on a suitable macroscopic scale. Our model accounts for the progressive failure of damaging materials due to the growth of these defects. The main emphasis of the presented work is put on the propagation of sets of cracks in mode II. This case occurs when the loading axis does not coincide with the plane of the initial cracks. Thus, our model is not restricted to proportional loading. Assuming the existence of a Helmholz free‐energy function and a dissipation potential in the space of affinities we have derived a constitutive equation and a damage propagation law by means of the thermodynamic principles of irreversible processes. Within the framework of the small deformation theory, the proposed formulation considers both brittle and ductile materials.

The present paper concentrates on two‐dimensional static and dynamic fluid‐structure force effects. Forces acting on elongated bluff bodies like long‐span bridge decks have been described by theories and analytical formats strongly influenced by analogous expressions found in two‐dimensional airfoil theory. These theories are first reviewed. The resulting formats are seen to contain some formalisms that may overly constrain the force descriptions when applied to bluff bodies. The particular circumstances where this is evident are pointed out. An important point of the present paper is to emphasize the need to employ a format that can be applied directly to design studies of real bridges and that can be reinforced by experiment. The nature of experiments needed to support design calculations for bridge decks is briefly discussed. In sum, the paper offers an integrated version of aeroelastic theory applicable to long, flexible, bluff bodies such as suspended‐span bridges. Emphasis is placed upon origins and legacies of aeronautical theory and upon identification of the key parameters that must be measured experimentally in the present context.

Experimental errors are inevitable in pseudodynamic testing. Some of these errors can be monitored during the test, but, due to limitations in control system, they cannot be eliminated. For example, one cannot control exactly the displacements that are actually imposed on the structure at each time step. This paper focuses on a technique to minimize the cumulative effect of such control errors. For this purpose, a posterior adjustment of the time increment from a target value $\Delta t$ to an adjusted value $\Delta t_n$ is performed to minimize the effect of the control errors. The method is particularly for effective single‐degree‐of‐freedom systems and systematic errors. These systematic errors can have a very detrimental effect, and they are eliminated almost completely for the single‐degree‐of‐freedom example considered. For random errors that are probabilistically independent from one time step to the next, the method can have a deleterious effect on the error propagation characteristics, even though the control errors at each time step are reduced. However, since the effect of such random errors is small, this is not a serious draw‐back. For multi‐degree‐of‐freedom systems, posterior time step adjustment can also improve the error‐propagation characteristics for certain systematic errors but its effectiveness is more limited.

This paper investigates both experimentally and theoretically the free rocking of a prismatic block supported by a stationary, horizontal foundation: the block is tilted, almost to the point of overturning, and released from this position. It is shown that the standard mathematical model for this problem is often inaccurate. A critical review of the implicit assumptions behind the standard model reveals that the free‐rocking response of short blocks depends crucially on bouncing after each impact; out‐of‐plane effects are significant in very short blocks. The response of slender blocks is found to be easier to predict. Rocking has been observed during earthquakes in structures that consist of fairly rigid, unbonded elements, e.g. stacks of graphite blocks in nuclear reactors, and ancient Greek columns, and also in slender structures with foundations unable to resist uplift.

Earthquake response of reservoir sediment and its dynamic interaction with the impounded water are analyzed using a two‐dimensional model of poroelastic media. The pressure wave equation for the pore water and the sediment is solved by an implicit finite difference method coupled with a fast Poisson solver. The numerical scheme requires a conversion of the boundary condition on the rigid dam face to a Dirichlet boundary condition. For incompressible impounded water, a reduction in the dynamic pressure appears at the onset of ground motion when the bulk modulus of pore water in the sediment is compressible. The pressure rises rapidly with the celerity of pressure wave and exceeds that of Westergaard's solution for the incompressible case without the sediment. Augmentation of the pore pressure is primarily caused by the inertia of the sediment and the Stokes drag. The hydrodynamic pressures on the dam face could exceed significantly those calculated by an incompressible two‐fluid model for an idealized liquefied sediment.

A numerical method is presented for determining scattered pressures from a submerged infinite cylindrical shell with radial plate appendages subjected to a transverse incident plane Heaviside pressure wave. Inside a cylindrical fluid‐control surface circumscribing the appendages, finite‐difference equations in the cylindrical domain govern the fluid‐structure interaction. The infinite region outside the control surface is transformed mathematically into a finite rectangular domain, within which finite‐difference equations with unequal spacing govern. A conditionally stable explicit scheme is used to solve the array. Numerical results indicate that the characteristic transient echo of the cylinder is obscured when the appendages are present.

In this paper it is shown that the order of time derivative and the coefficients in linear viscoelastic models can be generalized to complex quantities. In this approach, the storage and loss moduli are not regarded as two independent real functions but rather as the real and imaginary parts of a complex function. The problem of calibration of models with complex parameters is solved by resorting to methods of nonlinear regression in the complex space. The conditions for existence of complex‐order time derivatives are examined and the transformation of these derivatives in the frequency domain is derived. The procedure is applied in the development of models for viscous dampers. The models are shown to produce results in good agreement with experimental data.

A model that combines plasticity and damage mechanics is developed to assess both multiaxial monotonic and cyclic behavior of concrete. The model adopts a bounding surface concept and combines plastic deformation with the deformation due to damage. Plastic strain components are calculated by using the plastic modulus that is a function of the distance from the current stress point to the bounding surface along the deviatoric stress direction $S_{\mathrm{ij}}$. Similarly, damage growth rate is obtained by the hardening modulus, which is a function of the distance just defined. The hardening behavior of concrete is assumed herein to be controlled by both damage and plasticity, while the strain‐softening regime is controlled by damage processes only. The simultaneous use of the plasticity surface and the damage surface, leads to a constitutive model that accounts for the essential features of concrete such as pressure sensitivity, shear compaction‐dilatancy, stiffness degradation, and softening behavior.

Based on wave theory and the concept of the equivalent foundation for the soil, a simplified method for the dynamic analysis of tapered structures during earthquakes is presented in this paper. The merit of this simplified method is its inclusion of important factors that may affect the responses of tapered structures. Further, the method is sufficiently simple that the dynamic analysis of a tapered structure can be accomplished with a microcomputer or a calculator.

In the present technical note, the stresses and displacements are determined in an infinitely long circular cylindrical shell reinforced by a single frame. In the solution, the shell and the ring are considered separately. External load and interaction force arising from separation are expressed as harmonic series, namely Fourier series. A unit displacement matrix is obtained for the ring and as well as for the shell under the interaction forces. Imposing the compatibility conditions, the amplitudes of the unknown harmonics are obtained. The solution technique presented can be used for the shell having different boundary conditions and different external load configurations.