Journal of Engineering Mechanics

Within the framework of critical state soil mechanics concepts, a rate‐independent constitutive model for soil response to complex, three‐dimensional loading is proposed. For any loading excursion, the material response is assumed to be elastoplastic. The approach proposed permits description of continuous and transitional yielding of material by adopting a combination of isotropic and kinematic hardening law. The capability of the model to represent anisotropic hardening behavior of soils and soil behavior under cyclic loading is particularly emphasized. Predicted response of Kaolin samples is compared with experimental results from various types of laboratory tests, including true triaxial tests.

An efficient computational procedure is presented for the buckling and vibration analyses of symmetric anisotropic panels. In the proposed procedure, the size of the analysis model of the anisotropic panel is reduced to that of the corresponding orthotropic panel. The two key elements of the procedure are: (1) application of operator splitting technique through the decomposition of the material stiffness matrix of the panel into the sum of orthotropic and nonorthotropic (anisotropic) parts; and (2) use of a reduction method through successive application of the finite element method and the classical Rayleigh‐Ritz technique. The finite element method is first used to generate a few global approximation vectors (or modes). Then the classical Rayleigh‐Ritz technique is used to substantially reduce the size of the eigenvalue problem. The global approximation vectors are selected to be a few of the eigenvectors corresponding to zero nonorthotropic matrix, and their various‐order derivatives with respect to an anisotropic tracing parameter, identifying all the nonorthotropic material coefficients. The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding orthotropic panel. The effectiveness of the proposed procedure is demonstrated by means of numerical examples.

It is well known that Leonhard Euler contributed a great deal to structural analysis; an example is the column formula that goes by his name. However, his seminal contribution to statically indeterminate analysis has generally been overlooked. Euler published the first paper on statically indeterminate analysis in 1773, and an edited version of this paper was published in 1795. A translation of the edited version of this paper is presented here since it illustrates the concepts developed by Euler but is without the large number of examples of the longer paper. The problem analyzed by Euler is a rigid table resting on an elastic foundation. Forces are related to displacements in the foundation by a linear constitutive law. Euler recognizes that a statically in‐determinate problem such as this can be solved uniquely by considering deformations in addition to forces. Although Euler's paper is rarely cited in text‐books or in historical studies, it was the first to contain the fundamentals of today's method of compatible deformations.

The usual description of the force exerted by a stochastic wave is extended to include the non‐normality of that force. In particular, the Morison equation is used to describe the force resulting from a sea state with stationary, normally distributed water velocities. Thus, the force non‐normality which is considered results only from the nonlinearity of the Morison equation. The fourth order cumulant function is used to describe the non‐normality of the force. The same information is also represented as a three‐dimensional spectral density, which results from a three‐fold Fourier transform of the cumulant function. Closed form solutions are not found, but the results of a power series expansion method appear to give good approximations. Potential applications of the results involve determinations of the non‐normality of the response of a structure subjected to a Morison‐type wave force. Such response non‐normality can then be used to substantially Improve estimates of structural failure, due to either first passage or accumulation of fatigue damage.

A formulation of the theory of plasticity in the strain space, which is a special case of the theory developed by Naghdi and coworkers, is presented here. A method to develop hardening functions to treat softening materials is discussed and illustrated. The applicability of the method is demonstrated by applying it in the analysis of the behavior of a geological material on axial compression and plane strain.

Normalized minimum light intensity of a three‐dimensional photoelastic medium, measured in a direct illumination polariscope by crossed arrangement of filters, is explored as a reliable characteristic quantity. The variation of the light intensity, for a given wavelength, resulting from superimposing noncoinciding coplanar bending and membrane stresses is studied as a function of their ratio. The graphical representation of this relation yields interesting novel information. This relation has been formulated in a mathematical model that might be used to determine the ratio for measured values of the light intensity. An additional independent experimental set of data can be obtained by varying the wavelength of the light source. It is shown that the quality and interpretation of the data so obtained is affected significantly by the selected wavelength. Furthermore, it appears that the discrete representation of photoelastic medium as a pile of birefringent plates is applicable only for low values of the stress ratio.

An autoregressive moving‐average model (ARMA) for univariate two‐dimensional homogeneous Gaussian processes is introduced. At the same time, an efficient technique for numerically generating sample functions of such two‐dimensional random processes is developed. The technique uses a recursive equation whose coefficient matrices are determined in accordance with the prescribed autocorrelation function. Using the recursive equation with these coefficient matrices, we can generate with substantial computational ease, sample functions over a large two‐dimensional domain; in principle, we can generate sample functions over an infinite domain. In the present study, sample functions of two‐dimensional, homogeneous, Gaussian random processes with four different analytical forms of the autocorrelation function are generated with the aid of a digital computer. The results indicate that the sample functions reflect the prescribed probabilistic characteristics extremely well. This is seen from the closeness between the analytically prescribed autocorrelation functions and the corresponding sample autocorrelation functions computed from the generated sample functions.

A new approach is outlined for BEM formulations for elastoplasticity, which exploits certain features of the constitutive relationships involved. The unknown nonlinear terms in the interior are now defined as scalar variables. A new direct numerical solution scheme comparable to the variable stiffness method used in the finite element analyses has been developed and applied to a number ol standard plasticity problems.

An analytical procedure is presented for determining the statistical properties of seismic motions at points below the ground surface on the basis of statistical information available at the surface. This procedure closely parallels methods used to study the amplification and propagation of waves in layered soils. Application of the method to some rather simple wave models shows that the dominant wave components of actual recorded motions cannot, in general, be estimated on the basis of cross‐correlation analyses. The reason for this is that the averaging process involved in the computation of the coefficient of cross‐correlation emphasizes some phase velocities more than others.

A radially reinforced hollow cylinder subjected to a combined action of axial pressure and radial pressures at both inside and outside radii is considered. These radial pressures are induced by hoop rebars. Due to uniform cross-sectional area of radial rebars, the reinforcement ratio is inversely propertional to the radius, and the cylinder is radially nonhomogeneous. Assuming the radial rebars to be perfectly bonded to the matrix, a closed-form solution for the problem is obtained. When radial pressures vanish, hoop stress distribution varies drastically from the inside to the outside radii and is much smaller than the radial stress. With the presence of hoop rebars, radial and hoop stresses become uniform across the thickness and are of the same order of magnitude. Therefore, the axial capacity of hollow cylinders can be effectively enhanced with proper arrangement of radial and hoop rebars when the confining effect of material, such as concrete is considered.