Journal of Engineering Mechanics

The writers are concerned with the free vibration of discrete undamped linear dynamic systems commonly designed in structural engineering. The primary purpose is to present a rational method for improving the natural modes and frequencies computed by incomplete modal coupling, without increasing the order of the resultant eigenvalue problem. Improvement is accomplished through use of a candidate table in an iterative process that introduces significant modes into sequential modal analyses. The error trend and sensitivity analysis due to modal truncation is evaluated by computation of a scalar number called significance index which represents an approximation to the error in a certain eigenvalue due to omission of a certain mode shape. This information forms the basis of the candidate table, which serves as a guide for the optimal automated selection of modes for modal substitution. The method of analysis is demonstrated for a discrete model containing 378 degrees‐of‐freedom.

An approximate numerical solution is developed for the two‐dimensional linearized equations for stratified flow. Applications of the approximate solution to the shear driven stratified cavity flow are presented. The parameters which determine the predicted circulation cells in this flow are discussed.

The constitutive equation for cohesionless soil is developed within the framework of the endochronic theory of plasticity. It is found that three groups of internal state variables should be used to describe the complex behavior of soil. To each group of internal variables there corresponds an evolution equation for the variables and an intrinsic (endochronic) time. The theory is shown to predict essential features of the mechanical behavior of cohesion‐less soil under static loading conditions. These include: (1) The nonlinear volumetric response at isotropic consolidation; (2) densification due to the change in the deviatoric state; (3) the deviatoric response and its dependence on normal stress; and (4) the effects of unloading and reloading during isotropic consolidation and shearing.

Dynamic stability of a Kelvin‐viscoelastic column subjected to a time varying axial load is considered. Deterministic loads with sinusoidal time variation is studied which reduces to a Mathieu equation. Special attention is given to stationary random excitations. Sufficiency stability criteria for columns subjected to white noise, Gaussian and general stationary random loadings are established. The stability conditions for certain class of nonstationary random forcing are also discussed.

A predictive model is developed for transient heat transfer analysis of structures with layered heterogeneous media. The model is particularly suited for the analysis of refractory concrete lined coal gasification and other similar chemical processing vessels. To allow for the effects of high conductivity gases in voids and cracks on the overall conductivity of the media, an effective conductivity model is developed. The model incorporates the effects of temperature dependent nonlinear material properties. Validity of the model is shown by comparing the predictions with those from an analytical solution for a special case, another numerical solution, and experimental measurements from an actual test vessel. Sensitivity of the temperature distribution to the presence of hydrogen gas in the vessel environment is evaluated.

General piecewise‐linear yield criteria exhibiting 30°, 60°, or 120° symmetry in the octahedral plane are expressed in terms of the canonical invariants of the deviator stress, $J_2$ and $J_3\text{.}$ Criteria of the type often associated with granular media, in which strength is proportional to the hydrostatic component of stress, are also reviewed. In the particular case of the Coulomb criterion, it is shown that compact expressions can be found through the use of the canonical invariants of stress $I_1\text{,}$ $I_2\text{,}$ and $I_3\text{.}$

The Sequential Unconstrained Minimization Technique (SUMT) offers an easy way of solving nonlinearly constrained problems. However, this algorithm frequently suffers from the need to minimize an ill‐conditioned penalty function. An ill‐conditioned minimization problem can be solved very effectively by posing the problem as one of integrating a system of stiff differential equations utilizing concepts from singular perturbation theory. This paper evaluates the robustness and the reliability of such a singular perturbation based SUMT algorithm on two different problems of structural optimization of widely separated scales. The report concludes that whereas conventional SUMT can be bogged down by frequent ill‐conditioning, especially in large scale problems, the singular perturbation SUMT has no such difficulty in converging to very accurate solutions.

A brief overview of the available experimental data regarding distortional hardening of metals is first presented. This material is subsequently used to motivate the need for accurate distortional hardening rules in computation. A general expression for the yield surface of a plastic material is proposed that includes the isotropic‐kinematic von Mises model as a particular case and that can be systematically used to incorporate distortional hardening features into the material modeling in a simple manner. This expression is complemented with suitable rate equations for the parameters involved. The proposed model is particularly convenient for computer implementation.

Innovative techniques for the measurement of mean and fluctuating wind loads acting over various tributary areas of wind tunnel models are described. Pneumatic manifolding, designed to provide good dynamic response, allows effective loads over large areas to be measured which inherently account for lack of spatial and temporal correlation in the unsteady pressure field. On‐line integration utilizes such effective area loads as inputs to computer models of structural systems to directly determine dynamic structural responses. Examples of applications are given which illustrate the simplicity and economy of the technique, and the importance of the tributary area in determining the effective design load. Potential future applications are also discussed.

A new form of endochronic constitutive model is presented to describe the behavior of dry or drained sand, and its parameters are determined by extensive comparisons with published test data. Jump‐kinematic hardening is used to guarantee that the hysteresis loops always close, yield positive energy dissipation, and give an increase in tangent modulus when unloading changes to reloading. Criteria for virgin loading, unloading and reloading are formulated in terms of deviatoric work, and changes of material parameters at loading‐unloading‐reloading transition points are determined. Two endochronic units coupled in parallel are used to describe the measured response over a broad range of strain amplitude. The inelastic volume change is characterized so as to include both densification and dilatancy. Certain material properties are determined as functions of the void ratio. Calculations show that the lateral stress in a simple shear test quickly becomes almost equal to the vertical stress. A three‐dimensional finite element analysis of the simple shear test with endochronic theory reveals significant stress nonuniformity; but this is found to have little effect on the resulting hysteresis loops.

Arguments are given in favor of the point of view that structural safety should be quantitatively expressed in terms of a pair of numbers, ($p_{\mathrm{th}}\text{,}$ $p_{\mathrm{gr}}$), rather than by a single number. In this pair, $p_{\mathrm{th}}$ is the theoretical failure probability as it results from the structural reliability theory disregarding the existence of gross errors. The second number, $p_{\mathrm{gr}}\text{,}$ is some measure of proneness to failure due to gross errors. It is postulated that structural optimization is a two variable problem with $p_{\mathrm{th}}\text{,}$ and $p_{\mathrm{gr}}$ as independent variables. The paper is a reaction to recent suggestions of merging reliability theory results given in terms of probabilities with judgements concerning gross errors expressed, for example, by use of the concept of fuzzy sets.

A finite element method utilizing quadrilateral elements to obtain an efficient solution to determining the opening‐mode stress intensity factor $K_I$ is presented. Two plane stress element types are constructed: (1) “Regular” which does not contain a crack but which may be in the interior or on a boundary; and (2) “singular” or “super element” which contains the crack and is assumed to be on the boundary which is a line of symmetry. Each element utilizes as primary unknowns the displacements and strains at each node. Hermitian interpolation functions are used to describe the displacements in the regular element and Williams' stress function is used to develop the singular element. Good agreement with published results is obtained for single‐edge‐notch beams in three‐point bending and four‐point bending for relatively coarse meshes.

Nonlinear dynamic behaviors of plates of various geometries have been studied by several investigators in the past. Almost all of these investigations are based on the classical von $\acute{K}$r$\acute{m}$n‐type plate theory. Due to the complex nature of these class of problems, multiple‐mode solutions are very rare. This paper is concerned with nonlinear flexural vibrations of moderately thick circular plates using an improved nonlinear theory to account for transverse shear and rotatory inertia effects. Multiple‐mode analysis is carried out by means of Galerkin's method and numerical Runge‐Kutta procedure for clamped plates with both movable and immovable edges. For the multiple‐mode considered here an exact solution to stress function is reported. Amplitudeperiod response curves are presented and discussion includes the effect of coupling of vibration modes. Present results for all special cases are in excellent agreement with existing solutions. The analysis given here provides improved results and a clear insight into the effects of geometric nonlinearity due to large deformation coupled with the effects of transverse shear, rotatory inertia and modal interation.

This paper discusses the deformation imposed on an elastic tape wrapped helically around an elastic cylinder which is then subjected to pure bending. Applications to problems which occur during the manufacture and subsequent service life of insulating tapes for buried high‐voltage transmission systems are also discussed.

The response of a lightly damped single‐degree‐of‐freedom oscillator to a random excitation with an evolutionary broad‐band power spectrum is considered. Analytical solutions are given for the transition, joint, and marginal probability densities of a Markovian approximation of the response amplitude. Digital data generated by extensive simulations of the response amplitude statistics are presented as well. These data are discussed in context with an assessment of the reliability of the developed analytical solutions.