Journal of Engineering Mechanics

Reliability analysis of highly redundant ideal‐plastic structures is difficult due to the existence of a very large number of possible failure modes. If only some of the failure modes are identified and included in the reliability calculation, the result will be an overestimation of the reliability. However, the lower bound theorem of plasticity theory allows for a calculation that underestimates the reliability. This theorem is applied to construct lower bounds that are optimized in a certain sense. Only a suboptimization is practicable. Therefore the resulting lower bounds are not particularly close to the exact reliability. However, some theorems originating from the lower bound optimization analysis turn out to be useful for defining a strategy of search for the most important collapse mechanisms of certain general types of models of plastic frame and truss structures. The total reliability can only be calculated up to upper and lower bounds, but examples show that the upper bound defined by the identified mechanisms is close to the mathematically exact reliability.

A simple penalty finite element formulation is presented for the large‐rotation and postbuckling analyses of curved beams. The analytical formulation is based on a form of Reissner's large‐deformation theory with the transverse shear deformation and the extensibility of the center line constrained through the use of the penalty method. Reduced integration is used in evaluating the elemental arrays, and a procedure is outlined for determining the critical points in the solution path. Numerical results are presented to demonstrate the effectiveness of the finite elements developed.

Unsteady flow of viscous incompressible fluid caused by oscillations of a naturally permeable wall bounding the fluid is examined in this theoretical paper. Solutions of the governing Navier‐Stokes equations, subject to slip condition at a porous interface, have been obtained by considering oscillatory solutions and an initial value problem. The effect of the permeability of the porous medium enters through a slip grouping parameter, whose influence on the structure of the Stokes' layer has been shown graphically. As a particular case of an initial value problem we have obtained Rayleigh layer over a naturally permeable wall and compared it with the classical Rayleigh layer for a range of nondimensional parameter.

A review and analysis of forces, equations and data for free‐surface intake vortices is presented. The effects of viscosity and surface tension are examined, in particular as they apply to Froude models. A comparison of vortex formation in a prototype and a 1:100 scale model is also presented. The analysis supports the use of Froude models, with certain provisos and limitations regarding in particular small‐scale models of air entraining vortices, and indicates at the same time a need for additional data to quantify scale effects.

The overall uncertainty of an aging stochastic system is analyzed through the consideration of both objective uncertainty and subjective imprecision. The updated probability distribution of a normal variate is determined through the constructions of global and local entropy equations. A subjective pairwise comparison method is applied in transforming subjective information concerning the overall uncertainty of the stochastic system to fuzzy support. A comparison of two fuzzy entropy functions is made. Since the fuzzy entropy function is not unique, calibration on the actual probability distribution is needed in order to justify the use of the proposed expressions. However, in many practical situations it is possible to make sensible pairwise comparisons without being able to make sensible parameter estimates. In such circumstances the proposed scheme will be of value.

An improved version of momentum‐energy‐integral solution for the developing laminar flow of Power‐law fluids in a flat duct is presented. Closed form expressions for the boundary layer development and entrance region pressure distribution are obtained. Results are illustrated graphically and compared with other integral solutions. Analysis predicts the continuity of the slope of pressure drop‐distance curve at the beginning of the fully developed state.

Earthquake motions as felt by structures along three orthgonal directions are, in general, statistically correlated. Here the effect of this correlation on structural response is studied. Assuming the existence of principal axes of excitations, along which the components of motion are uncorrelated, the mean square and design responses are obtained in terms spectral characteristics of these uncorrelated components. These responses depend upon the relative orientation of the structure with respect to the principal excitation components. For each response quantity, there exists a set of three orthogonal directions along which if principal excitations are applied they will cause a maximum response. Identification of these directions is necessary to obtain the worst case response for design purposes. A methodology to obtain such a maximum response of a quantity of design interest is outlined.

Tresca type yield surfaces suitable for a kinematic hardening formulation of incremental theory of plasticity are presented. A uniaxial symmetric Tresca yield condition, along with a linear kinematic hardening rule, is utilized to formulate a small displacement, plane stress incremental theory of plasticity. This theory is applicable to materials with both equal and unequal tension and compression yield stress. Constitutive laws for sides and corners of the yield surface are derived. Finite element formulation, numerical solution and application are discussed.

An extension of the Sanders shell theory for doubly curved shells to a shear deformation theory of laminated shells is presented. The theory accounts for transverse shear strains and rotation about the normal to the shell midsurface. Exact solutions of the equations are presented for simply supported, doubly curved, cross‐ply laminated shells under sinusoidal, uniformly distributed, and concentrated point load at the center. Fundamental frequencies of cross‐ply laminated shells are also presented. The exact solutions presented herein for laminated composite shells should serve as bench mark solutions for future comparisons.

A method is presented, employing Flügge and Donnel type theories, for obtaining the dynamic characteristics of cylindrical panels of noncircular cross section, having simply supported curved edges and any boundary conditions along their straight edges. The method may be viewed as a direct extension of the one employed in establishing the dynamic characteristics of cylindrical panels of circular cross section. Special formulas are derived for symmetric and doubly‐symmetric cylindrical panels.

Input excitations of certain intensity that maximize the structural response have been an interesting subject of several investigations since the early 1970s. The basis of this lies in a worst case type of analysis that can be conservatively used in defining the seismic input. Such an approach may complement currently used procedures which are based primarily on design spectra. However, when maximizing inputs are considered in seismic assessments, inelastic behavior should be anticipated. This paper presents some seismic inputs that may be used for nonlinear structures. They are generated from recorded earthquakes and produce maximum nonlinear response.