Journal of Engineering Mechanics

Nonlocal continuum damage mechanics and random field theory are used to model the stochastic damage behavior of a strain‐softening material with random field properties. The randomness in the damage process is introduced by considering the initial damage threshold and the local strain‐softening behavior as a bivariate random Nataf field, defined by the marginal distributions and correlation matrix. A key component of the model is the introduction of two different length parameters: the characteristic length of the nonlocal damage model and the correlation distance for the random field. The probabilistic nonlocal damage model is illustrated by presenting finite‐element analyses of direct‐tension tests. It is found that the specimen exhibits a structural behavior representing a nonsymmetrical deformation and nonlinear stress‐displacement curve. The influence of the cross‐correlation coefficient between the initial damage and the strain‐softening behavior is discussed. The probabilistic nonlocal damage model is also capable of describing the deterministic and probabilistic size effect of structures.

Time‐dependent distributions for temperature and moisture content in a concrete wall subjected to fire are determined by a model of heat and mass transfer in porous media. Free‐water flow, bound‐water diffusion, gas‐phase flow, water‐vapor diffusion, and thermal energy are accounted for in the model. The governing transient differential equations are discretized by a control‐volume formulation reported by Patankar in 1980, and solved in time using a fully implicit scheme. Two different fire exposure curves (namely, standard curve according to ASTM E‐119 and a more realistic curve reported by Ellingwood in 1991) are employed in the analysis. The assessment of two simplified models, in which all pore water is assumed to evaporate at 100°C, is performed by comparing their predictions to the full analysis. For temperature and saturation, the time developments predicted by the two simplified models and by the full analysis present similar trends; however, the simplified models seem to be appropriate only for very preliminary fire safety analyses, since they tend to underestimate temperatures.

Analytic three‐dimensional thermoelasticity solutions are presented for static problems of simply supported sandwich panels and cylindrical shells subjected to mechanical and thermal loads. The panels and shells have laminated composite face sheets of arbitrary thickness separated by a core. Each of the individual layers of the face sheets and the core is modeled as a three‐dimensional continuum. Analytic first‐order sensitivity coefficients are evaluated to assess the sensitivity of the responses to variations in material parameters of the face sheets and the core, as well as to variations in the curvatures and thicknesses of the sandwich and face sheets. Also, the strain energy associated with various stress components in the face sheets and core are calculated and compared. The information obtained in the present study can aid the development and assessment of two‐dimensional models for sandwich structures and illuminate the role of particular material parameters in an equivalent model for the core.

An extensive investigation on the buckling and large displacement behavior of thin‐walled circular beams has been conducted theoretically. Equilibrium equations governing the linear, the bifurcation buckling, and the large displacement behavior have been derived using the principle of minimum total potential energy. An explicit and clear approximation of the curvature effect is made in the derivation process. The paper concludes with a series of fundamental nonlinear equations that describe the elastic behavior of thin‐walled curved beams. A companion paper examines closed‐form solutions for arch‐buckling problems based on the formulations presented in this paper and demonstrates the rigor and the validity of the present formulation.

In recent years, after Yoo queried the validity of Vlasov's equations regarding the lateral buckling of a circular arch, there has been a number of papers published with a certain degree of disagreement among various researchers. Based on a comprehensive and consistent formulation of curved beam theory presented in the previous paper, closed‐form solutions thus obtained are used for comparison of the present theoretical study to others. In the present paper, major potential sources of discrepancies are traced, thereby the rigor and validity of the present formulation is demonstrated. Also, the study on the buckling modes of arches subjected to the condition of uniform bending gives an insight for better understanding of lateral buckling characteristics of arches.

The purpose of this paper is to demonstrate the efficacy of using Chebychev polynomials in the Rayleigh‐Ritz method. For purposes of illustration, the problem of free torsional vibration and buckling of doubly symmetric thinwalled beams of open section of constant cross section subjected to an axial compressive static load and resting on a continuous elastic foundation is considered. Both simple polynomials as well as orthogonal functions are used as displacement functions in order to demonstrate the advantages of the latter over the former. Two sets of boundary conditions are treated: (1) Fixed‐fixed; and (2) fixed‐simply supported. Wherever possible, the functions are chosen so that the kinematic boundary conditions are satisfied. In the cases in which the functions do not satisfy all the kinematic boundary conditions, the penalty‐type approach is adopted. In this approach, appropriate springs with large stiffness coefficients are provided to simulate the kinematic boundary conditions. Numerical results for natural frequencies and buckling loads for various values of warping and elastic foundation parameters are obtained and compared with those obtained by other researchers. A good agreement is observed.

A method for solving the finite‐displacement problem of a curved elastic beam with axial, shear, and flexural deformation subject to distributed and point loads is presented. Within the context of the kinematic assumptions of the Timoshenko theory, a Lagrangian formulation of the problem is developed. In terms of three cross‐sectional stress resultants, three Euler equations of equilibrium for the beam are derived with the aid of a variational principle for finite deformation. Upon linearization to small strains and the adoption of a linear elastic constitutive relation between the stress and strain tensors, it is shown that the problem is reducible to a single second‐order nonlinear ordinary differential equation. Subject to appropriate boundary conditions, the resulting two‐point boundary‐value problem is solved by a finite‐element method. By virtue of a continuation algorithm, accurate solutions of the system of nonlinear equations can be obtained for a variety of bifurcation and buckling problems. Comprehensive results are presented for two cantilever beams as illustrations.

This paper presents several analytical solutions for problems of harmonic wave propagation in a poroelastic medium. The pressure‐solid displacement form of the harmonic equations of motion for a poroelastic solid are developed from the form of the equations originally presented by Biot. Then these equations are solved for several particular situations. Closed‐form analytical solutions are obtained for several basic problems: independent plane harmonic waves; radiation from a harmonically oscillating plane wall; radiation from a pulsating sphere; and the interior eigenvalue problem for a sphere, for the cases of both a rigid surface and a traction‐free surface. Finally, a series solution is obtained for the case of a plane wave impinging on a spherical inhomogeneity. This inhomogeneity is composed of poroelastic material having different properties from those of the infinite poroelastic medium in which it is embedded, and the incident wave may be composed of any linear combination of Biot “fast” and “slow” waves.

This paper investigates how the two‐surface plasticity theory predicts material behavior under nonproportional loading conditions. Closed‐form solutions are found for a thin‐walled tube subjected to combined internal pressure and axial load, and the tube response under cyclic linear stress paths is discussed. The investigation shows that according to the two‐surface plasticity theory, the response of the material will stabilize immediately during the first cycle. That is, the memory surface reaches its maximum size with a radius equal to the maximum effective stress and then remains unchanged thereafter, while the yield center translates along a line parallel to the stress path, thus always yielding a constant plastic strain growth rate. As a result, the two‐surface plasticity theory predicts that under any cyclic linear loading conditions, the response of the material can always be ratchetting, with no possibility of shakedown of any kind, which violates those aspects of material behavior that are generally deemed essential.

The present paper proposes two rules to develop a new kinematic hardening model. The first rule regulates the movement of the yield surface. It states that during loading, the yield center moves such that the kinematic hardening of the yield surface results in a plastic strain rate that an isotropic hardening model would also predict. The second rule introduces a new concept, the hardening center, and assumes that whenever the direction of the loading path undergoes abrupt change, the hardening center immediately shifts to the current center of the kinematic hardening yield surface. A tube problem is solved to demonstrate this new model. It is shown that this model is able to describe all the possible responses of the material, satisfy those aspects of material behavior that are generally deemed essential, and permit various forms of the plastic modulus to be used to correlate with experiments, while still being simple and mathematically tractable.

No‐choke flow in a trapezoidal channel with a change in bed elevation is analyzed assuming there is no change in channel sections before and after the transition. The energy and continuity equations are solved for the subcritical and supercritical approach‐flow regimes to obtain the maximum limiting dimensions of bed elevation, considering there is no head loss in the transition zone. Also, the ranges of upstream‐flow depths are obtained from this approach.