Journal of Engineering Mechanics

An interactive zonal numerical method has been developed for the prediction of free surface flows around surface-piercing bodies, including both viscous and nonlinear wave effects. In this study, a Laplace solver for potential flow body-wave problems is used in conjunction with a Reynolds-averaged Navier-Stokes (RANS) method for accurate resolution of viscous, nonlinear free surface flows around a vertical strut and a series 60 ship hull. The Laplace equation for potential flow is solved in the far field to provide the nonlinear waves generated by the body. The RANS method is used in the near field to resolve the turbulent boundary layers, wakes, and nonlinear waves around the body. Both the kinematic and dynamic boundary conditions are satisfied on the exact free surface to ensure accurate resolution of the divergent and transverse waves. The viscous-inviscid interaction between the potential flow and viscous flow regions is captured through a direct matching of the velocity and pressure fields in an overlapping RANS and potential flow computational region. The numerical results demonstrate the capability of an interactive RANS/Laplace coupling method for accurate and efficient resolution of the body boundary layer, the viscous wake, and the nonlinear waves induced by surface-piercing bodies.

Marked differences have been observed between the global and local responses of tensile steel bars—the first traditionally defined by considering average strains (displacement of the bar's ends divided by its undistorted length), and the second obtained by local strain measures through high performance resistance strain gauges. This distinction highlights the peculiarities of various qualities of steel normally employed as reinforcement in concrete. In particular, the phenomenon of serrated deformation at yielding (the Portevin-Le Chatelier effect) and the peculiarities of this metastable state, when unloading sequences are performed, will be discussed. It will be shown how the presence of ribs can influence the local behavior and how this is reflected in the gross response. In the analysis, the importance of strain hardening in improving the ductility performance of steel bars is observed.

This paper focuses on the relationship of the stress intensity factor (SIF) between biaxial compression K_II and uniaxial compression K_II0. This relationship is very important for the study of biaxial failure criterion because if this relationship can be found, the biaxial failure criterion can be easily set up by use of the uniaxial failure criterion, which is very simple (K_II0 ≤ K_IIC or σ ≤ σ_C). For this purpose, a new model for a brittle material plate containing an inclined crack in compression, based on the theoretical analysis and the calculated results of the boundary collocation method (BCM), is proposed. By using this model and the BCM results, the following topics are first discussed: (1) The orientation of the most unfavorable crack; and (2) the stress condition for a crack with zero SIF value. Second, the relationship between K_II and K_II0 is found and described in a simple formula. Finally, a new biaxial failure criterion, which is expressed in terms of the principal stresses, is developed, and several conclusions are presented.

The pseudodynamic thermoelastic response of functionally graded ceramic-metal cylinders is studied. This paper presents the finite-element formulation of the 1D, axisymmetric heat transfer equation and the thermoelastic radial boundary value problem. A two-step solution of the governing equations of thermoelasticity is presented. Thermoelastic coupling is considered by taking into effect the temperature dependence of the constitutive equations. Nonlinearity due to the temperature dependence of the material properties of the constituent ceramic and metal is considered. A parametric study with respect to varying volume fraction of the metal is conducted. Temperature and radial/hoop stress distributions arising due to rapid heating of the inner surface of the functionally graded cylinder are presented.

Pseudo-strain-hardening behavior of quasi-brittle materials reinforced by discontinuous, aligned fibers subjected to uniaxial tension is studied in this paper. An R-curve was used to describe transverse cracking of fiber-reinforced composites. The equivalent inclusion method and Mori-Tanaka theory were used to derive the strain energy release rate of the composites. The proposed model takes into account the influence of fiber distribution. When properties of fiber and matrix are known, the proposed model is capable of predicting whether or not a composite will fail with a single crack or multiple cracks. If a composite fails due to multiple cracks, the model can further predict its pseudo-strain-hardening behavior after the formation of the first transverse crack. The theoretical calculation reasonably matched the experimental results.

A finite-element-based linear elastic fracture mechanics analysis of the pullout of headed anchors is presented. The anchor is modeled as a vertically loaded crack of diameter c, embedded at a depth d, with a rigid upper surface, and traction-free lower surface. The fracture toughness and Poisson's ratio of the surrounding matrix are K_Ic and ν, respectively. For selected values of d/c, the mode-I stress intensity factor is calculated for each increment of the crack growth, which emanates from the edge of the anchor, and follows the direction of zero mode-II stress intensity factor. The stress intensity factors are used to calculate the ultimate load P_u, which is written as P_u = g(d/c, ν)d^3/2K_Ic. For ν = 0.2 and relatively large values of d/c, g = 2.8 for axisymmetric anchors and g = 1.2 for plane strain anchors.

Crack damage is commonly observed in cementitious granular materials. Previous analytical models based on continuum mechanics have limitations in analyzing localized damages at a microscale level. In this paper, a micromechanics approach is adopted that considers a contract law for the interparticle behavior of two particles connected by a binder. The model is based on the premises that the interparticle binder initially contains microcracks. As a result of external loading, these microcracks propagate and grow. Thus, binders are weakened and fail. Theory of fracture mechanics is employed to model the propagation and growth of the microcracks. The contact law is then incorporated in the analysis for the overall damage behavior of material using a discrete element method. Using this model, the stress-strain behaviors under uniaxial and biaxial conditions were simulated. A reasonable agreement is found between the predictions and experimental results.

A solution method that can calculate the eigenproblem for large structures with multiple or close natural frequencies is presented. The method is formulated by the accelerated Newton-Raphson method for the transformed problem. The method can calculate the natural frequencies and mode shapes without any of the numerical instability that may be encountered in the inverse iteration process with a shift of the well-known methods, such as the subspace iteration method or the determinant search method, which have been widely used for solving an eigenproblem. The efficiency of the method is verified by comparing convergence and solution times for numerical examples with those of the subspace iteration method and the determinant search method.

Exact explicit eigenvalues are found for compression buckling, hygrothermal buckling, and vibration of sandwich plates with dissimilar facings and functionally graded plates via analogy with membrane vibration. These results apply to simply supported polygonal plates using the first-order shear deformation theory and the classical theory. A Winkler-Pasternak elastic foundation, a hydrostatic inplane force, hygrothermal effects, and rotary inertias are incorporated. Bridged by the vibrating membrane, exact correspondence is readily established between any pairs of eigenvalues associated with buckling and vibration of sandwich plates, functionally graded plates, and homogeneous plates. Positive definiteness is proved for the critical buckling hydrostatic pressure and, in the range of either tension loading or compression loading prior to occurrence of buckling, for the natural vibration frequency.

The analysis of adhesive-bonded joints using a closed-form high-order theory (CFHO theory) is presented, and its capabilities are demonstrated numerically for the case of single lap joints with and without a “spew-fillet.” The governing equations based on the CFHO theory are presented along with the appropriate boundary/continuity conditions at the free edges. The joints consist of two metallic or composite laminated adherends that are interconnected through equilibrium and compatibility requirements by a 2D linear elastic adhesive layer. The CFHO theory predicts that the distributions of the displacements through the thickness of the adhesive layer are nonlinear in general (high-order effects) and are a result of not presumed displacement patterns. The spew-fillet is modeled through an equivalent tensile bar, which enables quantification of the effects of the spew-fillet size on the stress fields. Satisfactory comparisons with two-parameter elastic foundation solution (Goland-Reissner type) results and finite-element results are presented.

The size effect on the nominal strength of steel-concrete composite beams caused by shear failures of connectors such as welded studs is analyzed by two different approaches: (1) In this paper (Part I) by a fracture type analysis of the energy release caused by propagation of the zone of failed connectors along the beam; and (2) in a companion paper (Part II) by a direct solution of the load-deflection diagrams from the differential equations of beam bending theory. The former can capture the large size asymptotic size effect and yields simple formulas suitable for design, whereas the latter can provide the solution for small beam sizes for which the connector failure zone is not much shorter than the span. The force-slip diagram of the connectors exhibits postpeak softening, which engenders an energetic size effect on the nominal strength of the connector. If the connectors are geometrically scaled with the beam, the size effect in the shear failure of connectors (mesoscale) is superimposed on the size effect due to propagation of the zone of connector failures along the beam (macroscale), producing in the beam as a whole a compound size effect that is stronger than in linear elastic failure mechanics. If the connector sizes and the interface area per connector are not scaled with the overall dimensions of the composite beam, the size effect law proposed by Bažant in 1984 is applicable. Comparisons with available test results are presented in Part II.

After presenting an energy analysis of size effect in the first part of this study, the second part gives a solution by integrating the differential equations of beam bending theory, coupled with a softening force-slip law for the interface. This analysis is more accurate than the previous energy analysis but does not yield simple explicit formulas for the size effect. The results generally support the simple conclusion from energy analysis. They do not disagree with the available limited experimental evidence; however, measurements of size effect in geometrically scaled composite beams seem unavailable. Further tests are needed.

Based on the Mindlin-Deresiewicz displacement field solution, a simple method is presented to obtain the force-displacement relationship for a contact between two elastically similar bodies. The bodies are initially pressed together along the normal to their mutual tangential plane and subsequently loaded by a monotonically increasing tangential force acting at an angle to the axes of the contact ellipse. The results are derived based on both no-slip and microslip assumptions, and compared with the available solutions.

The dynamic instability of an elastically supported Timoshenko beam under the constant velocity traveling inertia load has been investigated. The regions of dynamic instability are determined for different values of the elastic foundation constant. Floquet theory is utilized to study the parametric regions of instability, which are displayed in graphical form.