Journal of Engineering Mechanics

The static and dynamic stability analysis of a beam subjected to a laterally distributed follower force is presented. The effect of the uniformly distributed follower force is considered in the work and energy terms, and the equations of motion are obtained using the extended Hamilton’s principle. Applying Galerkin’s technique, the resulting equations are transformed into a general eigenvalue problem. The effects of several physical parameters, such as mass centroid offset, radius of gyration of the cantilever, fundamental frequencies ratio, and magnitude of the distributed follower force, are investigated. Numerical results reveal that the load increment may cause either static or dynamic instability types.

This paper presents an elastic solution for one microvoid embedded in an adhesive layer close to a stiff bonding surface, which can be approximated as a semiinfinite domain with a fixed boundary. A Green’s function for a force in a semiinfinite solid with a fixed boundary condition is used to derive the stress field. By using the equivalent inclusion method, the microvoid has been replaced by the adhesive, but an eigenstrain is introduced to simulate the material mismatch. Through the stress equivalent condition, the eigenstrain is solved, and the stress concentration caused by the microvoid is evaluated considering the stress transfer caused by shear and tensile forces. A uniform normal stress and uniform shear stress are applied in the far field. The formulation is verified with finite-element simulation and can be extended to the case of multiple microvoids.

A simple and efficient procedure for the nonlinear analysis of frames is presented, which includes the elastoplastic behavior through the tangent elastoplastic stiffness matrix and the yield function affected by damage in each plastic beam end. An actual experiment and its modeling with finite-element software are used for the verification of the approach. An example is solved and compared with the finite-element study and the classic plastic method. The proposed method can be used to simply and accurately evaluate the collapse load of frames, considering a fully plastic nonlinear analysis and a bilinear constitutive law with hardening and damage.

An analytical solution in the realm of two-dimensional linear elasticity theory is presented for the soil reaction around a laterally loaded cylindrical pile segment surrounded by an annular zone of soft elastic material, under plane strain conditions. To this end, a seminal model is extended to account for different boundary conditions at the interfaces separating the annular zone from the pile and the outer material. Analytical closed-form solutions are derived for the stiffness of the system and the stress and strain fields in the annular zone, for the following combinations of shear boundary conditions: (1) perfectly bonded interfaces, (2) perfectly smooth interfaces, (3) perfectly bonded inner and perfectly smooth outer interface, and (4) perfectly smooth inner and perfectly bonded outer interface. It is shown that for both very thin and very thick soft zones, the stiffness of the system becomes independent of shear boundary conditions. The predictions of the model are compared against those of two models based on strength-of-materials theory. Three-dimensional effects and numerical simulation aspects are discussed.

An approximate solution to the nonlinear problem of an elastic stiffener welded to an elastic plate is obtained in the form of a finite sum of Chebyshev polynomials. To an exact first-order approximation, the deformed length of the stiffener is proved to be greater than its undeformed length. Other conclusions show that the longitudinal force decreases when elongation of the stiffener is included, whereas the concentration coefficient, defined in terms of the singular behavior of the interactive force between the stiffener and the plate that occurs at either end, decreases when the elongation is sufficiently large.

Elastic cables are structural elements with a one-sided constitutive law (compression is not allowed) that obtain their equilibrium configuration by adjusting their shape to satisfy static equilibrium. The loading of a cable is applied through body-type forces and through appropriate boundary conditions at its ends. The classic cable constitutive law is easily implemented by assuming small strains and a coordinate system that follows the rigid-body motion. This approach was selected in the present analysis in the context of micropolar elasticity. The analysis is two-dimensional (2D) and static. The results indicate the important role of the couple-type body forces in the cable’s deformation. This, in turn, is very advantageous in the design of smart cables and textiles that can utilize electromagnetic fields to actuate couple body forces and in this way exert control on their deformation.

This study proposes a procedure for determining the viscoelastic responses of multilayered asphalt pavements. A computer code is developed to determine the elastic responses of pavements subjected to uniform circular pressures according to the layered elastic theory. The results from the code were successfully verified. The viscoelastic behavior of asphalt concrete is characterized using a complex modulus model. Relaxation of asphalt concrete is obtained by replacing the corresponding variables in the complex modulus model and substituting the elastic solution to obtain the step response function in the transformed domain. The time-domain response is solved through numerical transform inversion and is then expressed in the form of an exponential series with the relationship between the exponential series coefficients and the step responses at zero and infinite time being satisfied. The response as a result of an arbitrary loading history is solved using an incremental formulation of the convolution integral, taking advantage of the exponential series representation of the step response function. A discrete formulation of the linear superposition principle is used to solve the response under a moving load. The computer code developed for elastic analysis is extended to implement the viscoelastic analysis procedure and the results are in good agreement with those obtained from finite-element analyses. The procedure developed in this study provides an effective tool for pavement analysis and design.

Mixed scaling that includes inner and outer variables is performed on open-channel flow over gravel and cobbles. A similarity analysis is performed following classification of the flow as an equilibrium turbulent boundary layer using the asymptotic invariance principle. A mixed scale that accounts for the variation of turbulent length in the vertical direction is used to parameterize the external boundary impact on the flow for the logarithmic and outer layers. The resultant scale uses free-stream velocity, hydraulic radius, and bed particle size in which 84% of the sediment is finer. The results are consistent with empirical gravel-bed river research and applications, and nicely include the variation of the turbulent flow structure into the scaling. The results are verified using data from gravel- and cobble-bed flumes and rivers and by comparison with earlier methods. A single coefficient, semitheoretical model collapses laboratory and field data well. An integral approach is applied to allow the asymptotic invariance principle equilibrium to be more applicable in future practice.

The author has discovered several errors that are not typographical in a famous governing differential equation and its general solution. The purpose of the current study is to reveal the errors, correct them, and present some numerical results.