Journal of Engineering Mechanics

This study solves the three-dimensional (3D) dynamic interaction problem between simply supported Timoshenko beams and vehicles by using theoretical equations. The model includes intermediate supports, so train-rail-soil interaction can be analyzed. The vehicle equations are formed by using a matrix method by the assemblage of spring-dampers and rigid links, and the bridge formulations are decoupled using the modal method. The Newmark method is then used to analyze these vehicle-bridge equations. Variable speed, road irregularities, vehicle eccentricities, and multiple vehicles are considered. The comparison of the beam displacements between the current and finite-element methods indicates that the accuracy of this method is acceptable.

As a global problem for reinforced concrete structures located in a chloride and/or carbon dioxide–laden environment, reinforcing steel corrosion in concrete costs approximately $100 billion per annum worldwide for maintenance and repairs. The continual demands for greater load for infrastructure exacerbate the problem. This paper attempts to examine the whole process of longitudinal cracking in concrete structures under the combined effect of reinforcement corrosion and applied load. A model for residual stiffness of cracked concrete is derived using the concept of fracture energy. It is found that the corrosion rate is the most important single factor that affects both the time-to-surface cracking and crack width growth. The paper concludes that the developed model is one of very few theoretical models that can predict with reasonable accuracy the crack width on the surface of reinforced concrete structures under such a combined effect. The developed model can be used as a tool to assess the serviceability of corrosion-affected concrete infrastructure. Timely repairs have the potential to prolong the service life of reinforced concrete structures.

A viscoelastoplastic continuum damage model has been derived and characterized for describing the behavior of asphalt concrete subject to an all-around confining pressure and deviatoric tension loading. The primary application of this model is to better understand the fatigue damage process in asphalt concrete pavements. As a result of this application and because of the bimodal behavior of this material outside the linear viscoelastic range, the modeling effort has focused primarily on the tensile characteristics. The developed model uses the elastic-viscoelastic correspondence principle, work-potential theory with damage mechanics, time-temperature superposition with growing damage, and strain-hardening viscoplasticity to arrive at a constitutive relationship. This relationship considers the experimentally observed transformation of asphalt concrete from an initially isotropic material to a transversely isotropic one by using a single-state parameter and three different damage functions. The relationship between these damage functions and the more conventional values of the modulus and Poisson’s ratio is shown to gain further physical insight into the material. Characterization of the model is performed by using constant crosshead rate monotonic tension tests with and without confinement and low strain temperature and frequency sweep complex modulus tests. The model is found to adequately describe the response of asphalt concrete under constant crosshead rate tension tests at various rates and two temperatures, the conditions that are not used in characterization.

The formulation of and solution to the problem of the free vibrations of a geometrically nonlinear column, supported at the loaded end by a spring with linear characteristics, are discussed in the paper. Transversal free vibrations around a rectilinear form of static equilibrium are considered in this work. The considered system was subjected to a generalized load with a force directed toward the positive pole. The boundary problem was formulated using Hamilton’s principle and the straightforward expansion method. A series of numerical simulations were conducted using the mathematical model. The characteristic curve in the plane of load versus natural frequency was assigned to different parameters of the considered system. Experimental research was carried out to confirm the accuracy of the assumed mathematical model. The research relied on modal analysis and the determination of the natural frequency of the system for chosen values of an external load.

A postbuckling analysis for a shear-deformable anisotropic laminated cylindrical panel of finite length is presented, subjected to external lateral pressure based on a boundary-layer theory of shell buckling. The material properties of each layer of the panel are assumed to be linearly elastic. The governing equations are based on a higher-order shear-deformation shell theory with a von Kármán–Donnell type of kinematic nonlinearity and including extension/twist, extension/flexural, and flexural/twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect moderately thick, anisotropic laminated cylindrical panels under different values of panel parameters and stacking sequence. The new finding reveals that a circumferential stress exists along with an associate shear stress and twisting when the moderately thick anisotropic laminated cylindrical panel is subjected to external lateral pressure.

This paper studies the aerodynamic stability of a tensioned, geometrically nonlinear orthotropic membrane structure with hyperbolic paraboloid. The aerodynamic force acting on the membrane surface is determined by the potential flow theory in fluid mechanics and the thin airfoil theory in aerodynamics. The interaction governing the equation of wind-structure is established on the basis of large-amplitude theory and the D’Alembert principle. Then, under the circumstance of single-mode response, the Bubnov-Galerkin approximate method is applied to transform the complicated interaction equation into a system of second-order nonlinear differential equations with constant coefficients. Through judging the stability of the system characteristic equation, the critical velocity of divergence instability is determined. Different parameter analysis shows that the orthotropy and geometrical nonlinearity is significant for preventing destructive aerodynamic instability in membrane structures. Compared to the planar model, there is a little inconsistency about the divergence instability regularities in the hyperbolic paraboloid model.

This study presents a combined numerical and experimental investigation of the free-surface variation and induced fluid motion for a solitary wave propagating past a submerged cavity (or trench). The formation of vortices and the trajectories of fluid particles showing the transport of fluid content within the cavity zone are examined. A two-dimensional viscous flow is simulated by solving the stream function and vorticity equations using the finite-analytic method. Equations of free-surface boundary conditions are discretized by a two-step finite-difference scheme. To obtain more detailed motions in a cavity, a transient boundary-fitted grid system with locally refined grids is adopted. Experimental measurements of the free-surface elevations and the visual observations of the vortex motion were carried out to compare to the numerical solutions. The simulated free-surface elevations and fluid particle motion at various times are found to agree reasonably well with measurements and recorded observations. The formation and subsequent growth of a pair of recirculating vortices around the front corner of the cavity are clearly simulated by the present model. The effects of cavity size and incident-wave height on the flow patterns and the transport displacement of the fluid particles along the vertical and horizontal directions are analyzed. The results indicate that the greater the incident-wave height, the larger the values of the horizontal and vertical transporting distances. With an increase of cavity length, the strength of induced up-rolling vortices and the amount of downstream transporting fluid particles increases. However, the depth of the cavity has an insignificant influence on the height of the up-rolling vortices.

After any terrorist attack or natural disaster, more research focuses on the dynamic response of structures under unexpected loads. Extreme loads such as explosions and earthquakes can cause enormous human and infrastructure losses. Rotating machinery can also routinely experience internal contact. Unpredicted failure may be caused by vibration-induced impact and is highly dangerous for both equipment and safety. For these reasons, the investigation of these beamlike structures under extreme loads is of importance. In this study, an Euler-Bernoulli beam with adjustable boundary conditions and variable impact is numerically studied under shock loading. Modal analysis and discrete time step methods are programmed in MATLAB to obtain linear analytical solutions. The influential parameters of structural stiffness, material modulus, contact stiffness, contact location, and damping ratio are examined. Their effects on different boundary conditions will be contrasted as well. This efficient model contributes to a better fundamental understanding of impact and will serve as a building block on which to introduce additional phenomena, such as multiple point contact, large deflection theory, and plastic material behavior.