Journal of Engineering Mechanics

Many civil-engineering materials and novel materials developed in recent years exhibit a property of different elastic moduli in tension and compression. One such material is graphene, a wonder material, which has the highest strength yet measured. However, the dominant failure of structures composed of this high-strength material is often attributed to buckling problems. Investigations on buckling problems for structures with different moduli are scarce. To address this new problem, the present paper develops a semianalytical method for the critical buckling loads of variable–cross section slender rods with different moduli. Based on the variational principle, a differential equation of the deflection of these structures is derived for the first time. By developing a nonlinear iterative program and using the variational iteration method, the critical buckling loads are obtained. Then, buckling tests and numerical simulation were conducted for slender rods made from graphite with different moduli. By comparing the semianalytical results with the laboratory tests and finite-element analysis results, the semianalytical model proposed in this paper was demonstrated to be accurate and reliable. The conclusion can be drawn that the characteristics of different moduli of materials have a significant influence on the buckling stability of structures. Therefore, it may lead to unsafe results if the classic theory is still adopted to determine the buckling loads of those rods composed of a material having different moduli. The proposed model could provide a novel approach for further investigation of nonlinear mechanical behavior for structures with different moduli.

Surface wave methods exploit the dispersive properties of Rayleigh and Love waves to estimate the shear wave velocity profiles in vertically heterogeneous subsurfaces. Typically, they rely on a simplified one-dimensional (1D) analytical forward model where the lateral variation of the layer thickness is neglected and so is the fraction of the incident energy of the fundamental mode that is reflected or converted to higher modes. A theoretical study is presented that attempts to define an analytical model that overcomes the limitations of 1D forward models. In particular, we revisit properties of semianalytical approaches that aim at solving the dynamics of Love waves in laterally heterogeneous media made of a soft upper layer of varying thickness lying over an infinitely deep hard layer. The novel analytical model stems from a local-mode expansion of waves with laterally varying amplitudes, which allows for both reflections of the incident modes and coupling to higher modes. The best wave approximation stems from an action principle that leads to a coupled system of second-order ordinary differential equations (ODEs) for the wave amplitudes. Last, an application of this model and its validity are discussed.

With the aid of a new complete scalar potential function, an analytical formulation for thermoelastic Green's functions of an axisymmetric linear elastic isotropic half-space is presented within the theory of Biot's coupled thermoelasticity. By using the potential function, the governing equations of coupled thermoelasticity are uncoupled into a sixth-order partial differential equation in a cylindrical coordinate system. Then, by using Hankel integral transforms to suppress the radial variable, a sixth-order ordinary differential equation is received. By solving this equation and considering boundary conditions, displacements, stresses, and temperature are derived in the Hankel integral transformed domain. By applying the theorem of inverse Hankel transforms, the solution is obtained generally for arbitrary surface time-harmonic traction and heat distribution. Subsequently, point-load Green's functions for the displacements, temperature, and stresses are given in the form of some improper line integrals. For more investigations, the solutions are also determined analytically for uniform patch-load and patch-heat distributed on the surface. For validation, it is shown that the derived solutions could be degenerated to elastodynamic and quasi-static thermoelastic cases reported in the literature. Numerical evaluations of improper integrals, which have some branch points and pole, are carried out using a suitable quadrature scheme by Mathematica software. To show the accuracy and efficiency of numerical algorithm, a numerical evaluation from this study is compared with the results of an existing elastodynamic case, where excellent agreement is achieved.

Among all the proportions, the golden ratio has been taken into consideration for its geometrical and morphological properties, which can be found in a huge number of natural patterns, and therefore has been always considered as a model of beauty. Nevertheless, as discussed for the first time in the present paper, the cracking phenomenon of quasi-brittle materials also brings the golden ratio into play. In particular, such an irrational number appears when the average crack spacing of RC ties and beams is evaluated at different scales. This conjecture is corroborated by the results of a tension-stiffening model capable of predicting both the crack width and the crack spacing measured by the tests. In other words, it can be argued that the centrality of the golden ratio in the crack pattern of concrete members has profound physical meanings and reveals the existence of a size-effect law of crack spacing. The practical interest of this law lies in the possibility of predicting the crack pattern of large structures without knowing the material performances but by testing prototypes of the lower dimensions.

This study presents a numerical structural damage detection method using interstory drift–based structural acceleration measurements in the time domain. The coupling effect of the damage at different locations in the multiple-degree-of-freedom building system is eliminated by projecting the measured accelerations onto specific independent subspaces. The damage in a region will only affect the output of the designed monitor observing the substructure within the region. The severity of the damage is estimated numerically using a model-based prediction curve of stiffness change. Results obtained by the present numerical simulations for the illustrative examples are validated by experimental investigations using a 3-story aluminum frame structure and a 12-story concrete frame structure, and the numerical simulation results are compared with some representative experimental data with favorable correlations. Incorporation of the incomplete measurement, different structural materials, and different excitations into the method are studied and discussed.

The purpose of the present paper is to investigate the mechanical behavior of mild steel at quasi-static ($0.001\hspace{0.17em}{\mathrm{s}}^{-1}$) and different rates of dynamic tensile ($5–750\hspace{0.17em}{\mathrm{s}}^{-1}$) and compressive ($125–\mathrm{2,350}\hspace{0.17em}{\mathrm{s}}^{-1}$) strain rates. Quasi-static experiments are conducted on a universal testing machine to study the stress-strain behavior of mild steel. A hydropneumatic machine and a modified Hopkinson bar are used to investigate the dynamic tensile behavior of mild steel specimens at medium and high strain rates, respectively, whereas the specimens are tested on a split Hopkinson pressure bar to acquire understanding of the strain rate sensitivity of mild steel under dynamic compression. The effects of a pulse shaper and gauge length of the specimen in the dynamic compression tests are investigated. High-speed photography has been used to monitor the deformation of the specimen at high strain rate experiments. The applicability of the existing Cowper-Symonds and Johnson-Cook material models to represent the mechanical behavior of mild steel in a plastic zone is examined. Finally, the fractographs of the tested tensile specimens are studied using a scanning electron microscope.

A numerical path integral solution approach is developed for determining the response and first-passage probability density functions (PDFs) of nonlinear oscillators subject to evolutionary broad-band stochastic excitations. Specifically, based on the concepts of statistical linearization and of stochastic averaging, the system response amplitude is modeled as a one-dimensional Markov diffusion process. Further, using a discrete version of the Chapman-Kolmogorov equation and the associated first-order stochastic differential equation, the response amplitude and first-passage PDFs are derived. The main concept of the approach relates to the evolution of the response PDF in short time steps, assuming a Gaussian form for the conditional response PDF. A number of nonlinear oscillators are considered in the numerical examples section including the versatile Preisach hysteretic oscillator. For this oscillator, first-passage PDFs are derived for the first time to the authors’ best knowledge. Comparisons with pertinent Monte Carlo data demonstrate the reliability of the approach.

Linear elastic-perfect plasticity using the Mohr-Coulomb yield surface is one of the most widely used pressure-sensitive constitutive models in engineering practice. In the area of geotechnical engineering, a number of problems, such as cavity expansion, embankment stability, and footing bearing capacity, can be examined using this model together with the simplifying assumption of plane strain. This paper clarifies the situation regarding the direction of the intermediate principal stress in such an analysis and reveals a unique relationship between hydrostatic pressure and the principal stress ratio for Mohr-Coulomb and Tresca perfect plasticity under those plane-strain conditions. The rational relationship and direction of the intermediate principal stress are illustrated through both material-point and finite-element simulations. The latter involves the analysis of a rigid strip footing bearing onto a weightless soil and the finite-deformation expansion of a cylindrical cavity.

This study is devoted to the investigation of the effects of inertial, centripetal, and Coriolis forces on the dynamic response of a simply supported beam with a single crack under moving mass load. As in the case of beams without a crack, it is shown that these forces must be considered in the analysis. The inertial, centripetal, and Coriolis forces are appreciably affected by the mass and the velocity of the moving load. The response of the system is obtained in terms of Duhamel integral. The differential equation that involves a nonlinearity on its right side is solved via an iterative procedure. The results are exemplified for various values of the variables.

Different phenomena in mechanics often possess sharp gradients in time. In the analysis of such phenomena, traditional time integration schemes often require a very small time increment. In this paper, the equations of motion and the compatibility equations of rate of deformations, which were used to form the mixed Lagrangian formulation (MLF), are integrated with respect to time. This produces the momentum equations and the compatibility of deformations equations. The use of these equations in a framework similar to the MLF enables an accurate and stable analysis of various discontinuous phenomena using relatively large time increments.

With crosswind actions, the wind loads on trains can change dramatically as the trains pass through the wake of bridge towers or when two trains pass each other, which will influence the stability of trains and the comfort of passengers. Taking advantage of the developed testing system of a wind tunnel test rig with moving train models, a three-car train model and a single-car train model were used to simulate rail vehicles and road vehicles, respectively. Sudden changes in the aerodynamic forces were measured when the train was passing through the bridge tower or when two trains were passing each other, and the effects of wind speed, train speed, rail positions of trains, and train types on the train’s aerodynamic coefficients were investigated. The analysis showed that for these studied cases, the aerodynamic coefficients of trains all have sudden changes. However, train-induced wind can weaken the sudden change of a train’s aerodynamic coefficients and lengthen the sudden-change region of wind shielding. The effect of sudden changes of wind loads acting on the road vehicle is more obvious than that on the rail vehicle.

A dynamic cylindrical cavity expansion model is presented herein to predict the penetration of concrete targets subjected to impact by conical-nosed projectiles at normal incidence. It is assumed that cavity expansion in an infinite concrete target produces three response regions: elastic, cracked, and comminuted regions. To allow for compressibility or dilatancy of the material in the comminuted region, a dilatant-kinematic relation is introduced in this paper. A procedure is first given to calculate the radial stress at the cavity surface, and then, a numerical method is used to calculate the results of penetration with friction being taken into account. It transpires that the present model predictions are in reasonable agreement with the available experimental data.

In this paper, a three-dimensional (3D) numerical simulation is performed on a stationary arc to study the effect of torch angles in gas tungsten arc welding (GTAW) of SS304 stainless steel. A comparison has been made to investigate 90 and 70° torch angles and analyze the effect on arc and weld pool shape. Current density, heat flux, and gas shear stress are calculated in the arc region and are used as input to the workpiece to determine the weld pool. Also, both buoyancy and Marangoni shear affect the weld pool shape and are taken into account. The computed and experimental results are observed as symmetric for the 90° torch angle. For the 70° torch angle, current density and hence the heat flux from electron contribution is found to be the maximum behind the electrode tip in the welding direction. Heat flux from conduction and convection is found to be the maximum ahead of the electrode tip in the welding direction. This makes the maximum of total heat flux symmetric along the arc center. Heat flux from conduction and convection decreases as the torch angle decreases resulting in a shallow weld pool. The nonsymmetric $w$-shaped weld pool is developed by the combined effect of the gas shear and Marangoni convection. It is found that for the 70° torch angle, the weld pool becomes nonsymmetric, shallow, and wide ahead of the electrode tip in the welding direction. The numerical weld pool shapes are verified through experiments.

Thermal analysis is one of the main components in the design and construction of roller-compacted concrete dams. In this article, the heat-fluid coupling method is introduced to perform the thermal analysis of a pipe cooling system in mass concrete structures. Several typical models and examples are selected to verify the performance of this method. The proposed method is then applied to a roller-compacted concrete gravity dam called the Guandi Dam, which is still under construction in China. The actual climatic conditions and thermal properties of the materials are considered in this analysis. The temperatures determined by numerical simulation are in good agreement with the actual monitored values. The simulation results indicate that the proposed method can accurately simulate the cooling pipe state, the temperature rise along the water flow, and the effect of directional changes of flow in temperature distributions. Moreover, cracking is shown to more likely develop in concrete near the cooling pipes, mainly from the extreme temperature gradient and fluctuation during the cooling process of concrete. The untimely application of water cooling systems during hot seasons will induce extreme tensile stresses and increase the risk of cracking.

In this paper, complex variable boundary element method (CVBEM) is used for the solution of de Saint-Venant’s torsion problem in homogenous isotropic elastic beams with a generic cross section, considering a complex potential function related to the stress field. Generally, CVBEM, when used for torsion problems, leads to evaluation of the stress field divided by the twist rotation. The latter has been evaluated by performing a domain integral. In this paper, taking advantage of the aforementioned potential function, it is possible, by applying CVBEM, to evaluate the complete stress distribution and the twist rotation of the cross section and the torsional stiffness factor, performing line integrals only. Numerical results were compared with both analytical and numerical results proposed by other authors, thus assessing the validity of the proposed method.

Multivariate random processes are usually simulated by the spectral representation method (SRM). According to the matrix for decomposition, the SRM has two main types, that is, the SRM based on the decomposition of the power spectral density (PSD) matrix denoting the PSD matrix-based SRM, and the SRM based on the decomposition of the coherency matrix denoting the coherency matrix based-SRM. The stochastic errors of the PSD for the PSD matrix-based SRM have been given. This paper presents the stochastic errors of the PSD for the coherency matrix-based SRM, and makes a comparison of these errors for the PSD matrix-based SRM. For the random amplitudes formulas and random phase formula and Cholesky decomposition method, the stochastic errors of the PSDs for the PSD matrix-based SRM are the same as or the coherency matrix-based SRM, whereas for the random phases formula and eigendecomposition method and random phases formula and root decomposition method, they are different. However, the differences are slight when taking into account the sum of the PSD functions’ stochastic errors.

The vibration of a two-section column under gravity effects is studied using an efficient initial value method. The problem is governed by the length and area ratios of the two sections in addition to gravity. For the standing column, the stability boundaries show looped properties. The first three frequencies for both standing and hanging two-section columns are determined. For given total volume or mass, there exists an optimum length and area ratios of the two sections for the highest fundamental frequency.

Although stress-strain models for the cyclic behavior of clay have been studied extensively, the models have not been examined from the point of view of the intercluster contact level. In the current paper, we extend the recently developed micromechanical approach to model the cyclic behavior of clay. Undrained triaxial tests under one-way and two-way cyclic loadings on normally consolidated and overconsolidated clay are simulated to evaluate the applicability of the approach. The computed evolution of local stresses and local strains at intercluster scale due to externally applied cyclic loads are also discussed.