Journal of Engineering Mechanics

Presented is a study on energy dissipation in dynamic inelastic systems due to material inelasticity, viscous damping, and algorithmic damping. Formulation for plastic dissipation is based on thermodynamics, with consideration of plastic free energy. Computation of viscous energy dissipation of the Rayleigh type is developed and discussed. Energy dissipation due to algorithmic damping is discussed as well, and compared with the previous two, physical energy dissipation mechanisms. Energy dissipation due to all three dissipation mechanisms is illustrated and discussed in relation to single-element tests and dynamic wave propagation problems.

Despite rapid development in computational fluid dynamics, semiempirical analyses based on parameters identified from spring-mounted sectional models are still widely used to examine wind-induced effects on bridges. In addition, wind tunnel results from full-bridge aeroelastic models, viewed as the most comprehensive representations, are typically a final check for wind design of long-span cable-supported bridges. There are several well-known limitations associated with conventional wind tunnel testing of both sectional and full-bridge models. For example, structural nonlinearities and large deformations are difficult to simulate in sectional models, and only a limited number of modes can be accurately simulated in full-bridge aeroelastic models. To advance aeroelastic modeling of flexible bridges in the wind tunnel, a slightly different version of the real-time hybrid simulation (RTHS) techniques, frequently used in various branches of engineering, is developed here. Specifically, the skeleton of the sectional or full-bridge model, characterizing the dynamic properties (e.g., mass, damping, and stiffness of the structure), is numerically simulated using computational structural dynamics, while its skin, characterizing the aerodynamic and aeroelastic properties, is physically modeled in the wind tunnel. Aerodynamic inputs (gusts) are applied directly on the skin in the wind tunnel, while aeroelastic inputs (motions) are represented by the simulation outputs of the bridge skeleton. On the other hand, the dynamic inputs to the bridge skeleton are acquired from the measured forces (and moments) on the bridge skin. The interactions between the skeleton and skin of the bridge are accomplished through a system consisting of sensors, a network of electromagnetic actuators, and controllers. The time history of the wind-induced bridge responses can be obtained at the end of the proposed real-time aerodynamics hybrid simulation (RTAHS). The feasibility of the RTAHS methodology is demonstrated by a numerical example involving both linear and nonlinear wind-induced forces on the bridge deck.

An investigation concerned with the dynamic response of a composite structure to a moving load on its uppermost rough surface has been carried out analytically. The composite structure is comprised of an incompressible fluid-saturated transversely isotropic poroviscoelastic layer of finite width imperfectly bonded with an underlying transversely isotropic viscoelastic semi-infinite medium. Closed-form expressions of induced stresses (shear and normal) and induced pore pressure are established analytically using the appropriate boundary conditions. The established results are validated with the preestablished results. The substantial effects of influencing parameters—porosity; frictional coefficient; shear and transverse imperfection (bonding) parameters; shear viscosity, volume viscosity, and extensional viscosity parameters; and the vertical depth (from the free surface) of the medium—on the induced stresses (shear and normal) of the layer and semi-infinite medium and the induced pore pressure of the layer of the considered composite structure are demonstrated graphically through numerical computation. Moreover, a comparative examination of distinct cases of the problem serves as the salient feature of the study and contributes better analysis than found in the literature.

Theoretical and laboratory studies were presented for the water column oscillation in a vertical tube partially immersed in a reservoir. Three types of oscillations were studied, with the top of the tube being fully open (free oscillation), the top capped with a hose for ventilation (damped oscillation), and the top fully capped (capped oscillation). Governing equations of the oscillations were established and good estimations of the oscillatory characteristics were obtained. In the experiments, the periods of the free oscillations and the damped oscillations were close, whereas the period of the capped oscillations was shorter, which was due to the effect of the trapped air in the tube above the water column. The damped oscillation had quicker decay than the free oscillation. Due to the finite size of the reservoir used in the experiments, the recorded oscillations were the superposition of the water column movement in the vertical tube and the surface wave of the reservoir. The former dominated the oscillation at the beginning, whereas the latter became dominant in the end. By approximating the two components as sinusoidal waves, the beats in the recorded oscillations were estimated, and the results were in good agreement with the experiments.

The concept of vacuum lighter-than-air vehicles is a generalization of the idea behind floating vehicles, which enclose a volume of gas that is lighter than air. In particular, the enclosed volume is completely evacuated. From a pure geometrical perspective, the sphere is appealing because of the symmetry properties and the best surface-area-to-volume ratio. However, the pressure differential between the external fluid and the internal vacuum imposes significant compressive forces, which put the structure at risk of instability due to buckling. At the present technology level, no available material can be used to create a shelled sphere with a relatively large radius-to-thickness ratio and an internal vacuum without buckling. This work explored the concept of a star polyhedron obtained from the pentakis icosidodecahedron by adding pockets on the triangular surfaces. Under the assumption of elastic linear isotropic material and using commercial software ABAQUS version 2016, it was demonstrated that the stability performance, postbuckling response, type of buckling and its location, and mesh convergence properties are significantly affected by the ratio of the radius of the circumscribed sphere to the shell thickness. The structure exhibits sensitivity to the geometric imperfections, as assessed by using different amplitudes and types of imperfections. However, it was demonstrated that the proposed shape presents a true buckling load approximately twice that of a sphere, indicating that the adopted geometry is less sensitive to manufacturing imperfections than is a circumscribed sphere. Using the Buckingham $\mathrm{\Pi }$ theorem, an empirical formula predicting the buckling load (eigenvalue analysis of the perfect structure) was derived and related to the corresponding relationship valid for spherical shells.

The possibility of testing irregular lumps under the point load strength test (PLST) was investigated theoretically and experimentally. In particular, a new analytical solution for stress distribution within a sphere under the diametral PLST was obtained by incorporating the classical solution with the Hertz contact stress. The stress distribution within the spheres was then compared with those of cylinders under the axial and diametral PLST, which were calculated by using the analytical solutions derived by the authors in 1999 and 2001, respectively. Numerical results showed that, if the dimensions of the spheres and cylinders are comparable, the stress distributions, especially the tensile stress distributions along the axis of loading within spheres and cylinders, are similar, both in terms of the magnitude and the pattern of stress distribution. The point load strength index was approximately the same for all three kinds of specimens. In addition, over 100 plaster specimens with different shapes (spheres, cylinders, hexagons, and cubes), three sizes (50, 60, and 75 mm), and two different strengths were tested using the axial or diametral PLST. The theoretical predictions agreed well with the experimental results. Thus, first by means of theoretical analysis, it was concluded that the point load strength index is not sensitive to the exact shape of the specimen, and secondly, it was further verified by experiments on plaster specimens.

Strand-based wood and bamboo composites are a class of structural materials which are increasingly being used in the construction industry. These bio-based composites consist of orthotropic wood or bamboo strands bonded together with small amount of resin (glue). In order to estimate the effective properties of such composites, a specific micromechanical approach from the literature, called the “morphological approach” (MA), is employed. The accuracy of the MA in estimating the effective elastic and viscoelastic properties of an idealized unit cell of a special strand-based wood composite product, a parallel strand lumber (PSL) beam, is investigated using numerical reference solutions obtained by full-field finite-element (FE) simulations. The MA is also compared to analytical micromechanics equations previously proposed by the authors for predicting the effective properties of strand-based composites. MA results are shown to be closer to the numerical reference solutions than previous analytical estimates. Thus, the MA can be used as a valuable alternative for computing the effective properties of strand-based composites with rectangular shaped orthotropic strands. More generally, it could be used in efficient multiscale analysis of large structural composites made from various wood and bamboo strands using less restrictive unit cells. From a fundamental viewpoint, this paper shows a novel application of the MA to orthotropic reinforcements in a Prony series–based viscoelastic matrix.

Longitudinal elastic wave propagation characteristics of a proposed inerter-in-lattice metamaterial (ILM) were investigated. Its local resonance emerges from the additional degree of freedom induced by a series combination of a spring element and an inerter in the lattice. The presence of inerters provides a means to reduce expenses in terms of the associated mass compared with locally resonant metamaterials (LRMs). Parametric studies of the number of cells, mass ratios, and damping ratios of finite ILM lattices were conducted. Those parameters affect not only widths and depths of attenuation zones but also resonant responses in nonattenuation zones, which is important for seismic applications. Wave propagations in finite lattices were investigated in perspective of energy, and it was found that both quantities of input energy and energy spatial distributions are different when excitation frequencies fall in passbands and stopbands, respectively. A conceptual configuration of the unit cell for ILMs applied as a seismic barrier was proposed. Numerical simulations of the barrier under excitations of three seismic records revealed its feasibility for the attenuation of ground motions.

This paper presents a computational model of a flexible pavement structure in finite elements (FE). The model is used to evaluate the response of a control (homogeneous) pavement structure, in contrast with equivalent random (heterogeneous) structures. One pavement structure is used as a control case, while 50 pavement structures with heterogeneous asphalt concrete (AC) layers are used in the random case. The AC layers in the random case exhibit spatially-varying mechanical properties; the instantaneous relaxation modulus ($E_o$) varies among the finite elements. AC variability propagated through the pavement layers. The uncertainty of critical responses was characterized, including longitudinal, transverse, shear, and vertical strains. The domain analysis (DA) method is applied to better understand the global (i.e., volumetric) response of the heterogeneous AC layers. Computational estimates of variability are presented, as predicted through the DA technique. Overall, for a fixed $E_o$ variability, response variabilities ranked as follows: (1) near-surface shear strain in the AC layer presented the most variation relative to its magnitude, followed by (2) transverse and longitudinal strains (at the bottom of AC layer), and (3) vertical strains on top of base and subgrade. The results provide ranges of uncertainty for the new DA tool for the first time.

To choose the maximum dividing sieve sizes for multiscale analysis, a mechanistic classification principle of sieve sizes is developed to characterize the size ranges of four inner structures in an aggregate’s gradation. A theoretical model of interlock check and stress evaluation is also established to evaluate the contact and interactive-filling status between the identified structures. Then, a discrete element (DE) simulation of triaxial compression tests of graded aggregates is built to validate the mechanistic classification principle. The contact force is extracted to calculate the contribution of each sieve size to bear the load and stabilize the structure. The size ranges of inner structures can be determined by the combined analysis of force occupation curves and mechanistic classification principle. The results show that the dividing sieve sizes for four gradations in the main classification system are different, but they are the same in the subclassification system. The sieve-size classification principle along with DE simulation can provide a basis of choosing appropriate sieve sizes to conduct multiscale analysis of asphalt mixtures and asphalt pavements.

Nonlinearity problems in engineering structures primarily involve material nonlinearity and geometric nonlinearity. Significant effort has gone toward developing accurate and efficient models and methods to simulate these nonlinear behaviors of structures. Although advanced hardware technology has greatly enhanced the computational performance of nonlinear analyses, many researchers still pay extra attention to developing more efficient numerical solution methods with the emergence of complex large-scale structures. The inelasticity-separated finite element method (IS FEM), as an efficient algorithm, is suitable for solving local material nonlinearity problems by keeping the global stiffness matrix unchanged throughout the whole computational process such that the Woodbury formula can be used as an effective tool. However, this procedure does not obviously improve the computational efficiency for structures with large deformation because widely distributed geometric nonlinearity commonly occurs throughout entire structures rather than in local domains. Furthermore, the global stiffness matrix, which is equal to the sum of the initial stiffness matrix and geometric stiffness matrix, changes in real time. This study proposes an efficient Woodbury-CA hybrid (WCH) method by incorporating the combined approximations (CA) method into the framework of the IS FEM to obtain the response of engineering structures with hybrid nonlinear behaviors (both material and geometric nonlinearities) under external loads. Within this framework, the solution of linear equations in the Woodbury formula, which is related only to the geometric nonlinear behaviors of structures, can be obtained by employing the CA method; two other global stiffness matrices, which are used to formulate the Schur complement matrices, are approximated as constant matrices for small periods of time. Additional error induced by these approximations can be eliminated by updating the global stiffness matrix when the optimal adaptive criterion (AC) used for evaluating the difference between the exact solution and approximate solution is not satisfied. Additionally, the time complexity theory is used to evaluate the computational efficiency of the proposed method; the results show that the WCH method has outstanding advantages over the conventional finite element method (FEM). The proposed method is validated against the FEM results via two different numerical examples and has greater potential for solving local material and global geometric nonlinearity problems.

In this paper, the exact solution of the Timoshenko beam vibration frequency equation under free-free boundary conditions is determined with an accurate shear shape factor. The exact solution is compared with a three-dimensional (3D) finite element calculation using ABAQUS, and the difference between the exact solution and the 3D finite-element model are within 0.05% for both the transverse and torsional modes. Furthermore, a relationship between the resonance frequencies and Poisson’s ratio was proposed that can directly determine the elastic modulus and Poisson’s ratio simultaneously, without the need for iteration, unlike the equations provided by an industry standard. The frequency ratio between the first bending and torsional mode for any combination of specimen dimensions can be directly estimated. Rectangular concrete beam specimens with three different mix designs were produced, and the transverse and torsional frequencies of these beams were tested. Results show that using the equations proposed in this study, the Young’s modulus and Poisson’s ratio of the concrete beams can be determined more directly than those obtained from the industry standard and with excellent accuracy.

The principle of folding analysis of frame structures with kinematical indeterminacy is widely used in the field of engineering. However, the design process of the efficient configuration for spatial structures in three-dimensional space is still a crucial problem. This paper presents a new methodology for finding the optimal folding strategy for frame structures, which is established on the basis of the generalized inverse theory and genetic algorithm (GA). Foldable structures are generated by inserting additional hinges into the appropriate locations of the spatial structures. Several numerical examples of spatial frame structures are analyzed using the proposed method. The results demonstrate that the proposed method is able to obtain the optimal foldable structures that have both high folding efficiency and a relatively simple folding mechanism. The characteristics of the obtained optimal results are discussed. The feasibility of this approach is demonstrated by the application of finding the optimal results of the spatial structures with several fundamental geometries.