Journal of Engineering Mechanics

A damage model for a dynamically loaded composite structure under severe loading conditions is presented. The model is based on a thermodynamic micromechanic approach making use of the conservation laws and the first and second laws of thermodynamics. It makes use of an irreversible thermodynamic concept where damage is introduced as an internal variable. The model characterizes micromechanical damages in an average sense where three modes of damage for composites are used: tensile, shear, and interphase damage. A homogenization or an averaging technique is implemented to simplify the representation of the nonhomogeneous material. The composite materials are modeled as being inelastic where the Maxwell viscoelastic constitutive relation is incorporated. The initiation of microcracks in the continuum is predicted based on a dissipation function. The coalescing of these microcracks and the onset of macrocracks is modeled where the macrocracks are assumed to initiate when the computed power of dissipation reaches a critical value. Verification analysis and numerical results to demonstrate the model's damage characteristics are also presented.

There are several approaches that can take into account the micromechanical and anisotropic behavior of soils. One is Dafalias's plastic spin approach. It is a convenient approach that utilizes an internal variable called “the plastic spin tensor.” The plastic spin is a function of the embedded stress (back stress) that causes the induced anisotropy and, consequently, the isotropic soil models cannot account for it. This paper presents a formulation of the plastic spin and related constitutive equations based on Dafalias's “anisotropic modified Cam clay model” with an updated Lagrangian reference frame. The required parameters are the typical consolidation and stress-strain parameters. The only additional parameters used in this work are the back-stress parameters c and x. These features are relatively simple and easy to use compared to other models.

Micromechanical and anisotropic behavior of soils is analyzed using the plastic spin and anisotropic modified Cam clay model (AMCCM) in an updated Lagrangian reference frame. The micromechanical behavior of soils is especially important in large strain problems. The anisotropic behavior inherently exists in soils. This study uses AMCCM with the plastic spin to evaluate the pore pressure response in cone penetration tests. This test is a typical example for large strain problems. The analytical results indicate that the predicted pore pressure is closer to the measured one when the plastic spin is incorporated in AMCCM. It also shows that the micromechanical behavior is paramount in the vicinity of the cone tip where large strains and rotations occur.

A strategy for optimal nonlinear stochastic control of hysteretic systems with parametrically and/or externally random excitations is proposed and illustrated with an example of a single-degree-of-freedom system. A hysteretic system subject to random excitation is first replaced by a nonlinear nonhysteretic stochastic system, from which an Itô equation for the averaged total energy of the system as a 1D controlled diffusion process is derived by using the stochastic averaging method of energy envelope. For a given performance index, a Hamilton-Jacobi-Bellman equation is then established based on the stochastic dynamical programming principle and solved to yield the optimal control force. Finally, the statistics of the responses of uncontrolled and controlled systems and those of the optimal control force are predicted analytically. Comparison with the modified optimal polynomial controller indicates that the proposed strategy is more effective and efficient.

A delaminated composite ring under external pressure is studied to understand the effect of curvature on delamination buckling and growth. Examples with differing crack lengths and delamination locations were considered. In all cases, the delamination surfaces come in contact rather early in the loading history, no matter what the initial imperfections are assumed to be. Furthermore, the delaminated part never becomes separated from the main ring. The modes of buckling given by standard linear stability analysis do not play any role in the behavior. Strain energy release rates were computed with the objective of predicting possible crack growth. Because of the contact, total energy release rate is dominated by the shear mode. Because the critical values of energy release rates are generally much higher in the shear mode than in the opening mode, one may conclude that shells tend to be more delamination tolerant than plates in which the opening modes tend to dominate.

In this paper, the axial and the secondary flow in a helical annular pipe are examined by a perturbation method in a curvilinear coordinate system, and the second-order perturbation solution is obtained completely. The secondary flow, the axial velocity, and the flux ratio are studied in detail. When the torsion is zero, the secondary flow behaves as four vortexes, and they are symmetrical up and down. When it is not zero, the symmetry is destroyed, and the intensity and number of the secondary flow vortexes are affected by the Dean number and the radius ratio of the inner/outer circle wall of the annular cross section. The maximum of the axial velocity appears near the inner bend when the Dean number is small, and it is moved toward the outer bend as the Dean number increases.

An analytical solution for waves propagating through a horizontal porous plate of finite thickness is obtained. The objective of the plate is to reduce the incident short-wave energy and the long-wave energy as well. Consequently, in this study the plate is analyzed in a global perspective [i.e., considering its response to obliquely incident short waves (both regular and irregular) and wave groups (with the consequent generation of free and locked long waves)]. To solve the propagation of regular and irregular waves, an eigenfunction expansion is used and the results are verified with experimental data showing good agreement. The propagation of a wave group past a horizontal porous plate is studied using a multiple-scale perturbation method, and an analytical solution is presented. The results show that the generated long waves are present on both sides of the plate and that maximum short-wave reflection is associated with maximum long-wave transmission.

In this paper, the multidomain spline fictitious boundary element method (SFBEM) is presented for analysis of elastic plane problems with different material constants or thicknesses throughout different domains. The problems are first reduced to nonsingular fictitious boundary integral equations with multidomain techniques being adopted. Then spline functions are adopted as trial functions to the unknown fictitious load functions in the deduced integral equations, and boundary-segment-least-squares techniques are used for eliminating the boundary residues. The proposed method is further applied in the analysis of high rise building structures, including framed shear walls, coupled shear walls, and frame-shear walls as well. Several typical numerical examples are given to show the accuracy and efficiency of the method.

When an oscillatory water wave propagates over a soft poroelastic bed, a boundary layer exists within the porous bed and near the homogeneous water/porous bed interface. Owing to the effect of the boundary layer, the conventional evaluation of the second kind of longitudinal wave inside the soft poroelastic bed by one parameter, ε₁ = k₀a, is very inaccurate so that a boundary layer correction approach for a soft poroelastic bed is proposed to solve the nonlinear water wave problem. Hence a perturbation expansion for the boundary layer correction approach based on two small parameters, ε₁ and ε₂ = k₀/k₂, is proposed and then solved. The solutions carried out to the first three terms are valid for the first kind and the third kind of waves throughout the whole domain. The second kind of wave is solved systematically inside the boundary layer, whereas it disappears outside the boundary layer. The result is compared with the linear wave solution of Huang and Song in order to show the nonlinearity effect. The present study is very helpful to formulate a simplified boundary-value problem in numerical computation for soft poroelastic medium with irregular geometry.

The trapping and generation of surface waves by submerged vertical permeable barriers or plates kept at one end of a semi-infinitely long channel of finite depth are investigated for various barrier and plate configurations. The various fixed barrier configurations are (1) a surface-piercing barrier; (2) a bottom-touching barrier; (3) a barrier with a gap; and (4) a fully submerged barrier. The different moving plate (or wavemaker) configurations are of types 1, 2, and 4, respectively. The boundary value problems are converted to dual/triple series relations by a suitable application of the eigenfunction expansion method and then the full solutions are obtained by the least-squares method. The variations of reflection coefficients are obtained and discussed for different values of the porous-effect parameter, the normalized distance between the barrier and the channel end-wall, and the length of submergence of barriers for all types of barrier configurations. The dynamic pressure distributions for various porous-effect parameters are analyzed for the three types of wavemakers. The wave amplitudes at large distances are obtained and analyzed for different values of the porous-effect parameter and the distance between the wavemaker and the channel end-wall.

Here the boundary integral equation method (BIEM) is used for 3D modeling of hydrodynamics and pollutant transport in stratified estuaries. The flow computations are made using a newly developed BIEM solution. The transport modeling has been done using an Eulerian-Lagrangian BIEM (ELBIEM) model. In ELBIEM, the advection part in the transport equation is treated by the concept of the Eulerian-Lagrangian scheme, which overcomes the limitation of traditional BIEM to deal with an arbitrary velocity field. The coupling of the 3D shallow water BIEM model and advection-diffusion ELBIEM model enables one to effectively deal with fluctuation of free surface and density stratification in an estuary. The main advantages of the BIEM model include reduction in computational dimensions, ease in discretization and data preparation, accurate free surface simulation, less numerical diffusion and dispersion problems, and direct flux solution at boundaries. The numerical simulation results are compared with other model results and found to be satisfactory. The illustrated case study shows the effectiveness of the model in the simulation of mass, momentum, and heat transfer due to air-water interaction in stratified estuary problems.

This paper presents a fully analytical solution, together with explicit expressions, for the steady-state response of a homogeneous 3D space subjected to a spatially sinusoidal, harmonic line load. In the literature, this problem is often referred to as the two-and-a-half-dimensional fundamental solution or two-and-a-half-dimensional Green's functions. These equations are of great usefulness in the formulation of 3D elastodynamic problems by means of integral transforms methods and/or boundary elements. The final expressions are validated here by applying the equations to the problem of a 3D point load, for which the solution is known in analytical form.

The Gaussian-vortex integral model is applied to laboratory data on an advected thermal and field experimental data for a single submerged sewage outfall. The Gaussian-vortex integral model is distinguished from other conventional jet integral models that do not consider vortex-pair formation effects on the behavior of a buoyant jet in the buoyancy- and ambient-dominated regions. The experimental data relative to an advected thermal, measured by a laser-induced fluorescence technique were used for verifications of the numerical model. With the incorporation of vortex-pair formation effects, the simulated results on the bulk characteristics of an advected thermal were in good agreement with the laboratory data, and for applications the simulated surface minimum dilutions also show fairly good agreement with field experimental data. Finally, the numerical model is applied to a horizontal buoyant jet in cross-flow to demonstrate the capability of the numerical model for the buoyant jet that has 3D characteristics.

This technical note points out that caution must be exercised in conducting time-domain and random-vibration analyses of noncausal systems with frequency-dependent parameters and hysteretic damping. It warns against indiscriminate extensions of certain common engineering approaches that can lead to erroneous results.

This note investigates the influence of shear lag for thin-walled curved box girders, including longitudinal warping. The longitudinal warping displacement functions of the flange slabs are approximated by a cubic parabolic curve instead of a quadratic curve of Reissner's method. On the basis of the thin-walled curved bar theory and the potential variational principle, the equations of equilibrium considering the shear lag, bending, and torsion (St. Venant and warping) for a thin-walled curved box girder are established. The closed-form solutions of the equations are derived, and Vlasov's equation is further developed. The obtained formulas are applied to calculate the shear lag effects for curved box girder bridges. Numerical examples are presented to verify the accuracy and applicability of the present method.