Journal of Engineering Mechanics

In this work a new Eulerian approach to large deformation generalized plasticity, within the context of affine tensor analysis in Euclidean spaces, is presented. The approach relies crucially on the systematic use of the Lie derivative concept. Classical plasticity is then derived, as a special case of generalized plasticity. The computational implications resulting from the absence of the requirement for the existence of a yield surface in the theory of generalized plasticity are discussed. On the basis of those implications a general integration scheme is proposed. As an application, a generalized plasticity model in large deformations is presented. The proposed model is then used for the solution of boundary value problems.

Large discrepancies exist among current classical theories for the in-plane buckling of arches that are subjected to a constant-directed radial load uniformly distributed around the arch axis. Discrepancies also exist between the classical solutions and nonlinear finite-element results. A new theory is developed in this paper for the nonlinear analysis of circular arches in which the nonlinear strain-displacement relationship is based on finite displacement theory. In the resulting variational equilibrium equation, the energy terms due to both nonlinear shear and transverse stresses are included. This paper also derives a set of linearized equations for the elastic in-plane buckling of arches, and presents a detailed analysis of the buckling of deep circular arches under constant-directed uniform radial loading including the effects of shear and transverse stresses, and of the prebuckling deformations. The solutions of the new theory agree very well with nonlinear finite-element results. Various assumptions often used by other researchers, in particular the assumption of inextensibility of the arch axis, are examined. The discrepancies among the current theories are clarified in the paper.

Capillary force and water retention between two uneven-sized spherical particles are investigated. Previous studies have been limited to systems with even-sized particles. The appropriate definition of the boundary value problem for a water lens between two uneven-sized particles is presented under the consideration of thermodynamic free energy at the microscopic level. Capillary force and water retention under the consideration of toroidal approximation are also derived for a system with two uneven-sized particles. Comparison of normalized capillary force and water retention calculated by the free energy approach and toroidal approximation are conducted. The quantitative analysis shows that for a system with two identical particles, the behavior of water retention and normalized capillary force is very similar to some recent studies by others, confirming that the toroidal approximation provides reasonably good estimations for both capillary force and water retention. For a system with uneven-sized particles, it is shown that error in normalized capillary force could be significant as the matric suction approaches zero and the particle sizes become very different. The errors for the mean curvature of the meniscus for the toroidal approximation are significant where the matric suction is near zero. Thus for soils with varying particle sizes, it may be necessary to employ the exact solution to meniscus shape in order to accurately quantify normalized capillary force and water retention. The induced normalized capillary force increases inversely with the particle size, and is generally insensitive to the water content. For soil assembly with particle size of $0.01\mathrm{mm}$ , the normalized capillary force could reach $10\mathrm{kPa}$ , whereas for soil assembly with particle size of $1\mathrm{mm}$ , the normalized capillary force is on the order of $100\mathrm{Pa}$ .

The recently established theoretical results of the solid-water characteristic curve (SWCC) and capillary force characteristic curve (CFCC) are experimentally verified for mechanical and hydrologic interaction between uneven-sized spherical particles under partially saturated conditions. It is shown that the theoretical framework, based on the minimization of the free energy of the liquid meniscus between the two uneven-sized particles, can predict both water retention and capillary force accurately for spherical particles ranging in radius from $165\text{to}252\mu \mathrm{m}$ . The experimental technique is novel and the results at such scale are valuable for the understanding of gas-solid-liquid interaction among granular media, since there is very limited experimental data available in the literature. The comparisons between the theoretical and experimental predictions of the SWCC and CFCC indicate that the agreements are generally very good, confirming the validity of the theory.

Dynamic characteristics are analytically investigated for a single degree of freedom structure with a Maxwell element (SSME). Eigenvalues are obtained analytically and approximated by a perturbation method. Then, cases are sorted by a stiffness ratio $\lambda$ : the ratio of a structural spring to an auxiliary spring. For a small $\lambda$ , the optimal damping ${\varphi }_c$ provides the maximum damping ratio. For a large $\lambda$ , the lower and upper critical dampings ${\varphi }_a$ and ${\varphi }_b$ provide duplex eigenvalues. These values are approximated by simple terms. To reduce transient response, $\lambda$ should be large, and $\varphi$ should be around ${\varphi }_c$ , ${\varphi }_a$ , and ${\varphi }_b$ , which provide the SSME with large damping. For a stationary excitation, the optimal damping ${\varphi }_d$ is introduced to produce the minimum peak deformation. In fact, ${\varphi }_d$ is larger than ${\varphi }_c$ and ${\varphi }_b$ , and provides larger stiffness and a smaller damping ratio. For a seismic excitation, some cases with ${\varphi }_d$ might reduce deformation more than those with ${\varphi }_c$ and ${\varphi }_b$ , but must support larger stress in the Maxwell element. Thus, $\varphi$ should be based on design constraints.

Extensive numerical analysis indicates that the conventional spline functions semidiscretization analysis for orthotropic plates and shells reported by Li et al. (Journal of Engineering Mechanics, 2003) cannot be directly employed in the vibration analysis of orthotropic rectangular plates with the free $\left(F\right)$ and/or guided $\left(G\right)$ edges. The modified spline function based method then is presented in this paper to cope with the vibration analysis of isotropic and orthotropic rectangular plates with possible combinations of the free $\left(F\right)$ , simply supported $\left(S\right)$ , clamped $\left(C\right)$ , and guided $\left(G\right)$ edges at the four bounds. Through dividing the rectangular plate into $N$ and $M$ equal subintervals along the $x$ and $y$ directions, the modified spline functions consisting of $N+3$ and $M+3$ local $B_3$ spline functions with respect to $N+1$ points and two extended additional points in the $x$ direction and $M+1$ points and two extended additional points in the $y$ direction, in which the first and last three local $B_3$ spline functions have been modified for accommodating to any one of the $F$ , $S$ , $C$ , and $G$ boundary conditions, are used as the displacement trial functions. Employing the modified spline functions, only one unknown coefficient is required to be determined for the deflection and its first and second derivatives, respectively, at a certain bound. The modified spline function matrix based characteristic equation of the orthothopic rectangular plate is derived using its potential energy functional. In comparison to the finite-element method and the spline finite strip method (SFSM), the present method has remarkably fewer numbers of degrees of freedom, and thus it is computatively more efficient. Likewise, the computational program with minimal preparation of input data can be easily developed through the present formulation. The results indicate that the present method can render both very high accuracy and fast convergence.

This paper investigates the performance of unidirectional and bidirectional tuned liquid dampers (TLDs) under random excitation. The performance of the tuned liquid dampers is measured in terms of efficiency and robustness. A series of experimental tests are conducted on model scale structure-tuned liquid damper systems to evaluate their performance, which is then compared to that of the well known tuned mass damper. The effective damping is calculated for each test conducted and the efficiency and robustness are subsequently examined. The performance of a mistuned TLD is experimentally investigated to highlight the robustness of these passive dynamic vibration absorbers. A nonlinear numerical model is used to conduct an extensive parametric study on the performance of a tuned liquid damper. This study has resulted in the development of performance charts for a tuned liquid damper. These charts allow the efficiency of a tuned liquid damper to be examined for a number of varying parameters, which include the excitation amplitude, water depth, and building frequency. These charts are particularly useful for the initial design of a tuned liquid damper when the precise frequency of the structure is not known.

To investigate the effect of control-structure-interaction (CSI) between the innovative electromagnetic mass damper (EMD) control system and the test structure, three computational models are first developed in this paper. Then, typical driving voltages are applied to the servo-amplifier of the EMD system to excite the structure and to examine the dynamic behavior of the EMD system when it is implemented into the structure. Furthermore, the test results are compared with the predictions based on the proposed parametric models, namely on-line examination. Finally, shaking table tests of structural seismic response control employing the EMD control system are conducted to validate and compare the effectiveness of those parametric models. All the test results have shown that only when the CSI effect (especially the higher-order CSI effect) is fully considered, can the on-line dynamical property of the EMD system be accurately predicted and its control performance fully exerted. This is essential to achieve the highest performance when employing such EMD systems in suppressing structural vibrations.