This paper firstly reviews the studies of the effective stress of unsaturated soils and points out that two stress variables are preferred to be chosen to establish a constitutive model at present. The paper also explains the definition of the matric suction, which involves the effects of the capillary component and the adsorptive component. Secondly the paper discusses the strength of unsaturated soils. The shear strength is usually formulated by the extended Mohr-Coulomb Criterion. The tensile strength also affects the soil behavior due to the capillary effect and thus cannot be ignored. Thirdly, the paper reviews the studies of the constitutive models for unsaturated soils, including the models based on the net stress and the matric suction and that based on the Bishop effective stress and the matric suction. The double pore structure model is also discussed. Finally, the paper addresses the applications of the thermodynamic method and the porous media theory in unsaturated soils. It is shown that these two methods-using the thermodynamic principles to establish the constitutive framework, and using the porous media theory to study the complicated coupling effect of unsaturated soils are subjects very worthy to be developed.
In the reliability-based topology optimization, the uncertainty is considered during the engineering practice, which is important in a structural reliability design. At present, the most commonly used reliabilitybased topology optimization methods for a continuum structure are: the nested optimization method, the decoupling method, the single-loop method and the reliability safety coefficient method. Firstly, the mathematical models of the reliability-based topology optimization are introduced. Then, the theoretical basis of above methods are systematically discussed, and their current researches and applications are briefly reviewed. Finally, the advantages, disadvantages and development trends of above methods are discussed.
The random vibration of a coupled vehicle-bridge system with sprung masses under moving vehicular loads is studied. The mode shapes of the bridge with sprung masses are obtained. The vehicle is modeled as a two-DOF system with linear suspensions and tire flexibility. The power spectral density of the bridge's surface irregularity is taken as input. According to the state space theory and the general evolutionary random processes, the controllable method of analyzing the random response of the coupled system is derived. The numerical studies show that the sprung masses have no effect on the random response of the vehicle, but the random response of the bridge is reduced. The effects of the mass ratio μ, the quantity of sprung masses on the random response of the coupled vehicle-bridge system are discussed.
This paper studies the Legendre pseudo-spectral method for solving the 3D rigid pendulum motion optimal control problem. For the 3D rigid pendulum constrained mechanical model, a 3D Legendre pseudospectral method is proposed based on the rigid body posture and the optimal control method. By using the Legendre interpolation approximation method to design the 3D rigid pendulum motion optimal control algorithm, the optimal attitude control trajectory of the 3D rigid pendulum is obtained, and combined with the relaxation factor control, a satisfactory feasible solution can be found. The simulation results show that with the optimal Legendre pseudo-spectral method control algorithm, the 3D rigid pendulum goes to the end effector pose with a smaller error motion, at a fast calculation speed, and the control inputs can be obtained with a high precision. This paper also verifies the feasibility of the proposed optimal control algorithm.
The purpose of this paper is to study the optimization method for problems of rigid body dynamics systems based on the Gaussian principle of the least constraint in generalized coordinates. Compared to the current modeling methods with the Gaussian principle of the least constraint in the form of the particles, it is shown that modeling the Gaussian principle of the least constraint in generalized coordinates has no requirements upon the coordinates, and the modeling process becomes easy and versatile. Two different optimization models are established in this paper under constrained and unconstrained conditions in the example of a double pendulum. A dynamical numerical simulation and a comparative analysis are carried out with a model treated with the Lagrange differential equation using a software MATLAB and the effectiveness of the method proposed in this paper is verified.
Based on the theory of the complex stiffness and taking the advantage of the orthogonal experimental method, the dynamic performance tests for rubber elastic brackets of wind turbines are carried out to study the influences of the load frequency, the load amplitude and the preloading on the rubber elastic brackets. Experimental results show that there is a significant correlation between the dynamic performance of rubber materials and the load frequency or the load amplitude. The elastic stiffness and the damping factors of the rubber elastic brackets increase significantly with the increase of the load frequency; the elastic stiffness decreases but the damping factors increase gradually with the increase of the load amplitude. Analysis of variance based on the orthogonal experiment data shows that the load frequency is the most important factor for the dynamic performance, the second important factor is the load amplitude, and the effect of the preloading is very limited.
The discrete mechanics and optimal control (DMOC) is a recently developed effective method to solve the optimization control problem. However, the original DMOC usually leads to some numerical oscillation of the control forces, which is unfavorable for the control output. In this paper, the causes of the numerical oscillation are analyzed. Then a feasible solution by introducing a gradient penalty term to the objective function is proposed. Finally, numerical examples validate the effectiveness of the proposed method. The simulation results show that the improved algorithm can ensure smoothness of the control forces under the condition of the minimization of the total control forces.
In some engineering problems, multi-models are used to simulate the structural behavior. In order to obtain reliable prediction results, the model selection uncertainty and the model form uncertainty should be considered. In this paper, different model's degrees of confidence are computed by combining the Bayesian method with the test data. The adjustment factor approach is used to pass the model selection uncertainty into the prediction of a system response, and then the response confidence interval is obtained from the results of the synthesis model. The final simulation results are obtained by combining the confidence interval of the model form uncertainty with the results of the synthesis model. The confidence interval at the prediction position is calculated by the interpolation method. Finally, the methodology is applied to the prediction of the aerodynamic coefficient of some aircraft subjected to different angles of attack. The agreement between the prediction results and the test results shows that the method in the paper is feasible in the engineering simulation.
In order to simplify the local buckling analysis of vacuum towers with outside suspensions, a reduced mechanical model is built for the buckling analysis of a thin-walled cylinder under local radial load and external pressure. Pop cans are used as the thin-walled cylinder specimen. Local radial critical loads are measured under different external pressures. The eigenvalue buckling analysis is used to determine the local radial critical load of the specimen,which agrees well with the experimental result. With the orthogonal design method,an empirical formula for the local radial critical load is obtained by the parametric eigenvalue buckling analysis. Verification example indicates that the empirical formula yields slightly conservative results, which may be used for the local buckling analysis of vacuum tower with outside suspensions.
Based on the method of Westergaard, the mode Ⅰ crack stress field is obtained for related boundary conditions. The tangent plane at the crack tip is used as the stress field area at the pipe crack tip. The mode Ⅰ crack tip stress field and its influence area are obtained, and the differences of the crack tip stress fields are shown between the pipe and the flat plate. The theoretical result shows that the influence area of the crack tip stress field is related to the crack length and the tensile stress.
To study the aerodynamic performance of the soccer ball, computational models with/without spinning are set up and verified with previous studies. It is shown that the separation lines on the surface of the soccer ball are very different from those on a smooth ball surface due to presence of the seams. It is shown that the seams greatly affect the three-dimensional separation and the lift force acted on the soccer ball in non-spinning case. In the spinning case, not only the Magnus force but also the drag acted on the soccer ball increase with the increase of the rotation speed. Furthermore, the effect of spinning on the flight trajectory of the soccer ball is discussed with the penalty kick as an example.