In the development of mechanics, the geometrization of theoretical systems of mechanics, is introduced. Dynaminc systems of mechanics reduced to Riemann geometry and Symplectic geometry are presented, the concepts of duel space, symmetry, transform, invariant, and there general applications in mechanics are introducd.
Pavements during or after rain are prone to become considerably slippery for pedestrians and motor vehicles. This natural phenomenon is investigated by using the Terzaghi's consolidation model, the shear strength theory and the effective stress principle, within the scope of soil mechanics. A methodology for assessing the slippery pavement is established on the assumption of a simplified 1D equivalent model. A safety factor against sliding along the pavement surface is proposed in terms of the shear strength of the consolidating soil divided by its shear stress. Based on the engineering empirical parameters of common soils, a case study of pedestrians on the sidewalk is statistically conducted to qualitatively and quantitatively reveal the control factors of the pavement slipperiness. It is shown that the evaluated safety factor against sliding for the sandy pavement is approximately 6.0 to 9.0 times greater than that for the clayey pavement. The soil mechanics-based modeling is a promising novel approach to the slip resistant or anti-skid pavement design and evaluation.
Epoxy resin (ER)-concrete pavement will be delaminated at the edges between layers due to temperature changes. In this paper, based on a two-variable analytical model for thermal stresses of laminated structures, the interlayer peeling moment and shear force are derived. In this way, the difficulty in solving the local variables by theory of elasticity is circumvented, and an alternative approach to coping with the edge delamination problem of multilayer structures is presented. Thereout, we investigate the impact of the thickness, elastic modulus of the ER layer on the internal forces of edge delamination and the maximum tension stress of the concrete layer. The calculated results show that the peeling internal forces could be effectively reduced by controlling the thickness and the elastic modulus of the ER-layer, thus the debonding failure is avoided.
The present paper analyzes the vibration of simply supported plates of functionally graded materials resting on viscoelastic foundations. Based on the Reddy's higher-order shear deformable plate theory and the general Karman-type equations derived by Shen, the analytical solutions for the free vibration and the transient response are obtained by using the double Fourier series. The natural frequencies and the transient response are obtained, and the results are compared with those of other papers. The effects of the volume fraction index, the parameters of the viscoelastic foundations and the ratio of the length to the thickness are analyzed. The results show that the natural frequencies rise, but the transient responses decrease with the increase of the pressed and sheared parameters of the viscoelastic foundations, and the viscous parameter also has an effect on the natural frequencies and the transient response.
For insufficient of minimum potential energy method research, model of shear potential with static equilibrium equation of sliding body virtual displacement is proposed, which can solve shear strength on failure surface. Moreover, stability analysis method of multi layer slope is forwarded. Results of paper examples show that:shear potential energy of sliding mass can influence stability factor of slope, and it can obtain reasonable result; paper method is feasible and reasonable, which result from stability factor of proposed method is close to limit equilibrium method; analysis method of multi layer slope not only considers contribution of sliding surface length and normal force, but also it is simple and easy to be used by engineering.
The boundary displacement in the unsteady Couette flow stage of Newtonian fluid is investigated in this paper. The top wall is always kept stationary and a constant velocity or a sudden constant tangential surface force is imposed on the bottom wall. The fluid velocity distributions are obtained by solving the problems. The time periods for the flow to reach the steady state under different situations are obtained by using the asymptotic analytic method. Then the boundary displacements in the unsteady stage are obtained from the time periods and the boundary velocities. With the shear stress on the inner surface of the bottom wall and the boundary displacements, the work done by the Couette system under different situations is obtained. From the increase of the fluid kinetic energy, the energy dissipations caused by the viscous friction in the unsteady Couette stage are obtained.
The equilibrium of a pole supported on a parabola wall is related to its length, slope angle and the frictional factor between them. Under the action of gravity, the pole can move clockwise under the focus of parabola, and move counterclockwise or slide down at two ends over the focus. The state of pole, i.e. disequilibrium, stable and unstable equilibrium with friction, is determined on the support force at the boundary of friction cone. The equilibrium set is a pitchfork bifurcation with width related to the frictional factor.
To study the impact of human body in the stationary state on the lateral vibration performance of structure, an experimental platform is built up and the horizontal natural frequency of the vibration and the damping ratio of the mass-structure system and the human-structure systems are tested and analyzed. Two static lateral coupling models of the human-structure system are used, to obtain the range of the lateral vibration frequency of human body. It is shown that the human body in the stationary state could not be simplified as a mass block as in a mass-springs-damping system to evaluate the impact of the human body on the lateral vibration performance of the structure, and a mass-spring-damper system should be adopted with the human body as a rigid mass. Based on the experimental data and the human-structure coupling model, the ranges of the lateral frequency and the fore-and-aft frequency of the human are calculated, with the results of 0.236~3.748 Hz and 0.194~5.32 Hz, respectively.
The element displacement modes of the extended finite element method for plane crack problems are discussed in this paper. The governing equations for the extended finite element method are derived based on the principle of virtual work. The numerical integration technique is adopted for special elements. The displacement extrapolation method is formulated to calculate the stress intensity factor based on the least square method. The numerical computation programs are developed by using the MATLAB, and the numerical calculations are carried out by the extended finite element method for the problem of plane crack. Based on the results of the extended finite element method, the stress intensity factors of plane crack are calculated by the displacement extrapolation method and the interaction integral method, respectively. Numerical results show that with the displacement extrapolation method, the stress intensity factors can be obtained more easily and precisely than the interaction integral method.
The new-old concrete composite beams are considered as an important engineering beam with a bond-slip in the composite surface. Based on the deformation compatibility relationship across the composite surface of the new-old concrete composite beam, a nonlinear differential equation is derived, for the axial force of the new-old concrete composite beam. The theoretical expressions of the section coordination coefficient are obtained from the equation. With the coordination coefficient, a practical nonlinear analysis method is established, which can exactly describe the shrinkage and the creep of the new-old concrete composite beams. The Bernoulli assumption and the coordination coefficient of the section are duly combined. Compared with the existing analytical solutions, the accuracy can meet the engineering requirements.