A nonlocal Timoshenko curved beam model is developed using a modified couple stress theory and Hamilton's principle. The model contains a material length scale parameter that can capture the size effect, unlike the classical Timoshenko beam theory. Both bending and axial deformations are considered, and the Poisson effect is incorporated in the model. The newly developed nonlocal model recovers the classical model when the material length scale parameter and Poisson's ratio are both taken to be zero and the straight beam model when the radius of curvature is set to infinity. In addition, the nonlocal Bernoulli–Euler curved beam model can be realized when the normal cross-section assumption is restated. To illustrate the new model, the static bending and free vibration problems of a simply supported curved beam are solved by directly applying the formulas derived. The numerical results for the static bending problem reveal that both the deflection and rotation of the simply supported beam predicted by the new model are smaller than those predicted by the classical Timoshenko curved beam model. Also, the differences in both the deflection and rotation predicted by the current and classical Timoshenko model are very large when the beam thickness is small, but they diminish with the increase of the beam height. Similar trends are observed for the free vibration problem, where it is shown that the natural frequency predicted by the nonlocal model is higher than that by the classical model, and the difference between them is significantly large only for very thin beams. These predicted trends of the size effect at the micron scale agree with those observed experimentally.
Static uniaxial compressive experiments were conducted to study the mechanical behaviors of polyvinyl alcohol (PVA) hydrogels in ambient conditions. It was found that water is expelled during the compression of hydrogels that have high water contents. It means hydrogels may be a mass variable under the compression. In order to depict the mechanical properties intrinsically, a variable mass model with meso-scale cells was proposed to simulate PVA hydrogels. In the model, there are uniform cells with frames of polymer fibers and water, and a virtue membrane designed to wrap up the boundary of the model. The model not only depicts the behaviors of the compressive mechanics and the expelled water, but also explains the nonlinear stress–strain relation of PVA hydrogels and why the hydrogels with high water content demonstrate a modulus considerably lower than the bulk modulus of water.
The feasibility and effectiveness of treating pollutants in slightly polluted raw water by variable charge soil and polyaluminum chloride (PAC) was investigated. Removal efficiencies of turbidity, phenol, aniline, algae and heavy metals (Cu(2+), Zn(2+) and Pb(2+)) were used to evaluate the coagulation performance. The results indicated that the addition of variable charge soil as a coagulant aid is advantageous due to the improvement of removal efficiencies. The tests also demonstrated that the presence of variable charge soil increased the removal of turbidity rather than adding residuary turbidity. The use of variable charge soil produced settleable flocs of greater density and bigger size. The main mechanism involved in the PAC coagulation was supposed to be sweep flocculation as well as charge-neutralization. Variable charge soil played a promoted aid role by adsorption in the enhanced coagulation process. It is concluded that the enhanced coagulation by PAC and variable charge soil, as coagulant and adsorbent, is more effective and efficient than traditional coagulation.
It has been widely acknowledged that traditional packers will lose their elastic performance in the context of long periods of operation due to plastic deformation. This paper will introduce a swellable packer that can reduce the failure cases of production effectively. The deformation of the packer rubber in different media and temperatures has been analyzed. The pressure test of several packer rubber under different media is carried out in this paper. The reasonable expansion clearance between the rubber tube and the well wall is obtained by strength calculation to ensure the sealing reliability of the packer. Finally, the thermomechanical coupling calculation of the packer with different structural sizes is carried out. Experiments at different temperatures show that the higher saline concentration is associated with a lower expansion rate and a larger expansion rate in clear water. At the same time, the expansion of volume in clear water increases. In addition, the higher the external temperature is, the larger the temperature gradient is. When the temperature of the outer ring is between 100°C and 140°C, the internal temperature rises to 37°C under the thermomechanical coupling effect.
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