Abstract: In the case of small elements, it is difficult to obtain accurate stress fields and stress concentration with existing nonuniform models. An optimization algorithm for the theory of the PHSEM (polygonal hybrid stress element method) was proposed with the direct restriction method. The advantages of the PHSEM in the construction of stress functions and the division of integral regions make it more suitable for complex model boundaries and material boundaries and easier to realize-element meshing. The complete computing program was made according to the theoretical analysis. The results show that, the PHSEM can obtain macroscopic nonlinear mechanical responses, highly accurate stress fields and obvious stress concentration phenomena in the powder compaction process, which provides an effective means for the solution of the complex optimization problems.
Abstract: The anti-plane problem of cracks near regular hexagonal holes in 1D hexagonal piezoelectric quasicrystals was studied. By means of the Cauchy integral formula in the complex variable functions and through construction of conformal mapping functions, the analytical solutions of stress distribution and field intensity factors at the crack tip near the hole were obtained under the electrically impermeable boundary condition. The effects of the edge length and the crack length of the regular hexagon as well as the shear stress on the field intensity factors were discussed with numerical examples.
Abstract: The problem of lateral vibration of axially moving beams and the method for studying lateral vibration of axially moving beams were discussed. Some errors in the previous research of lateral vibration of axially moving beams were pointed out and corrected. For the axially moving cantilever beam with one end in fixed boundary condition, the calculation formula for the dynamic responses of the beam with self-weight effects was derived based on the modal superposition method for the continuum. The calculation was carried out and the calculation results were discussed in detail. The results show that, the factors that influence the vibration responses of the axially moving beam mainly include the speed and the direction of motion.
Abstract: The transformation method with which the surrounding rock stress was mapped to an actual area, has been more and more widely applied to engineering practice, which is of practical guiding significance to the stress calculation method and the study on stability of tunnel surrounding rock. A mechanical model was established for circular tunnels in rock mass, with a mapping function obtained from a unit circle to a polygonal rock mass in the complex plane through the Schwarz-Christoffel transformation method based on the complex variable function theory. Then the solution of the stress distribution in the polygonal rock mass was studied in the complex function field, and subsequently the formulas of complex stress functions Φ(ξ) and φ(ξ) for circular tunnels in irregular rock masses were derived based on the elasticity theory. Finally, the analytical formulas of stress components σρ and σθ for any point in the surrounding rock mass were obtained. Analysis of examples indicates that the shape of the rock mass has large influence on the stability of circular tunnels. Here is the maximum stress distribution law for 4 shapes of rock masses: the maximum stresses in the roof and floor of the hexagon, the pentagon, the quadrilateral and the circle decrease in order; otherwise, those in the sidewalls of the circle, the quadrilateral, the pentagon and the hexagon decrease successively.
Abstract: A semi-analytical 1D consolidation solution of saturated soft clay was derived via the Laplace transform by means of the spring pot-based fractional-order Kelvin model and in view of changing inner stresses along the depth of the soft clay. Firstly, the validity of the semi-analytical solution was verified through comparison with the referential results. Then, the effects of different fractional orders, total stress ratios and multi-grade linear loadings on the consolidation settlement and the pore water pressure of the saturated soft clay were analyzed based on the semi-analytical solution in detail. The work provides a theoretical basis for the related practical geotechnical engineering.
Abstract: Based on the definition of the distortion angle presented for trapezoidal-section box girders, according to the theories for the traditional concrete box girder and the mechanical properties of the corrugated steel web, the distortion warping stresses of the corrugated steel web composite box girder were deduced. The governing differential equations for the distortion angle were established with the energy variation calculus method based on the principle of stationary potential energy, and the initial parameter solutions to the equations were achieved. With the initial parameter method the distortion angle and the distortion double moment of the corrugated steel web composite box girder were obtained. Finally, the longitudinal distortion warping stresses were got. Contrastive analysis of the distortion warping stresses were done between the traditional concrete box girder and the corrugated steel web composite box girder. The analysis results show that, due to the negligible longitudinal stiffness of the corrugated steel web, the warping stress at the web-bottom intersection of the corrugated steel web composite box girder is much larger than that of the concrete box girder.
Abstract: Some Duffing systems with external excitation and quintic nonlinear restoring forces were considered, the amplitude-frequency response equation for the system was obtained with the multi-scale method, and the amplitude-frequency characteristic curves and their changing rules under different parameter changes were given. At the same time, the singularity theory was applied to get the transition sets and the corresponding topological structures of the system in 3 cases. Second, the fixed point of the system was determined, and the Hamiltonian function was used to get the heteroclinic orbit of the system, so the threshold of chaos in the Smale horseshoe sense was obtained with the Melnikov method. Then, the dynamic bifurcation and chaotic behavior of the system under external excitation and quintic nonlinear coefficients were given through numerical simulation. It is found that there are nonlinear phenomena such as periodic motion, period doubling motion, quasi periodic motion and chaos. The correctness of the theory was verified with nonlinear methods such as the Lyapunov exponent, the phase diagram and the Poincaré sections. The work provides a theoretical reference for further understanding of the nonlinear characteristics of Duffing systems and their evolution laws.
Abstract: Simulation of the non-Newtonian fluid flow is an interesting problem for engineers. As a relatively new particle-based method, the material point method (MPM), combining the advantages of both the Lagrangian algorithm and the Eulerian algorithm, has been widely and effectively used to solve complex engineering problems. The plane Poiseuille flow and Couette flow of the shear thickening and shear thinning cross fluid and power-law fluid were studied with the artificial state equations for the MPM. The results show that, the simulation with the MPM for the Newtonian fluid is in good agreement with the theoretical solution and the MPM simulates the shear thinning and shearing thickening of the non-Newtonian fluid exactly. The results confirm the applicability of the MPM for simulation of the non-Newtonian fluid flow and expand the application field of the MPM.
Abstract: The naturally vuggy and fractured carbonate rock plays an important role in China's oil and gas resources. Therefore, it is of great significance to study the characteristics of well bottom pressure in fracture-vug carbonate rock for hydraulic fractured wells. According to the basic principle of seepage mechanics, the well test model for carbonate reservoirs in view of the stress sensitivity and the threshold pressure gradient was established. The point source function method, the Laplace integral transform and the Fourier cosine integral transform were used to obtain the point source solution with impermeable top and bottom and lateral infinite boundary in the Laplace space. The surface source solution was obtained with the integral of the point source solution; the real-space well bottom pressure solution was obtained through the Stehfest numerical inversion and the well test curves were drawn. The simplified model solution matches with the related literature calculation results as to the threshold pressure gradient. The larger the stress sensitivity coefficient is, the more obviously the pressure and the pressure derivative curve will go up; the larger the threshold pressure gradient is, the earlier the pressure derivative curve will rise up; the smaller the open degree is, the more obvious the spherical flow characteristics will be; the larger the interporosity flow coefficient is, the earlier the 'concavity' will appear; the larger the elastic storage ratio is, the wider and deeper the 'concavity' will be. The proposed model can be effectively applied to analyze the well test curves of hydraulic fractured wells in naturally vuggy and fractured carbonate reservoirs of low permeability.
Abstract: The slotting method is a simple flow passive control method. In order to search for a passive control method that can effectively mitigate the bladevortex interaction effects, a NACA 0012 airfoil was used as the research object, 4 kinds of the NACA 0012 airfoil models with differently slotted leading edges were designed. Numerical simulations of 2D parallel bladevortex interaction (airfoilvortex interaction) were performed for the slotted airfoils and the benchmark airfoil to examine the effects of the freestream velocity, the vortex strength and the disturbing distance on the lift coefficient. The results show that, the slotted leading edge can mitigate the airfoilvortex interaction effects, but with an influence on the lift coefficient. The vertical cavity with a width of 2.5% of the chord length can obviously mitigate the airfoilvortex interaction effects with low lift coefficient penalties, having a wide application range.