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In this investigation, a new simple triangular strain based membrane element with drilling rotation for 2-D structures analysis is proposed. This new numerical model can be used for linear and dynamic analysis. The triangular element is named SBTE and it has three nodes with three degrees of freedom at each node. The displacements field of this element is based on the assumed functions for the various strains satisfying the compatibility equations. This developed element passed both patch and benchmark tests in the case of bending and shear problems. For the dynamic analysis, lumped mass with implicit/explicit time integration are employed. The obtained numerical results using the developed element converge toward the analytical and numerical solutions in both analyses.
In this paper, progressive crushing of prismatic multi-corner thin walled metal tubes under quasi-static axial load is investigated in detail. The novelty of the paper is mainly in considering strain hardening effect during plastic deformation instead of rigid plastic model and also the effect of curvature in forming the folds instead of plastic hinges. For this purpose, a new geometric model based on FEM and experimental observations is used which is capable of being adapted with new crushing configurations during crushing. Based on this model, the instantaneous energy associated with plastic deformation of different regions are calculated and finally by summing all energies and using minimum absorbed energy, mean crushing force and collapse parameters are determined. To evaluate the results, a detailed finite element study using ABAQUS and LS-Dyna solver is conducted on some regular polygonal mild steel tubes under axial crushing. Comparing the results of the new theoretical approach with FEM results show very good capability of that in predicting collapse behavior of these structures.
The exact solutions of Pochhammer — Chree equation for propagating harmonic waves in isotropic elastic cylindrical rods, are analyzed. Spectral analysis of the matrix dispersion equation for the longitudinal axially symmetric modes is performed. Analytical expressions for displacement fields are obtained. Variation of the wave polarization due to variation of Poisson’s ratio for mild auxetics (Poisson’s ratio is greater than -0.5) is analyzed and compared with the non-auxetics. It is observed that polarization of the waves for both considered cases (auxetics and non-auxetics) exhibits abnormal behavior in the vicinity of the bulk shear wave speed.
The concepts of nodal value and grid average in cell centered finite volume method (FVM) are clarified in this work, strict distinction between the two concepts in constructing numerical schemes is made, and common fault in misidentifying the two concepts is pointed out. The expansion based on grid average, similar to Taylor’s expansion, is deduced to construct correct scheme in terms of grid average and to obtain modified partial differential equation (MPDE) which determines the order of accuracy of numerical scheme theoretically. Correct high order scheme, taking QUICK (Quadratic Upstream Interpolation for Convective Kinematics) scheme as an example, is constructed in different approaches. Furthermore, the property of interpolation coefficients is analyzed. We also pointed out that for high order schemes, round-off error dominates the absolute error in fine grid and truncation error dominates the absolute error in coarse grid.
An algorithm for the computation and analysis of the Cosserat spectrum for an axisymmetric elasticity boundary-value problem in a finite-length solid cylinder with boundary conditions in terms of stresses is proposed. By making use of the cross-wise superposition method, the spectral problem is reduced to systems of linear algebraic equations. A solution method for the mentioned systems is presented and the asymptotic behavior of the Cosserat eigenvalues is established. On this basis, the key features of the Cosserat spectrum for the mentioned problem are analyzed with special attention given to the effect of the cylinder aspect ratio.
A mechanical beam resonator engineered at nanoscale for suppressing thermoelastic damping to obtain ultrahigh quality factor is reported. The resonator employs the torsion mode of a spring beam to excite the rotation oscillation of a nanoscale resonant beam. The ultralow thermoelastic damping in the resonator is obtained by employing torsion oscillation. Optimal study of thermoelastic damping is carried out by varying the dimensional parameters of the resonator. The resonator operating in the MHz regime with the quality factor over one million is obtainable by the proposed oscillation exciting method and appropriate design of dimensional parameters of the beams. In order to obtain such overall intrinsic quality factor, virtual supports are employed to eliminate attachment loss in the resonator.
The mechanical properties of thin-walled plate with close-packed film cooling holes are studied based on the equivalent solid material concept. The equivalent principals of the method of equivalent strain energy, homogenization theory and uniform static deformation are considered. A simplification method of square penetration pattern for pitch and diagonal direction loading is presented. The goodness of fit is calculated to determine the optimal method. The tensile deformation, bending deflection, rotation displacement and maximum Mises equivalent stress of simplification plate models are in good agreement with plate models with close-packed film cooling holes. For square penetration pattern for pitch direction loading, the equivalent errors of Mises equivalent stress are all less than 10% when the ligament efficiency is more than 0.6.
The finite element method (FEM) was used to study the elastic-plastic contact in the coating systems with interlayer. The results reveal that with the increase of interlayer thickness, the maximum shear stress of coating/interlayer and interlayer/substrate interfaces decreases. Moreover, the sharply changed shear stress between the interfaces of coating/interlayer and interlayer/substrate decreases too. There is no further decrease when interlayer thickness increase to 0.04 mm and above. With the increasing of interlayer elastic modulus, the shear stress of coating/interlayer interface decreases while the shear stress of interlayer/substrate interface increases. Meanwhile, the higher elastic modulus leads to the intensive tensile stress concentration on the interface of coating/interlayer. Hence, the interlayer with appropriate elastic modulus not only reduces the shear stress of coating/interlayer and interlayer/substrate interfaces but also decreases the tensile stress of coating/interlayer interface. The mechanical properties of coating systems were investigated with different interlayer yield strength. The effective hardness and elastic modulus increase with the increase of interlayer yield strength, which is good to protect the substrate from the deformation. In addition, higher indentation load can lead to the decrease of effective hardness and elastic modulus.
The present model is devoted for the steady stagnation point flow of a Williamson micropolar nanofluid with magneto-hydrodynamics and thermal radiation effects passed over a horizontal porous stretching sheet. The fluid is considered to be gray, absorbing-emitting but non-scattering medium. The Cogley-Vincent-Gilles formulation is adopted to simulate the radiation component of heat transfer. By applying similarity analysis, the governing partial differential equations are transformed into a set of non-linear ordinary differential equations and they are solved by using the bvp4c package in MATLAB. Numerical computations are carried out for various values of the physical parameters. The effects of momentum, microrotation, temperature and nanoparticle volume fraction profiles together with the reduced skin friction coefficient, reduced Nusselt number and reduced Sherwood number of both active and passive controls on the wall mass flux are graphically presented. The present results are compared with previously obtained solutions and they are in good agreement. Results show that the skin friction is increasing functions of the Williamson parameter in both stretching and shrinking surfaces.
In this study, cooling of a constant temperature cube that represents electronic components inserted inside a channel are investigated. For this purpose, primary air with constant velocity is transferred from channel input, and secondary air with impinging jet is transferred to channel upper surface which corresponds to top part of the components. The flows are in contact with the cube that has constant temperature and effects the thermal boundary layer on the cube surfaces to create a heat transfer from cube to fluid. This situation is simulated under turbulence conditions for different values of nozzle jet input velocity (Vj) and channel input velocity (Uc) using Reynolds number between 30000-90000 based on channel input velocity. For this purpose, velocity, temperature, and pressure distributions are obtained for the solution region using CFD package program. As a result, flow and thermal characteristics inside the channel are parametrically calculated based on Reynolds number, Nusselt number, and cube surface temperature.
In the present paper, we investigate the hydrodynamic instability of Dean flow under different Dean numbers ranging from 1 to 2500, curvature ratios from 0.0001 up to 1000 and temperatures ranging from 273.15 K to 373.15 K. To study of fluid flow instability, analytical velocity profiles under intended conditions and energy gradient function K in the energy gradient method are evaluated. The results of present study show that, as the curvature ratio increases the flow becomes more stable. Moreover, no regular and significant effects on the energy gradient function K were achieved by increasing of temperatures. We found that, the origin of instability in the entire flow field is located on the inner wall of the parallel curved walls, especially for larger curvature ratios. We also reported the critical value of the energy gradient function K for the onset of instability corresponding to the critical Dean number.
In this article, random flutter of multi-stable airfoils in steady flow is investigated by means of the analytical method for stochastic P-bifurcation, where the effect of the stochastic disturbance in the generalized flow speed on the airfoils is considered. The results show that under constant stochastic disturbance intensity, the coherence resonance could be induced by the variation of generalized flow speed. In addition, if the generalized flow speed keeps unchanged and its stochastic disturbance is sufficiently large, the response of the system will tend to be a stable equilibrium. It indicates that the parametric stochastic disturbance is effective to maintain system stability. Moreover, it is shown in this paper that the analytical method for stochastic P-bifurcation can be extended to study stochastic P-bifurcations in other high-dimensional systems.
This study investigates numerically the performance of applying aerospike nozzle in a hydrogen peroxide mono-propellant propulsion system. A set of governing equations, including continuity, momentum, energy and species conservation equations with extended k-ε turbulence equations, are solved using the finite-volume method. The hydrogen peroxide mono-propellant is assumed to be fully decomposed into water vapor and oxygen after flowing through a catalyst bed before entering the nozzle. The aerospike nozzle is expected to have high performance even in deep throttling cases due to its self-compensating characteristics in a wide range of ambient pressure environments. The results show that the thrust coefficient efficiency (Cf,η) of this work exceeds 90% of the theoretical value with a nozzle pressure ratio (PR) in the range of 20 ~ 45. Many complex gas dynamics phenomena in the aerospike nozzle are found and explained in the paper. In addition, performance of the aerospike nozzle is compared with that of the bell-shape nozzle.