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[en] Steady two-dimensional turbulent free-surface flow in a channel with a slightly uneven bottom is considered. The shape of the unevenness of the bottom can be in the form of a bump or a ramp of very small height. The slope of the channel bottom is assumed to be small, and the bottom roughness is assumed to be constant. Asymptotic expansions for very large Reynolds numbers and Froude numbers close to the critical value , respectively, are performed. The relative order of magnitude of two small parameters, i.e. the bottom slope and , is defined such that no turbulence modelling is required. The result is a steady-state version of an extended Korteweg–de Vries equation for the surface elevation. Other flow quantities, such as pressure, flow velocity components, and bottom shear stress, are expressed in terms of the surface elevation. An exact solution describing stationary solitary waves of the classical shape is obtained for a bottom of a particular shape. For more general shapes of ramps and bumps, stationary solitary waves of the classical shape are also obtained as a first approximation in the limit of small, but nonzero, dissipation. With the exception of an eigensolution for a ramp, an outer region has to be introduced. The outer solution describes a ’tail’ that is attached to the stationary solitary wave. In addition to the solutions of the solitary-wave type, solutions of smaller amplitudes are obtained both numerically and analytically. Experiments in a water channel confirm the existence of both types of stationary single waves.
[en] The steady-state diagnostic and prognostic simulation for the Xiao Dongkemadi glacier (XD) of the Tibetan Plateau was performed with the thermo-mechanically-coupled-with-Full-Stokes code Elmer ( http://www.csc.fi/elmer/ ). In this paper, some changes of glacial thermodynamic parameters caused by ice thickness and atmospheric temperature variation were simulated in view of different thickness. The purpose of this study was to fill the gap in analyzing the ice dynamic characteristic of a polar continental glacier. The diagnostic simulation revealed the following conclusions: (1) when the thickness change was small, surface velocity, ice temperature, and deviation stress variation in the bedrock showed a tendency to change with thickness, and when the terrain was gentle, the thickness variation dominated the ice velocity. (2) The ice temperature of the bedrock was high in the whole profile and reached the pressure melting point in the terminus, and it was easy to slide at the bottom, which was consistent with the measured ground penetrating radar data near the terminus. (3) The static friction forces decrease with thickness, and they showed a complex nonlinear relationship, which revealed that the deviation stress in the bottom was influenced by thickness and ice temperature at the bedrock. The prognostic simulating from 2007 to 2047 presented: (1) The simulation forecasted a shrinkage of nearly 600 m in the terminus and the longitudinal section, and wound up diminished by nearly 25% by the end of 2047; (2) the change of thickness was small at the region between 5650 and 5700 m.a.s.l, which might be related to lower atmospheric temperature; (3) thickness dominated the deviation stress ( and ) in the bottom, and the impact of the terrain was little higher compared to deviation stress (). In other words, the glacial thickness dominated the glacial force and movement to a great extent and the low temperature at high altitude reduced the XD’s sensitivity facing future climate warming.
[en] This paper deals with the coupled bending–torsional vibrations of beams carrying an arbitrary number of viscoelastic dampers and attached masses. Exact closed analytical expressions are derived for the frequency response under harmonically varying, arbitrarily placed polynomial loads, making use of coupled bending–torsion theory including warping effects and taking advantage of generalized functions to model response discontinuities at the application points of dampers/masses. In this context, the exact dynamic Green’s functions of the beam are also obtained. The frequency response solutions are the basis to derive the exact dynamic stiffness matrix and load vector of a two-node coupled bending–torsional beam finite element with warping effects, which may include any number of dampers/masses. Remarkably, the size of the dynamic stiffness matrix and load vector is and , respectively, regardless of the number of dampers/masses and loads along the beam finite element.
[en] The fundamental concepts of material configurational mechanics are formulated in piezoelectric materials. A consistent thermodynamic framework is outlined to develop the corresponding theory of material configurational stresses and forces associated with the -, M- and L-integrals by the gradient, divergence and curl operation of the electric enthalpy density, respectively. The physical interpretation of material configurational stresses is explored, and they can be explained as the energy release rates due to the translation of material point along -direction, the self-similar expansion, the rotation of material element, respectively. The path independence or path dependence of variant integrals such as the -, M- and L-integrals is examined in piezoelectric material. As an application of material configurational mechanics in piezoelectric materials, an explicit method is derived to calculate the change of the J-integral as a dominant fracture parameter for a crack interaction with domain switching near the crack tip. It is concluded that domain switching has an obvious shielding effect on the fracture toughness in piezoelectrics by the present explicit forms. The present framework of material configurational mechanics is expected to provide an effective and convenient tool to deal with various crack or damage problems in piezoelectric materials.
[en] Bimodal nanostructured (NS) metals possess both ultrahigh strength and good ductility. It is the nanograined (NG) matrix phase that leads to their ultrahigh strength and the coarse-grained (CG) inclusion phase that renders their good ductility. But the overall strength and ductility can also be significantly affected by the behavior of the interface regions. In this study, we employ a cohesive finite-element method to investigate the tensile fracture process of the bimodal NS Cu that includes the interface effects. We develop three types of cohesive elements in the bimodal NS Cu: (i) cohesive elements in the CG phase, (ii) those in the NG phase, and (iii) those at the CG–NG interface. Our objective is to uncover how the strength and ductility of the bimodal NS Cu can be affected by the interface property. In this process, we will also examine how the distribution and shape of the CG inclusions can contribute to the variation of the tensile fracture behavior of the bimodal NS Cu. By an extensive simulation, we find that, even at the small ratio of 1.6% of interface cohesive elements to all cohesive elements, a small change in the cohesive strength of interface elements could lead to a significant change in the overall strength and ductility. We also find that, when the cohesive strength of interface elements exceeds a certain level, the strength and ductility of the bimodal NS Cu will reach a saturation state.
[en] The nonlocal effect on functionally graded multilayered quasicrystal nanoplates is investigated. The functionally graded quasicrystal is assumed to be exponentially distributed along the thickness direction of the simply supported nanoplates. The exact solution for functionally graded multilayered two-dimensional quasicrystal nanoplates subjected to a patch loading on their top surfaces is derived using the extended nonlocal elastic theory, pseudo-Stroh formalism, and propagator matrix method. The patch loading is indicated by the form of a double Fourier series expansion. Numerical examples are presented to reveal the influences of patch size, nonlocal parameter, and stacking sequence on the phonon, phason, and electric fields.
[en] In the numerical prediction of the homogenized macroscopic properties of an arbitrary heterogeneous material with periodic microstructure, a general formulation of the first-order perturbation-based stochastic homogenization method is presented in a discretized form based on the finite element method in order to consider the variability or uncertainty of the mechanical properties of the material models. Many random parameters are defined for each material model and for each component of the stress–strain matrix of the constituent’s material model. The first-order terms of the characteristic displacement are thoroughly studied both theoretically and numerically, and are also used in the verification of the developed computer code. The comparison with the Monte Carlo simulation also supports the proposed formulation.
[en] The transverse-horizontal wave propagating in a semi-infinite piezoelectric solid with hexagonal symmetry subject to initial electromechanical fields is investigated in this paper. The electromechanical boundary value problem is solved, and the phase velocity, the displacement, and the electric potential are obtained. For a metallized boundary surface, the dependency of the solution on the initial fields for several piezoelectric crystals is analyzed. These results may be proved useful to model the propagation of waves in anisotropic piezoelectric structures subject to a bias, serving as a benchmark for further numerical and experimental approaches.
[en] A new high-voltage electricity wire model is proposed to simulate the dynamic behavior of the wire after tension failure and the nonlinear sliding joints between the wire and the iron tower. A previously developed piecewise cable element based on the absolute nodal coordinate formulation is used with its computer implementation given in this paper. In order to describe the initial tension in the wire, a static solving approach is used to achieve equilibrium between the element elastic force and the external force including the tension. The obtained configuration of the wire is then used as the initial configuration of analysis in case of unloaded external tension force. Thereby, the dynamic behavior of the wire can be modeled. The sliding joint constraint is used to describe the motion of the wire going through the iron tower after tension failure. A new static solution approach is developed to avoid the sliding joint constraint violation in the resulting equilibrium configuration. The convergence of the piecewise cable element based on the absolute nodal coordinate formulation is tested. A set of comparative results is presented to demonstrate the feasibility of the method proposed in this investigation.
[en] In this paper, we proceed to develop a new approach which was formulated first in Ershkov (Acta Mech 228(7):2719–2723, 2017) for solving Poisson equations: a new type of the solving procedure for Euler–Poisson equations (rigid body rotation over the fixed point) is suggested in the current research. Meanwhile, the Euler–Poisson system of equations has been successfully explored for the existence of analytical solutions. As the main result, a new ansatz is suggested for solving Euler–Poisson equations: the Euler–Poisson equations are reduced to a system of three nonlinear ordinary differential equations of first order in regard to three functions (); the proper elegant approximate solution has been obtained as a set of quasi-periodic cycles via re-inversing the proper elliptical integral. So the system of Euler–Poisson equations is proved to have analytical solutions (in quadratures) only in classical simplifying cases: (1) Lagrange’s case, or (2) Kovalevskaya’s case or (3) Euler’s case or other well-known but particular cases.