正交各向异性厚板的边界元解法

本文利用 Hormander 算子法和平面波分解法导出了计入剪切变形的正交各向异性厚板的基本解。建立了计入剪切变形的正交各向异性厚板的边界积分方程。文中详细地讨论了基本解的数值计算,并用边界元法分析了一些算例。     

Microstructure in a Cubic to Orthorhombic Transition

Microstructures for a cubic to orthorhombic transition are constructed using a geometrically nonlinear, thermoelastic theory of martensitic transformations. Such microstructures are of interest because they provide low energy paths along which a specimen can transform. The particular microstructures considered are the twinned martensite, austenite–martensite, wedge, triangle, and diamond. More specifically, all possible twins are found along with the corresponding twinning elements and magnitude of the twin shear. Further, two kinds of austenite–martensite microstructures are studied: those with a single variant of martensite and those with twinned martensite. The regions in the space of transformation stretches in which each of these microstructures exist are determined, and the shape strains and habit plane normals are found as well. In addition, special microstructures, the wedge, triangle, and diamond, are constructed with both the austenite-single variant and austenite-twinned martensite microstructures. These special microstructures are of interest because they provide a mechanism through which the transformation may proceed more easily, and they are possible only in alloys with particular transformation stretches. Numerically computed level curves in the space of the stretches are presented on which the special microstructures are possible. These results may be useful in providing guidelines for alloy design.     

Exact solution to peristaltic transport of power-law fluid in asymmetric channel with compliant walls

Effects of compliant wall properties on the peristaltic flow of a non-Newtonian fluid in an asymmetric channel are investigated.The rheological characteristics are characterized by the constitutive equations of a power-law fluid.Long wavelength and low Reynolds number approximations are adopted in the presentation of mathematical developments.Exact solutions are established for the stream function and velocity.The streamlines pattern and trapping are given due attention.Salient features of the key parameters entering into the present flow are displayed and important conclusions are pointed out.     

Method of molecular dynamics in mechanics of deformable solids

The basic principles of the method of molecular dynamics are analyzed. Symplectic difference schemes for the numerical solution of molecular dynamics equations are considered. Stability is studied, and the errors in the energy conservation law, which are induced by using these schemes, are estimated. Equations of mechanics of continuous media are derived by means of averaging over the volume of an atomic system. Expressions for the stress tensor are obtained by using the virial principle and the method of averaging over the volume. The principles of construction of EAM and MEAM potentials of atomic interaction in crystals are analyzed. Two problems of fracture of copper-molybdenum composites are solved by the method of molecular dynamics.     

Approximate symmetries of creeping flow equations of a second grade fluid

Creeping flow equations of a second grade fluid are considered. Two current approximate symmetry methods and a modified new one are applied to the equations of motion. Approximate symmetries obtained by different methods and the exact symmetries are contrasted. Approximate solutions corresponding to the approximate symmetries are derived for each method. Symmetries and solutions are compared and advantages and disadvantages of each method are discussed in detail.     

根部柔性梁的不确定性建模与确认

首先导出了包含根部挠性参数的悬臂梁动力学方程近似解,将平动和转动柔性参数作为不确定性源,根据若干预紧力矩下的模态实验结果完成了柔性参数识别,并假定其服从正态随机分布,识别了均值与标准差,进而通过回归分析建立了不确定参数随预紧力矩变化的数学模型.最后通过新的模态实验结果对所建模型进行了确认,通过确认结果,明确了该模型的使用范围.     

张拉膜结构力密度法混合找形分析

论述了张拉膜结构力密度法混合找形的基本理论;所谓力密度法混合找形,即部分单元力密度控制,部分单元弹性控制;力密度控制采用线性求解,弹性控制采用非线性求解,通过迭代计算混合找形求出各结点的坐标值。据此编制了相应的计算软件;对工程实例进行了验算,结果表明,本文给出的计算结果与德国著名软件easy的计算结果相吻合。     

Analysis of Isolation Effectiveness of Shear Waves by a Row of Hollow Pipe Piles in Saturated Soils

Wave numbers about the three types of waves in saturated soils are firstly given in this paper. The lengths of the pipe piles are much larger than their diameters, so the isolation problem about SV waves by discontinuous barriers composed of a row of pipe piles can be simplified as a two-dimensional scattering problem. The expansion method of wave functions is adopted, the stresses and displacements at the boundaries between the pipe piles and adjacent soils are considered as continuous and the inner sides of the pipe piles are free, and then the theoretical solutions are obtained about this two-dimensional scattering problem. Normalized displacements are introduced, which are the displacements behind the barriers caused by both the incident and scattered waves to those only by the incident SV waves, contours and curves of the normalized displacements are drawn, and the influences of wall thickness of pipe piles, modulus ratio of pipe piles to soils, spacing distance between the pipe piles and pipe pile numbers on the isolation effectiveness are analyzed.     

Generalized hydrodynamical equations obeying the entropy principle

Three generalizations of classical hydrodynamic theories that are compatible with equilibrium thermodynamics and that are suitable for an appropriate macroscopic dynamical theory of polymeric liquids are considered. The strain tensor, the stress tensor and the chain segment distribution function (introduced in the network theory of polymeric liquids) are accepted as new state variables. We find that the generalized hydrodynamic equations are compatible with equilibrium thermodynamics provided certain conditions restricting the freedom of choice of constitutive relations are satisfied. In some particular cases the conditions are known from other considerations. We say that a dynamical theory is compatible with equilibrium thermodynamics, or equivalently, that it obeys the entropy principle if the properties listed in section 2.1 are satisfied.     

Supersonic Inviscid Corner Flows with Regular and Irregular Shock Interaction

The results of a numerical and analytical investigation of steady-state supersonic inviscid flows in corners formed by intersecting compression wedges are presented. The flows considered are symmetric about the corner bisector. The distinctive features of flow pattern formation related with the reflection of wedge-generated shocks from the bisector plane are studied. The wedge angles at which transition from regular to irregular shock reflection occurs are determined both numerically and analytically using the criteria available for plane flows; the data thus obtained are found to be in agreement. Flow patterns with irregular shock reflection, namely, single, transitional, and double Mach, as well as von Neumann reflection, are identified; they are similar to the known types of reflection for plane quasi-steady-state flows. Varieties of these types not observed in the plane flows are found to exist. The effects of the angle of inclination of the plane surfaces of the corner to the freestream direction, the sweep angle of the leading edges, and the dihedral angle are investigated. Some previously unknown parameters of corner configurations for which transition may occur in accordance with the von Neumann criterion are determined.     

DYNAMIC STRESS INTENSITY FACTORS AROUND TWO CRACKS NEAR AN INTERFACE OF TWO DISSIMILAR ELASTIC HALF－PLANES UNDER IN－PLANE SHEAR IMPACT LOAD

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Forced vibrations of orthotropic shells: nonclassical boundary-value problems

The forced vibrations of a cylindrical orthotropic shell are studied. Two types of boundary conditions on the outer surface are examined considering that the displacement vector prescribed on the inner surface varies harmonically with time. Asymptotic solutions of associated dynamic equations of three-dimensional elasticity are found. Amplitudes of forced vibrations are determined and conditions under which resonance occurs are established. Boundary-layer functions are defined. The rate of their decrease with distance from the ends inside the shell is determined. A procedure of joining solutions for the internal boundary-layer problem is outlined in the case for the, if clamping boundary conditions are prescribed at the ends     

Mesh effects on the computation of non-linear gravity waves of arbitrary discharge

Numerical computations of non-linear gravity waves are presented and the effects of mesh variations on the results are discussed. Waves are regarded as two-parameter families (λ,A)_Q of arbitrary discharge Q, and computations are carried out using a new Kantorovich algorithm. Mesh effects are to a large extent dependent on the particular wave region under consideration. Three such regions are identified and typical examples are computed and discussed.     

Topology Optimization of Perforated Continua Based on Truss-Like Material Model

A topology optimization method from truss-like continua to perforated continua is studied, which is based on the concept of force transmission paths. The force transmission paths are optimized utilizing a truss-like material model. In the optimization procedure, parts of the force transmission paths are removed. Finally, perforated optimal continua are formed by further optimizing the material distribution field. No intermediate densities are suppressed; therefore, no additional technique is involved and no numerical instabilities are created. Structural topologies are presented using material distribution fields rather than the 'existence' or 'inexistence' of elements. More detailed structures are obtained utilizing less dense elements.     

Nonlinear flexural waves in fluid–filled elastic channels

Nonlinear waves on liquid sheets between thin infinite elastic plates are studied analytically and numerically. Linear and nonlinear models are used for the elastic plates coupled to the Euler equations for the fluid. One-dimensional time-dependent equations are derived based on a long-wavelength approximation. Inertia of the elastic plates is neglected, so linear perturbations are stable. Symmetric and mixed-mode travelling waves are found with the linear plate model and symmetric travelling waves are found for the nonlinear case. Numerical simulations are employed to study the evolution in time of initial disturbances and to compare the different models used. Nonlinear effects are found to decrease the travelling wave speed compared with linear models. At sufficiently large amplitude of initial disturbances, higher order temporal oscillations induced by nonlinearity can lead to thickness of the liquid sheet approaching zero.     

Identification of small well-separated defects in an isotropic elastic body using boundary measurements

An inverse problem of identification of a finite number of small, well-separated defects in an isotropic linear elastic body is considered. It is supposed that the defects are cavities or inclusions (rigid or linear elastic). If the defects are cavities then their boundaries are supposed unloaded. If the defects are inclusions it is supposed complete bonding between the matrix and inclusions. It is assumed also that as a result of static test the loads and displacements are measured on the external boundary of the body. A method for determination of centers of the defects projections on an arbitrary plane is developed. If the defects are ellipsoids their geometrical parameters (directions and magnitudes of the ellipsoids axes) are determined also. Numerical examples illustrating efficiency of the developed method are considered.     

An error analysis of holographic strains determined by cubic splines

Holographic measurements of an idealized cantilever beam under end-loading and uniform-loading conditions are simulated on a computer. Cubic splines are fitted to the simulated data and then used to evaluate the shear strain and bending moment. Controlled data errors are introduced into the simulated measurements and the strain and bending-moment results are compared with the known analytic results. When the data are not resolution limited, the accuracy of the results increases as more cubic splines are taken. However, when the data are resolution limited, the accuracy of the results is a maximum for an optimum number of cubic splines and the use of more splines actually decreases the accuracy.     

Comparison of methods for calculating the shock hugoniot of mixtures

Various methods used to determine the shock Hugoniot of condensed phase multi-component mixtures are reviewed and compared to available experimental data. The assumptions inherent in the different models are presented in this overview and their implications are discussed. The comparisons of the various models demonstrate that the predicted shock Hugoniots are in good agreement with published data despite the simplifying assumptions that are associated with the models. Averaging models are shown to be among the simplest methods to implement and result in the closest agreement with experimental data.     

Simulation of spatial multibody systems with friction

A formulation for modeling and simulation of friction effects in spatial multibody systems is presented. Constraint reaction forces on rigid bodies that are connected by joints that support friction are derived as functions of Lagrange multipliers, using D’Alembert’s principle. Friction forces acting on bodies are calculated as a function of joint geometry, constraint reaction forces that are functions of Lagrange multipliers, and relative velocities at constraint contact points that are determined by system kinematics. Friction forces are implemented in index 0 differential-algebraic equations of motion that are solved numerically using explicit and implicit numerical integration methods. Spatial examples are presented, yielding accurate results and demonstrating that the systems are not stiff, even in the presence of friction and stiction.