Solution of bending of cantilever rectangular plates under uniform surface-load by the method of two-direction trigonometric series

The bending of a cantilever rectangular plate is a very complicated problem in thetheory of plates.For a long time,there have been only approximate solutions for thisproblem by energy methods and numerical methods.since 1979,Prof.F.V.Chang of Tsing Hua University obtained,by the method ofsuperposition,a series of analytic solutions for cantilever rectangular plates under uniformload and concentrated load.In this paper,the two-direction trigonometric series is used to obtain the solution forthe bending of cantilever rectangular plates under uniform load.The obtained results arecompared with the results by the method of superposition.The comparison shows that theresults of these two methods are in good agreement,hence they are mutually confirmed to becorrect.     

Characterization of material mechanical properties using strain correlation method combined with virtual fields method

Acta Mechanica Sinica - The isotropic and anisotropic behaviors are considered as the important formats of the constitutive behaviors, and can also be called the global properties. To improve the...     

计算重根特征向量导数的消元法

本文提出了重根特征向量导数计算的消无法，它分为若干直接算法和一种迭代算法。这种方法概念简单、实施容易、精度良好。该方法可经简单移值用于非重根情况。     

精细时程积分法及其数值衍生格式应用评估

旋翼气动弹性耦合动力学方程本质上是一组刚性比较大的非线性偏微分方程。在有限元结构离散后,可改写为非齐次微分方程组,其中非齐次项是桨叶运动量（位移与速度）和气动载荷的函数。针对这类方程,本文尝试引入精细积分法及其衍生格式,借助数值方法计算Duhamel积分项。从积分精度与数值稳定性方面比较研究具有代表性的精细库塔法和高精度直接积分法。结合隐式积分算法,评估精细积分法应用于旋翼动力学方程的可行性。算例表明,精细积分法对矩形直桨叶动力学方程具有足够的求解精度。     

车桥系统非平稳随机振动的PEM-PIM算法

研究了车桥耦合系统受到路面不平激励而发生的非平稳随机振动.采用虚拟激励方法(PEM)将路面的竖向随机不平度精确地转化为一系列竖向简谐不平度的叠加,从而简化了运动方程的求解,在此基础上用精细积分法(PIM)的三种格式进行数值计算.这种基于虚拟激励法的精细积分(PEM-PIM)算法比通常的数值积分方法更真实地模拟了车辆作用力在时间域和空间域上的连续变化,也更精确地实施了数值积分.与广泛采用的Newmark方法比较,三种PEM-PIM格式处理这类问题时在分析精度和计算效率上都有显著的改善,而又各有特色.     

Gradient elasticity in statics and dynamics: An overview of formulations,length scale identification procedures,finite element implementations and new results

In this paper, we discuss various formats of gradient elasticity and their performance in static and dynamic applications. Gradient elasticity theories provide extensions of the classical equations of elasticity with additional higher-order spatial derivatives of strains, stresses and/or accelerations. We focus on the versatile class of gradient elasticity theories whereby the higher-order terms are the Laplacian of the corresponding lower-order terms. One of the challenges of formulating gradient elasticity theories is to keep the number of additional constitutive parameters to a minimum. We start with discussing the general Mindlin theory, that in its most general form has 903 constitutive elastic parameters but which were reduced by Mindlin to three independent material length scales. Further simplifications are often possible. In particular, the Aifantis theory has only one additional parameter in statics and opens up a whole new field of analytical and numerical solution procedures. We also address how this can be extended to dynamics. An overview of length scale identification and quantification procedures is given. Finite element implementations of the most commonly used versions of gradient elasticity are discussed together with the variationally consistent boundary conditions. Details are provided for particular formats of gradient elasticity that can be implemented with simple, linear finite element shape functions. New numerical results show the removal of singularities in statics and dynamics, as well as the size-dependent mechanical response predicted by gradient elasticity.     

Modeling of wrinkling of thin circular sheets

A version of the imperfection method is used to investigate the wrinkling (tension buckling) of thin, elastic, homogeneous, isotropic circular plates of uniform thickness undergoing small deflections without inplane twisting. A numerical procedure based on the finite difference approach is employed to quantitatively predict wrinkling loads and wrinkling patterns for three sets of support conditions. Representative numerical results are presented in tabular and graphical formats and used to illustrate interesting aspects of the predictions.     

结构动力分析中的逐级近似缩聚法

本文基于逐级逼近理论建立了一种动力模型缩聚的逐级近似减缩法。该方法具有协调和非协调格式。本文基于ＳＡＲＴ导出了一般的ｋ级递推减缩公式，其中一级近似和二级近似减缩式就是现有的Ｇｕｙａｎ／Ｉｒｏｎｓ减缩和ＩＲＳ减缩。算例表明，在物理型减缩技术方面，本文的三级近似减缩模型精度最好。     

Spectral analysis of pump-cavitation noise

Pressure-transducer and accelerometer data accumulated during several water tests of a liquid-rocketengine pump were subjected to spectral analysis. The analyzer used allows signal amplitude to be displayed as a continuous function of frequency for each instant of time. Various filter bandwidths, integration times, frequency spans and display formats have been used to present the data for visual inspection. Results of attempts to discern the signature of various phases of the cavitation phenomenon occurring within the pump are reported.     

ILUS: An incomplete LU preconditioner in sparse skyline format

Incomplete LU factorizations are among the most effective preconditioners for solving general large, sparse linear systems arising from practical engineering problems. This paper shows how an ILU factorization may be easily computed in sparse skyline storage format, as opposed to traditional row-by-row schemes. This organization of the factorization has many advantages, including its amenability when the original matrix is in skyline format, the ability to dynamically monitor the stability of the factorization and the fact that factorizations may be produced with symmetric structure. Numerical results are presented for Galerkin finite element matrices arising from the standard square lid-driven cavity problem. © 1997 John Wiley & Sons, Ltd.     

Genetics teaching for non-geneticist health care professionals in the UK

OBJECTIVES: It was the aim of this study to describe the structure and content of training in genetics for non-genetics specialist health care professionals in the UK. METHODS: Data were collected by assessment of published syllabi and curricula and through contact with educational leads at responsible organisations. RESULTS: Twenty-six universities, 7 Royal Colleges and various intercollegiate boards and committees are involved in the provision of medical education at various levels, in addition to institutions offering nursing and/or midwifery training. Genetics is taught in variable formats, quantities and contents, and although some institutions are moving to adopt minimum competencies in genetics, this is by no means widespread. CONCLUSIONS: Given the wide number of stakeholders in the field, consensus competencies seem most likely to advance practice, and thus, phase II of the GenEd project will survey professionals to ascertain their priorities for genetic education.     

Finding the operating point of Eulerian flow machines

Examples of Eulerian flow machines (EFM) are turbomachines, jet pumps and vortex amplifiers working with incompressible non-cavitating flow. They are ‘Eulerian’ in the sense used by Paynter² in his work on turbomachines subject primarily to dynamic flow forces. Efficient methods are specified in this paper for finding the operating point of an EFM from its characteristics and any two state-defining variables. A trivial example is to find the torque and pressure of a pump when the speed and flow are given. This is simple because the usual constant-speed characterisation favours the solution, but if other pairs of variables are given, the problem is less simple. For jet pumps or the many ‘power fluidic’ devices the variety of problems is much greater because of combinatorial aspects, although the fluid mechanics is analogous to that of the turbomachine. Solution procedures are specified first for turbomachines; there are six ‘algorithms’. For general ‘3-terminal’ EFM (jet-pumps etc) it is shown that there are 108 characterisation formats and that the 30 listed algorithms enable any of them to be solved given any possible variable-pair. Graphical and computational implementations are described     

On the generalized virial theorem for systems with variable mass

We presently extend the virial theorem for both discrete and continuous systems of material points with variable mass, relying on developments presented in Ganghoffer (Int J Solids Struct 47:1209–1220, 2010). The developed framework is applicable to describe physical systems at very different scales, from the evolution of a population of biological cells accounting for growth to mass ejection phenomena occurring within a collection of gravitating objects at the very large astrophysical scales. As a starting basis, the field equations in continuum mechanics are written to account for a mass source and a mass flux, leading to a formulation of the virial theorem accounting for non-constant mass within the considered system. The scalar and tensorial forms of the virial theorem are then written successively in both Lagrangian and Eulerian formats, incorporating the mass flux. As an illustration, the averaged stress tensor in accreting gravitating solid bodies is evaluated based on the generalized virial theorem.     

A parametric study for thick plates resting on elastic foundation with variable soil depth

The soil depth is generally considered to be constant for the analysis of plates resting on elastic foundation in the literature. However, it is most reasonable to have a variable subsoil depth as the plate dimensions get larger. In present study, linearly varying subsoil depth is considered as well as constant, linear and quadratic variation of modulus of elasticity with subsoil depth. Also, a parametric study is performed to demonstrate the behavior of thick plates on elastic foundations with variable soil depth. Modified Vlasov Model is used for the analysis of the plate foundation system, and 8-noded Mindlin plate element incorporating shear strain throughout plate thickness is used for the finite element model. Numerical examples are obtained from the literature to compare results and to show the influence of variable soil stratum depth on the behavior of plates. Displacements, bending moments, and shear forces are presented in tabular and graphical formats. As far as results are compared, it can be concluded that variable soil depth significantly affects the variation of the displacements and therefore the internal forces of the plate while keeping it constant ends up with unrealistic results.     

Comparison of the implementation of three common types of coupled CFD-DEM model for simulating soil surface erosion

Soil erosion is a common process studied by soil science, environmental engineering, geotechnical engineering, coastal engineering, and many other fields. In the areas of hydraulic engineering, the geotechnics of soil erosion remains a high priority topic as the bridge scour is a common cause of bridge failures. Accurate predictions of scour depth and soil erosion rate remain challenging, due to the limitations of existing scaled experimental approach in fulfilling the hydrological and hydrodynamic similarity requirements. Computational model offers a promising alternative to further the microscale understanding of soil erosion which can help to develop engineering tools in practice. Computational model that couples Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM) to simulate the behaviors of fluid-solid systems is promising to advance the current tools for soil erosion analyses. Different mathematical forms for laminar fluid flows exist for the coupled CFD-DEM model as documented in published literatures and implemented in commercial and open-source software; each of them is based on certain physics assumptions and corresponding mathematical treatments. There are, however, no direct comparison of the results of CFD-DEM models based on these seemingly different mathematical formulations, which would help researchers to select the proper simulation tool. This study implemented coupled CFD-DEM models based on three most common types of mathematical formats used in the previous modeling work. The results of different CFD-DEM models are firstly validated by comparing the results of simulating the free settling of a particle in fluid. A case study is then designed to compare the models in simulating the surface erosion of cohesionless soil inside a pipe flow using laminar flow equations. Comparison indicates that for a relatively sparse particle-fluid system, the difference of the three models is negligible. For a dense particle-fluid system, simulation with the three different mathematical formats can predict different results (as large as 10% in the fluid velocity and 20% in the particle drag force for the simulation case study analyzed). The results of this case study indicate that the three CFD-DEM models achieved comparable results for simulating soil erosion from an engineering perspective, however, the differences between these models, which originate from their underlying physics assumptions, must be kept in mind in selecting an appropriate simulation model as well as in comparing the results from different models.     

驻定斜爆轰波并行数值模拟

采用多组分化学反应Euler方程组对驻定在高速飞行弹丸上的斜爆轰波流场进行了数值模拟。计算中分别采用TVD格式和基元反应模型,并基于并行编程模型MPI（message passing interface）实现了非结构网格上的并行计算,对流项和化学反应项用时间分裂法进行处理。计算结果表明并行计算能有效地提高计算速度,扩展计算规模,为进一步研究超驱爆轰推进技术奠定基础。     

An image processing technique for measuring free surface of dam-break flows

This paper describes an imaging method for measuring water surface in rapidly varying flows based on light absorption. After preliminary spatially distributed calibration, the water depth field is obtained by processing the images of the free surface captured by a digital camera looking downstream at a back-lighted device. The water body is coloured so that it acts as a variable-density filter. This method was used to detect the topography of water surface in a series of laboratory dam-break tests. Its validity was assessed by locally comparing the water depth time series derived from images with the ones returned by six ultrasonic distance metres. The experimental results obtained starting from two different image formats show that the accuracy of this technique is comparable to that of conventional ultrasonic transducers. Therefore, the method can be considered as an effective tool for collecting high-resolution spatial distributed experimental data useful to validate numerical models.     

On configurational forces in multiplicative elastoplasticity

The main goal of this work consists in the elaboration of the material or rather configurational mechanics in the context of multiplicative elastoplasticity. This nowadays well-established approach, which is inherently related to the concept of a material isomorphism or in other words to a local rearrangement, is adopted as a paradigm for the general modelling of finite inelasticity. The overall motion in space is throughout assumed to be compatible and sufficiently smooth. According to the underlying configurations, namely the material and the spatial configuration as well as what we call the intermediate configuration, different representations of balance of linear momentum are set up for the static case. The underlying flux terms are thereby identified as stress tensors of Piola and Cauchy type and are assumed to derive from a free energy density function, thus taking hyperelastic formats. Moreover, the incorporated source terms, namely the configurational volume forces, are identified by comparison arguments. These quantities include gradients of distortions as well as dislocation density tensors. In particular those dislocation density tensors related to the elastic or plastic distortion do not vanish due to the general incompatibility of the intermediate configuration. As a result, configurational volume forces which are settled in the intermediate configuration embody non-vanishing dislocation density tensors while their material counterparts directly incorporate non-vanishing gradients of distortions. This fundamental property enables us to recover the celebrated Peach–Koehler force for finite inelasticity, acting on a single dislocation, from the intermediate configuration volume forces.     

On the use of the complementary energy in the solution of buckling problems

A systematic derivation of the expression for the complementary energy in elastic buckling problems is presented. Compatibility is identified with variation with respect to the stress components, and the resulting eigenvalue problem is shown to be equivalent to, and sometimes more convenient than, the corresponding formulation in terms of the potential energy. Similarly, approximate techniques may lead to better as well as simpler estimates, whose upper bound property can, however, be assured only through appropriate safeguards.The method is applied in some detail to buckling of columns of arbitrary boundary conditions and axial force distribution. Another example is the problem of lateral beam buckling, with the effect of warping restraint included. In both cases (and presumably in many others) the complementary energy formulation is of lower order than the conventional potential energy formulation, and it is clear that the same simplification should also apply to finite elements or other discrete formats. The method is restricted to the (technically significant) case of a linear prebuckling state.     

Low-rank solution of an optimal control problem constrained by random Navier-Stokes equations

We develop a low-rank tensor decomposition algorithm for the numerical solution of a distributed optimal control problem constrained by two-dimensional time-dependent Navier-Stokes equations with a stochastic inflow. The goal of optimization is to minimize the flow vorticity. The inflow boundary condition is assumed to be an infinite-dimensional random field, which is parametrized using a finite- (but high-) dimensional Fourier expansion and discretized using the stochastic Galerkin finite element method. This leads to a prohibitively large number of degrees of freedom in the discrete solution. Moreover, the optimality conditions in a time-dependent problem require solving a coupled saddle-point system of nonlinear equations on all time steps at once. For the resulting discrete problem, we approximate the solution by the tensor-train (TT) decomposition and propose a numerically efficient algorithm to solve the optimality equations directly in the TT representation. This algorithm is based on the alternating linear scheme (ALS), but in contrast to the basic ALS method, the new algorithm exploits and preserves the block structure of the optimality equations. We prove that this structure preservation renders the proposed block ALS method well posed, in the sense that each step requires the solution of a nonsingular reduced linear system, which might not be the case for the basic ALS. Finally, we present numerical experiments based on two benchmark problems of simulation of a flow around a von Kármán vortex and a backward step, each of which has uncertain inflow. The experiments demonstrate a significant complexity reduction achieved using the TT representation and the block ALS algorithm. Specifically, we observe that the high-dimensional stochastic time-dependent problem can be solved with the asymptotic complexity of the corresponding deterministic problem.