Mass-Stiffness Templates for Cubic Structural Elements Dedicated to Professor Karl Stark Pister for his 95th birthday

1 This paper considers Lagrangian finite elements for structural dynamics constructed with cubic displacement shape functions.The method of templates is used to investigate the construction of accurate mass-stiffness pairs.This method introduces free parameters that can be adjusted to customize elements according to accuracy and rank-sufficiency criteria.One-and two-dimensional Lagrangian cubic elements with only translational degrees of freedom(DOF)carry two additional nodes on each side,herein called side nodes or SN.Although usually placed at the third-points,the SN location may be adjusted within geometric limits.The adjustment effect is studied in detail using symbolic computations for a bar element.The best SN location is taken to be that producing accurate approximation to the lowest natural frequencies of the continuum model.Optimality is investigated through Fourier analysis of the propagation of plane waves over a regular infinite lattice of bar elements.Focus is placed on the acoustic branch of the frequency-vs.-wavenumber dispersion diagram.It is found that dispersion results using the fully integrated consistent mass matrix(CMM)are independent of the SN location whereas its lowfrequency accuracy order is O(κ8),whereκis the dimensionless wave number.For the diagonally lumped mass matrix(DLMM)constructed through the HRZ scheme,two optimal SN locations are identified,both away from third-points and of accuracy order O(κ8).That with the smallest error coefficient corresponds to the Lobatto 4-point integration rule.A special linear combination of CMM and DLMM with nodes at the Lobatto points yields an accuracy of O(κ10)without any increase in the computational effort over CMM.The effect of reduced integration(RI)on both mass and stiffness matrices is also studied.It is shown that singular mass matrices can be constructed with 2-and 3-point RI rules that display the same optimal accuracy of the exactly integrated case,at the cost of introducing spurious modes.The optimal SN location in two-dimensional,bicubic,isoparametric plane stress quadrilateral elements is briefly investigated by numerical experiments.The frequency accuracy of flexural modes is found to be fairly insensitive to that position,whereas for bar-like modes it agrees with the one-dimensional results.

Isogeometric Collocation:A Mixed Displacement-Pressure Method for Nearly Incompressible Elasticity Dedicated to Professor Karl Stark Pister for his 95th birthday

We investigate primal and mixed u−p isogeometric collocation methods for application to nearly-incompressible isotropic elasticity.The primal method employs Navier’s equations in terms of the displacement unknowns,and the mixed method employs both displacement and pressure unknowns.As benchmarks for what might be considered acceptable accuracy,we employ constant-pressure Abaqus finite elements that are widely used in engineering applications.As a basis of comparisons,we present results for compressible elasticity.All the methods were completely satisfactory for the compressible case.However,results for low-degree primal methods exhibited displacement locking and in general deteriorated in the nearly-incompressible case.The results for the mixed methods behaved very well for two of the problems we studied,achieving levels of accuracy very similar to those for the compressible case.The third problem,which we consider a“torture test”presented a more complex story for the mixed methods in the nearly-incompressible case.

Effects of Rotation on Turbulence Production

Direct numerical simulations (DNS) of non-rotating and rotating turbulent channel flow were conducted. The data base obtained from these DNS simulations was used to investigate the prominent coherent structures involved in the turbulence generation cycle. Predictions from three theoretical models concerning the formation and evolution of sublayer streaks, three-dimensional hairpin vortices and propagating plane waves were validated using visualizations from the present DNS data. Quadrant analysis was used to determine a phase shift between the fluctuating streamwise and wall-normal velocities as a characteristic of turbulence production in the suction region at a low rotation number.

利用COSMIC数据研究顶部电离层O~＋扩散流的统计特征

从等离子体运动方程出发,利用COSMIC星座的掩星数据,借助相关经验模式,计算了太阳活动低年顶部电离层O^+场向扩散速度和扩散通量,并分析了其全球分布和日变化特征.结果表明,白天等离子体扩散速度的方向随高度增加由向下(极向)逐步变为向上(赤道向),方向转变的高度一般在h_mF_2+80 km以下.在白天较高高度,南北磁纬10°～20°存在着向上方向的最大扩散速度和扩散通量;而在夜间,南北磁纬30°～40°存在向下方向的最大扩散速度和扩散通量.在分点,南北半球的扩散通量和扩散速度大致对称;而在至点,扩散通量存在着明显的南北半球不对称现象.另外,不同纬度的扩散速度有着不同的日变化特征.

Averaging analyses for spacecraft orbital motions around asteroids

This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orbits between the spacecraft mean motion and the central body＇s rotation. Averaging conditions for these cases are given. As a major extension, a few classes of near resonant orbits are analyzed by the averaging method. Then some resulted conclusions of these averaging analyses are applied to understand the stabil- ity regions in a numerical experiment. Some stability conclu- sions are obtained. As a typical example, it is shown in detail that near circular 1 ： 2 resonant orbit is always unstable.

Stable and Minimum Energy Configurations in the Spherical, Equal Mass Full 4-Body Problem

The minimum energy and stable configurations in the spherical,equal mass full 4-body problem are investigated.This problem is defined as the dynamics of finite density spheres which interact gravitationally and through surface contact forces.This is a variation of the gravitational n-body problem in which the bodies are not allowed to come arbitrarily close to each other(due to their finite density),enabling the existence of resting configurations in addition to orbital motion.Previous work on this problem has outlined an efficient and simple way in which the stability of configurations in this problem can be defined.This methodology is applied to the 4-body problem,where we find multiple resting equilibrium configurations and outline the stability of a number of these.The study of these configurations is important for understanding the mechanics and morphological properties of small rubble pile asteroids.These results can also be generalized to other configurations of bodies that interact via field potentials and surface contact forces.

Message from the Guest Editors of the Special Issue on Precise Orbit Determination

Dear authors and readers,Orbit determination is an old topic in celestial mechanics and astrodynamics.It originates from the need to determine the position and speed of natural or artificial objects in space through ground-station measurements,along with the need to estimate parameters involved in dynamics and observations.It has been the key to many important space applications.

Optimal motion cueing algorithm for accelerating phase of manned spacecraft in human centrifuge

This paper presents a novel optimal Motion Cueing Algorithm(MCA)to control the rotations of a Human Centrifuge(HC)and achieve the best simulation of a Space Craft(SC)motion.Relations of the specific forces sensed by astronauts of the SC and the HC have been derived and linearized.A Linear Quadratic Regulator(LQR)controller is implemented for the problem which tends to minimize the error between the two sensed specific forces as well as control input in a cost function.It results in control inputs of the HC to generate its sensed specific force as close as possible to the one in the SC.The algorithm is implemented for both linearized and nonlinear portions of a US space shuttle mission trajectory as a verification using MATLAB.In longitudinal direction,the proposed MCA,works well when the acceleration is less than 2 g in which the tracking error does not exceed 12%.In lateral direction the tracking is much better even in nonlinear region since the error remains less than 7%for tilting up to 50°.Finally,the effect of weight matrixes in the LQR cost function on overall weight and power of the HC motion system is discussed.

中国大陆现今地壳运动和构造变形

全球定位系统（ＧＰＳ）揭示的中国大陆现今运动场清晰地表现出了以活动地块 为单元的分块运动特征，不同的活动地块具有不同的运动和变形方式．ＧＰＳ观测到的阿 尔金断裂的左旋走滑速率仅（５．ｌ± ２．５）ｍｍ／ａ，龙门山断裂的挤压缩短速率为（６．７± ３．０） ｍｍ／ａ，华南地块相对于欧亚大陆向东的运动速率是 １１～１４ｍｍ／ａ，这些结果均不支持青 藏高原北部沿主要走滑断裂向东大规模挤出的假说．中国大陆以活动地块为单元的现 今构造变形可能与大陆岩石圈的结构和性质有关，上地壳以脆性变形为主，下地壳和 上地幔以粘塑性的流变为特征，从底部驱动着上覆脆性地块的整体运动．

Present-day crustal movement and tectonic deformation in China continent

Velocity field of China continent constrained by Global Positioning System (GPS) reveals both continuous and block-like styles of deformation. Continuous deformation commonly characterizes actively deforming mountain ranges such as the Tianshan Mountain, Qilian Mountain, and Tibet. The block-like movement often represents deformation in the tectonically stable regions such as Ordos, South China and Tarim blocks. GPS measurements indicate 5.1±2.5 mm/a left-lateral strike-slip rate along the Altun fault. Eastward convergence along the Longmenshan fault is less than 6.7±3.0 mm/a. South China moves 11-14 mm/a eastward compared with the stable Eurasia. These low slip rates do not imply rapid eastward extrusion of China continent predicted by the model of 'continental extrusion'. It appears that 'crustal thickening' model more properly describes both continuous and block-like styles of deformation in China continent.

A regularization scheme for explicit level-set XFEM topology optimization

Regularization of the level-set(LS)field is a critical part of LS-based topology optimization(TO)approaches.Traditionally this is achieved by advancing the LS field through the solution of a Hamilton-Jacobi equation combined with a reinitialization scheme.This approach,however,may limit the maximum step size and introduces discontinuities in the design process.Alternatively,energy functionals and intermediate LS value penalizations have been proposed.This paper introduces a novel LS regularization approach based on a signed distance field(SDF)which is applicable to explicit LSbased TO.The SDF is obtained using the heat method(HM)and is reconstructed for every design in the optimization process.The governing equations of the HM,as well as the ones describing the physical response of the system of interest,are discretized by the extended finite element method(XFEM).Numerical examples for pro?blems modeled by linear elasticity,nonlinear hyperelasticity and the incompressible Navier-Stokes equations in two and three dimensions are presented to show the applicability of the proposed scheme to a broad range of design optimization problems.

Representing dynamics in the eccentric Hill system using a neural network architecture

This paper demonstrates how artificial neural networks can be used to alleviate common problems encountered when creating a large database of Poincar´e map responses.A general architecture is developed using a combination of regression and classification feedforward neural networks.This allows one to predict the response of the Poincar´e map,as well as to identify anomalies,such as impact or escape.Furthermore,this paper demonstrates how an artificial neural network can be used to predict the error between a more complex and a simpler dynamical system.As an example application,the developed architecture is implemented on the Sun-Mars eccentric Hill system.Error statistics of the entire architecture are computed for both one Poincar´e map and for iterated maps.The neural networks are then applied to study the long-term impact and escape stability of trajectories in this system.