A hybrid brick element with rotational degrees of freedom

An 8-node brick element using Allman's displacement interpolation is proposed. The optimal number of 36 stress modes is identified. The six equal-rotation strainless modes which are intrinsic to Allman's interpolation are stabilized by using a penalty method. The penalty also enforces the equality of the nodal rotation and the continuum-defined rotation. To enhance computational efficiency, 39 stress modes are initially assumed, three constraints on the stress field are then imposed. The flexibility matrix is simplified, such that only four symmetric 3 × 3 matrices are required to be inverted. Numerical test results are presented, showing good accuracy.     

Solid elements with rotational degrees of freedom: Part II—tetrahedron elements

This is the second part of a two part paper on three-dimensional finite elements with rotational degrees of freedom (DOF). Part II introduces a solid tetrahedron element having 3 translational and 3 rotational DOF per node. The corner rotations are introduced by transformation of the midside translational DOF of a 10-node tetrahedron element. To further enhance the element performance a least squares strain extraction technique is also implemented to develop the stiffness matrix with a desired field. The strain smoothing improves performance without causing a loss in generality. As with the hexahedron in Part I, the element stiffness is augmented with a small penalty stiffness to eliminate any possible spurious zero energy modes. The new tetrahedron element passes the patch test and demonstrates much improved performance over the 4-node translational DOF only (constant strain) tetrahedron element.     

Solid elements with rotational degrees of freedom: Part 1—hexahedron elements

This is the first of a two part paper on three-dimensional finite elements with rotational degrees of freedom (DOF). Part I introduces an 8-node solid hexahedron element having three translational and three rotational DOF per node. The corner rotations are introduced by transformation of the midside translational DOF of a 20-node hexahedron element. The new element produces a much smaller effective band width of the global system equations than does the 20-node hexahedron element having midside nodes. A small penalty stiffness is introduced to augment the usual element stiffness so that no spurious zero energy modes are present. The new element passes the patch test and demonstrates greatly improved performance over elements of identical shape but having only translational DOF at the corner nodes.     

Futher limitations on general hexahedron finite elements with derivative degrees of freedom

It is shown that isoparametric finite elements with derivative degrees of freedom of second order or higher in the local curvilinear space demand an excessive number of degrees of freedom in the global space. To illustrate this limitation as it pertains to the continued development of higher order elements, discussion is centered around the general hexahedron element.     

Simulation of tension fields with in-plane rotational degrees of freedom

This paper introduces a novel multigrid approach for the geometric non-linear simulation of tension fields on the basis of a three-node membrane finite element. The element possesses, in addition to the nodal displacement degrees of freedom, an in-plane rotational degree of freedom inside the element domain that controls the direction of the tension field. This rotational degree of freedom allows the enforcement of continuity and tension field boundary conditions on the basis of a coarser mesh with varying size.     

On hybrid stress,hybrid strain and enhanced strain finite element formulations for a geometrically exact shell theory with drilling degrees of freedom

The paper is concerned with the finite element formulation of a recently proposed geometrically exact shell theory with natural inclusion of drilling degrees of freedom. Stress hybrid finite elements are contrasted by strain hybrid elements as well as enhanced strain elements. Numerical investigations and comparison is carried out for a four-node element as well as a nine-node one. As far as the four-node element is concerned it is shown that the stress hybrid element and the enhanced strain one are equivalent. The hybrid strain formulation corresponds to the hybrid stress formulation only in shear dominated problems, that is the case of the plate. © 1998 John Wiley & Sons, Ltd.     

Planar four node piezoelectric elements with drilling degrees of freedom

Several new planar four node piezoelectric elements with drilling degrees of freedom are presented. We begin by deriving two families of variational formulations accounting for piezoelectricity and in‐plane rotations. The first family retains the skew‐symmetric part of the stress tensor, while in the second, the skew part of stress is eliminated from the functional. The finite elements derived from two of the variational formulations derived in this paper are investigated. The first element is based on an ‘irreducible’ form, while the other is based on a fully mixed functional, with both stress and electric flux density assumed. Our new elements are shown to be accurate and robust in comparison with a number of existing elements, for several benchmark test problems. Copyright © 2005 John Wiley & Sons, Ltd.     

Formulation of a membrane finite element with drilling degrees of freedom

A 4-noded membrane element with drilling degrees of freedom is developed. A functional for the linear problem, in which the drilling rotations are introduced as independent variables, is obtained from the functional for the corresponding nonlinear problem, initially derived by Atluri. A careful examination of the Euler equations shows that the Allman-type element fails to pass a one-element patch test with a minimum number of constraints. A 4-noded element, which passes the one-element patch test without constraining the drilling rotations, is proposed here with the use of the separate kinematics variables of displacement and rotation. Detailed numerical studies show the excellent performance of the element.Paper presented at the Workshop on Reliability of Finite Elements, TICOM, Texas, Nov. 1989     

A robust quadrilateral membrane finite element with drilling degrees of freedom

A quadrilateral membrane finite element with drilling degrees of freedom is derived from variational principles employing an independent rotation field. Both displacement based and mixed approaches are investigated. The element exhibits excellent accuracy characteristics. When combined with a plate bending element, the element provides an efficient tool for linear analysis of shells.     

A highly efficient membrane finite element with drilling degrees of freedom

In this paper, the development of a new quadrilateral membrane finite element with drilling degrees of freedom is discussed. A variational principle employing an independent rotation field around the normal of a plane continuum element is derived. This potential is based on the Cosserat continuum theory where skew symmetric stress and strain tensors are introduced in connection with the rotation of a point. From this higher continuum theory a formulation that incorporates rotational degrees of freedom is extracted, while the stress tensor is symmetric in a weak form. The resulting potential is found to be similar to that obtained by the procedure of Hughes and Brezzi. However, Hughes and Brezzi derived their potential in terms of pure mathematical investigations of Reissner’s potential, while the present procedure is based on physical considerations. This framework can be enhanced in terms of assumed stress and strain interpolations, if the numerical model is based on a modified Hu-Washizu functional with symmetric and asymmetric terms. The resulting variational statement enables the development of a new finite element that is very efficient since all parts of the stiffness matrix can be obtained analytically even in terms of arbitrary element distortions. Without the addition of any internal degrees of freedom the element shows excellent performance in bending dominated problems for rectangular element configurations.     

A displacement scheme with drilling degrees of freedom for plane elements

A scheme of boundary displacements with drilling degrees of freedom for plane elements is presented. The scheme is free from zero displacement modes and allows the development of hybrid finite elements with vertex and mid-side nodes, each node including a drilling degree of freedom besides the translational ones. Four quadrilateral isoparametric hybrid stress elements are implemented, and numerical results for some current test problems are given.     

考虑界面转角自由度的频域子结构法研究

采用Jetmundsen频域子结构法,针对空间刚架结构的综合进行了数值仿真,研究了界面自由度的完整性对于综合结果的影响,讨论了一种间接获取转角自由度相关频响函数信息的方法.仿真结果显示,频域子结构综合法能够有效地预报结构的动力学性能,而通过引入间接获取的转角自由度的频响信息能在一定程度上改善预报质量.     

三转动数控台跃度逆解分析

针对机械加工对数控转台的需求,研究3PSS RU并联构型三转动数控台的跃度逆解,以分析驱动系统对数控转台机械结构的柔性冲击和振荡．首先对提出的数控台进行描述,利用矢量方程法建立三转动数控台运动学模型,对其进行位置、速度、加速度逆解计算,在加速度分析的基础上进一步求导进行跃度分析,最后通过给定末端动平台的运动规律,计算出三转动数控台滑块的位置、速度、加速度与跃度随时间变化曲线．结果证实,在给定的运动规律中滑块2的移动范围、速度、加速度与跃度均较滑块1与滑块3的大,表明滑块2所受的冲击和振颤也较大．     

An assumed-stress hybrid 4-node shell element with drilling degrees of freedom

An assumed-stress hybrid/mixed 4-node quadrilateral shell element is introduced that alleviates most of the deficiencies associated with such elements. The formulation of the element is based on the assumed-stress hybrid/mixed method using the Hellinger-Reissner variational principle. The membrane part of the element has 12 degrees of freedom including rotational or ‘drilling’ degrees of freedom at the nodes. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner-Mindlin plate theory which takes into account the transverse shear contributions. The element formulation is derived from an 8-node isoparametric element by expressing the midside displacement degrees of freedom in terms of displacement and rotational degrees of freedom at corner nodes. The element passes the patch test, is nearly insensitive to mesh distortion, does not ‘lock’, possesses the desirable invariance properties, has no hidden spurious modes, and for the majority of test cases used in this paper produces more accurate results than the other elements employed herein for comparison.     

Comment on hybrid finite elements

It is shown that an apparently sound selection of trial functions can give rise to hybrid elements with rank deficient stiffness matrices and unused interior fields. An account is given of modifications which overcome these problems for a particular plate bending element.     

论测量不确定度中的自由度问题

有效自由度是出具校准报告时完整信息中的一个重要技术参数，依据其数值的大小，可直观地感觉到校准工作的可靠程度。然而，按现在常规的做法，有效自由度会出现一系列不合理现象，并且还是一个普遍存在的共性问题。     

Geometrical localisation of the degrees of freedom for whitney elements of higher order

Low-order Whitney forms are widely used for electromagnetic field problems. Higher-order ones are increasingly applied, but their development is hampered by the complexity of the generation of element basis functions and of the localisation of the corresponding degrees of freedom on the mesh volumes. The paper aims to give a geometrical localisation of the degrees of freedom associated with Whitney forms of a polynomial degree higher than one. A conveniently implementable basis is provided for these elements on simplicial meshes. As for Whitney forms of degree one, the basis is expressed only in terms of the barycentric co-ordinates of the simplex     

Vibration analysis of rotating composite beams using a finite element model with warping degrees of freedom

A finite element beam formulation that properly takes into account the warping of the cross-sections has been extended to the free vibration analysis of rotating and nonrotating composite beams. The formulation allows transverse shear deformation and the warping effects are incorporated by superimposing warping displacements that are parallel to the beam axis in the deformed configuration. For modeling of thin and moderately thick walled sections, the strain is assumed to be linear through the wall thickness. Numerical tests were conducted to calculate the natural frequencies of cantilever composite beams with various ply layups. Correlations of the calculated natural frequencies with experimentally measured values demonstrate the validity of the present approach. Although only rectangular solid and box beams were considered for numerical tests, the formulation allows modeling of beams with complicated cross-sections, tapers, pretwists and arbitrary planforms.     

Impurities with internal degrees of freedom in superconductors

In this paper we investigate the properties of an electron gas interacting with a system of nonmagnetic impurities having internal degrees of freedom which allow the electrons to be scattered inelastically. We determine the modifications of the Green's functions in the normal and superconducting state due to this inelastic scattering, and calculate the change of the superconducting transition temperature, of the order parameter, and of the density of states. In our model the transition temperature and the order parameter are shown to increase, and the density of states is shown to change its functional behavior drastically. The elastic part of the scattering affects neither the transition temperature, nor the order parameter, nor the density of states.