Development of Revolute-Joint Element with Rotation Limits, Locking, Resistive Moment and Damping

. The revolute-joint is an important component of a mechanical system. Thus, the motion simulation of multibodies connected with revolute-joints is of common interest. A simple revolute-joint can be easily represented in a numerical way, whereby the bending moment at the particular joint equals zero. Formulation becomes complicated when involving bending limits, the resistive moment and the damping effect. Furthermore, several bodies connected with revolute-joints form a complex system. This has been particularly useful for simulating a multibody system. A novel revolute-joint model is proposed in this paper. Several possible methods are suggested to handle bending limits. The incor-poration of the resistive moment and damping effects are also presented. The numerical stability of the revolute element is discussed, and a stability criterion suggested. The revolute-joint element is incorporated into an explicit finite difference code developed by the authors. Numerical examples are shown for different methods and conditions.     

基于假定应变法的协同转动四边形复合材料壳单元

为对复合材料层合板壳结构进行精确的大变形数值模拟,提出一种采用假定应变法的能分析层合结构大转动问题的协同转动四边形壳单元.该方法在建立有限元公式时引入假定应变法以克服膜闭锁和剪切闭锁的不利影响.与其他能分析大转动问题的复合材料壳单元相比,在新的协同转动框架中采用矢量型转动变量,可大大降低在非线性增量求解过程中更新转动变量的难度,且能得到对称的单元切线刚度矩阵,提高单元的计算效率.分析两个典型算例,并与其他学者的结果进行对比,结果表明在计算层合结构大转角问题时拥有较好的精度和收敛性.     

The finite element solution of a class of elastica problems

A finite element procedure for the analysis of an inextensional elastica bent through frictionless supports is presented. Element displacements are expressed in terms of cubic Hermite polynomials with nodal displacements and derivatives being determined to minimise the strain energy. It is shown that the axial force at any point is proportional to the square of the bending moment, which enables member incremental stiffness matrices to be expressed in a similar form to those used in stability analysis. The iterative procedure proposed for solving the nonlinear stiffness equations may readily be incorporated into any continuous beam program by the modification and addition of very few statements. An example is considered which indicates that accurate solutions may be obtained to a wide range of practical problems using the proposed technique.     

Stabilised finite element methods for a bending moment formulation of the Reissner-Mindlin plate model

This work presents new stabilised finite element methods for a bending moments formulation of the Reissner-Mindlin plate model. The introduction of the bending moment as an extra unknown leads to a new weak formulation, where the symmetry of this variable is imposed strongly in the space. This weak problem is proved to be well-posed, and stabilised Galerkin schemes for its discretisation are presented and analysed. The finite element methods are such that the bending moment tensor is sought in a finite element space constituted of piecewise linear continuos and symmetric tensors. Optimal error estimates are proved, and these findings are illustrated by representative numerical experiments.     

Elastic-plastic analysis of composite beams with incomplete interaction by finite element method

This paper presents a nonlinear finite element analysis of composite beams with incomplete interaction. A simplified nonlinear model is assumed in this approach. This is applied to the elastic-plastic analysis of reinforced concrete beams and composite beams with incomplete interaction. The numerical results are compared with the test results and existing values based on other numerical methods, and found to be in good agreement. The elastic-plastic behavior of partial composite beams without shear connectors in the negative bending moment region is discussed by the proposed method.     

Analysis of propagation on open microstrip lines using mixed-order covariant projection vector finite elements

Many different procedures have been proposed for the finite element analysis of dielectric-loaded waveguiding structures. However, most of these approaches are unreliable because of the appearance of spurious modes. Mixed-order covariant projection finite elements have been shown to eliminate difficulties with spurious modes in vector waveguide formulations. The authors have developed a method to analyze open region dielectric-loaded waveguiding problems using mixed-order covariant projection finite elements. Details of the construction of the eigenvalue equation are presented. The treatment of open geometries using local absorbing boundary conditions is discussed. An efficient sparse eigensolver, based on iterative methods, that can solve the resulting nonlinear eigenvalue problem, is described. Analysis results are presented that demonstrate the ability of the formulation to solve for the propagating modes of open microstrip lines without the appearance of spurious modes.     

Arch shape optimization using force approximation methods

The objective of this paper is to provide a method of optimizing areas of the members as well as the shape of both two-hinged and fixed arches. The design process includes satisfaction of combined stress constraints under the assumption that the arch ribs can be approximated by a finite number of straight members.In order to reduce the number of detailed finite element analyses, the Force Approximization Method is used. A finite element analysis of the initial structure is performed and the gradients of the member end forces (axial, bending moment) are calculated with respect to the areas and nodal coordinates. The gradients are used to form an approximate structural analysis based on first order Taylor series expansions of the member end forces. Using move limits, a numerical optimizer minimizes the volume of the arch with information from the approximate structural analysis.Numerical examples are presented to demonstrate the efficiency and reliablity of the proposed method for shape optimization. It is shown that the number of finite element analysis is minimal and the procedure provides a highly efficient method of arch shape optimization.     

Eigenvalue inverse formulation for optimising vibratory behaviour of truss and continuous structures

This paper presents formulations for inverse optimisation of vibration behaviour of finite element models of both truss and continuous structures. The proposed algorithms determine the required modifications on truss and continuous structures to achieve specified natural frequencies. The modification can be carried out globally or locally on the structures stiffness and matrices and the formulation can also be used to add new structural members to achieve the desired response. Numerical examples and finite element implementation of the developed method are provided to demonstrate the feasibility of the formulations.     

Semi-analytical postbuckling analysis of stiffened imperfect plates with a free or stiffened edge

A large deflection, semi-analytical method is developed for pre- and postbuckling analyses of stiffened rectangular plates with one edge free or flexibly supported, and the other three edges laterally supported. The plates can have stiffeners in both directions parallel and perpendicular to the free edge, and the stiffener spacing can be arbitrary. Both global and local bending modes are captured by using a displacement field consisting of displacements representing a simply supported, stiffened plate and an unstiffened plate with a free edge. The out-of-plane and in-plane displacements are represented by trigonometric functions and linearly varying functions, defined over the entire plate. The formulations derived are implemented into a FORTRAN computer programme, and numerical results are compared with results by finite element analyses (FEA) for a variety of plate and stiffener geometries. Relatively high numerical accuracy is achieved with low computational efforts.     

Optimisation of tensile membrane structures under uncertain wind loads using PCE and kriging based metamodels

Tensile membrane structures (TMS) are light-weight flexible structures that are designed to span long distances with structural efficiency. The stability of a TMS is jeopardised under heavy wind forces due to its inherent flexibility and inability to carry out-of-plane moment and shear. A stable TMS under uncertain wind loads (without any tearing failure) can only be achieved by a proper choice of the initial prestress. In this work, a double-loop reliability-based design optimisation (RBDO) of TMS under uncertain wind load is proposed. Using a sequential polynomial chaos expansion (PCE) and kriging based metamodel, this RBDO reduces the cost of inner-loop reliability analysis involving an intensive finite element solver. The proposed general approach is applied to the RBDO of two benchmark TMS and its computational efficiency is demonstrated through these case studies. The method developed here is suggested for RBDO of large and complex engineering systems requiring costly numerical solution.     

Acoustic infinite elements for non-separable geometries

We present new infinite element formulations for solving acoustic scattering and radiation problems in the exterior of long, slender bodies. The new infinite elements are geometrically constructed from a prolate spheroid inscribed by the scatterer. These elements need not begin on a level surface of the prolate spheroidal coordinate system. Instead, they may be attached to any convex surface, including that of the scatterer itself. This scheme reduces, or even completely eliminates, finite element modeling of the exterior medium. The formulations may easily be extended to the cases of an interior oblate spheroid or ellipsoid. We present both conjugated and unconjugated formulations without any weighting factors, although it would be simple to include them. We describe a fast numerical scheme for computing the element integrals based on Chebychev approximation. We include numerical results for scattering from spheres and capped cylinders. These results demonstrate the accuracy and the dramatic reduction in computational expense of our new formulations compared to other coupled finite element/infinite element methods.     

Dynamic analysis of structures with uncertain parameters using the transfer matrix method

A combination of the transfer matrix method and a first order, second moment approach is used to perform dynamic analyses of structures with uncertain parameters. This technique provides relations between the vibrational characteristics of structures with uncertain parameters and the first and second statistical moments of these parameters. The proposed methodology leads to a straightforward analysis with calculations that are much simpler than those with other methods, such as the stochastic finite element method. The effectiveness of this method is verified by a numerical example.     

A simple isoparametric three-node shell finite element

A three-node isoparametric shell finite element including membrane and bending effects is proposed. The element is based on the degenerated solid approach and uses an assumed strain method to avoid shear locking. An intermediate convected covariant frame is used in order to construct the modified shear strain interpolation matrix. Validation tests show that shear locking is avoided and that a reduced integration procedure can be used without any loss of accuracy which is useful for the numerical efficiency.     

Adaptive p-version based finite element formulations for thermal modeling/analysis of structural configurations

Adaptive p-version based hierarchial finite element formulations in conjunction with a posteriori error estimation concepts are described with emphasis on applicability for thermal modeling/analysis of structural configurations. The basic concepts and formulations of hierarchical p-version finite elements for thermal analysis are first described. A posteriori error estimation features are utilized to steer the process of adaptive refinement. Several configurations comprised of one-dimensional structures are evaluated to validate the applicability of the proposed formulations and to demonstrate the potential of the p-version adaptive formulations for thermal modeling/analysis. The methodology offers potential and promises to be an attractive to conventional finite element thermal modeling/analysis approaches.     

Frameworks for finite strain viscoelastic-plasticity based on multiplicative decompositions. Part II: Computational aspects

Computational aspects of the two formulations of viscoelastic-plasticity at finite strains proposed in Part I of this work are examined in detail. These formulations are based upon distinct kinematic assumptions resulting from different multiplicative decompositions of the deformation gradient. However, the corresponding sets of local evolution equations consistent with continuum thermodynamics and adopted in this work have globally the same structures and, therefore, lead to similar algorithmic treatments. The key idea in the design of the integration algorithms is the systematic use of the nowadays well-known exponential mapping algorithms in conjunction with the notion of operator split methodology. These numerical approximations are then applied to the model examples proposed in Part I together with their extensions to incorporate rate-dependent plasticity. The implementation within the framework of the finite element method is described in detail and, finally, we present a set of representative numerical simulations to illustrate the features of the proposed models.     

Object-Oriented Symbolic Derivation and Automatic Programming of Finite Elements in Mechanics

Symbolic approaches to assist in the development of finite element formulations have been used since the late 1970s. Today, symbolic mathematical software such as Mathematica, Maple, etc., has proved to be helpful when testing formulations. In earlier work, the authors introduced a new way of integrating naturally symbolic concepts in numerical finite element codes, taking advantage of an objectoriented code organization. In this paper, we wish to prove on practical examples that the proposed approach is very attractive and promising today, leading to an alternative way of conceiving finite element codes. After presenting a state-of- the-art of symbolic approaches for finite element developments, we first give a practical application of symbolic developments (for discontinuous space-time formulations), and then examples of Computer Aided Software Engineering tools that can be introduced into such a finite element environment.     

Lateral buckling analysis of beams by the fem

Two new finite element formulations for the calculation of the lateral buckling load for elastic straight prismatic thin-walled open beams under conservative static loads, are presented. The stability criterion used is based on the positive definiteness of the second variation of the total potential energy. One formulation is suitable for sections where the initial bending is about a dominant major axis. The other finite element formulation takes account of initial bending curvature and essentially takes the form of a quadratic eigenvalue problem. Both formulations are tested with problems that have classical solutions or experimentally determined results and are shown to be accurate.     

某型整体式抗侧滚扭杆的弯曲变形分析

针对某型整体式抗侧滚扭杆在弯矩作用下产生的弯曲变形现象,通过理论公式计算结合有限元分析软件对其弯曲挠度进行研究,并将其与实测变形量进行对比分析,所得弯曲变形结果可供工程师在结构设计时作为空间干涉校核参考.