Element Subdivision Research Articles

ADAPTIVE SPACE FRAME ANALYSIS. PART II: A DISTRIBUTED PLASTICITY APPROACH.

In a previous companion paper (Part I: A Plastic Hinge Approach), adaptive elasto-plastic analysis of space frames was discussed in the context of a plastic hinge approach. The present paper extends the concept of automatic mesh refinement to deal with accurate elasto-plastic large displacement analysis accounting for the spread of yield within structural members. This is achieved through the use of the quartic formulation in the elastic range, and performing automatic subdivision of quartic elements into elasto-plastic cubic elements which account for the spread of plasticity across the section depth and along the element length. The main advantage of this approach is the ability to start full elasto-plastic large displacement analysis using only one element per member, with automatic mesh refinement performed only where and when necessary within the structure and during the analysis. The paper presents a description of the elasto-plastic cubic formulation, discusses the concept of automatic mesh refinement in the context of elastoplastic analysis, and provides verification examples using the computer program ADAPTIC to demonstrate the accuracy and extreme efficiency of the proposed nonlinear analysis procedure.

Discontinuous displacement approximation for capturing plastic localization

AbstractIt is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries (interfaces) of the finite element subdivision. The regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept. As a by‐product of the regularization, an intrinsic band width is introduced as a ‘constitutive’ property rather than a geometric feature of the finite element mesh. In this way the spurious mesh sensitivity, which is obtained when the displacement approximation is continuous, can be avoided. Another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material. An interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface (up to within a scalar factor). An analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a ‘shear’ band for a general plasticity model. The significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress. It is shown that a unique structural post‐peak response (in accordance with non‐linear fracture mechanics) can be achieved when the plastic softening modulus is properly related to the bandwidth. The paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope.

An algorithm for adaptive refinement of triangular element meshes

AbstractA simple algorithm is developed for adaptive and automatic h refinement of two‐dimensional triangular finite element meshes. The algorithm is based on an element refinement ratio that can be calculated from an a posteriori error indicator. The element subdivision algorithm is robust and recursive. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. Several example problems are presented to illustrate the utility of the approach.

An atomic force microscopical study of the synaptonemal complex

The chromosomal structure which is specific for meiosis, the synaptonemal complex (SC), plays a major role in chromosome pairing and the recombination of genetic material. The SC was studied using atomic force microscopy (AFM). The results of this study confirm the results of light and electron microscopic studies of the SC. The SC primarily shows a tripartite structure, composed of two lateral elements and a central element connected to each other by transversal elements. The lateral element of the SC shows a lateral subdivision in secondary lateral strands. In addition, a new repetitive transversal subdivision of the lateral elements was observed. Furthermore, the SC substructure which is probably responsible for recombination, the recombination nodule, could be observed ouside the confines of the SC.

A new decoupled finite element algorithm for viscoelastic flow. Part 1: Numerical algorithm and sample results

AbstractThis paper presents an algorithm for two‐dimensional Steady viscoelastic flow Simulation in which the Solution of the momentum and continuity equations is decoupled from that of the constitutive equations. The governing equations are discretized by the finite element method, with 3 × 3 element subdivision for the stress field approximation. Non‐consistent Streamline upwinding is also used. Results are given for flow through a converging channel and through an abrupt planar 4:1 contraction.

Hierarchical Bernoulli-Euler beam finite elements

A method is described to model the dynamics of a uniform Bernoulli-Euler beam finite element in terms of static constraint modes and interface restrained assumed modes. This is in contrast with the regular finite element method where no interface restrained assumed modes are retained. Element mass and stiffness matrices are developed using two different types of interface restrained assumed modes, namely, normal modes and trigonometric functions. The proposed models are hierarchical in the sense that lower order models are embedded into higher order models. Consequently, different levels of approximation can be obtained with little additional effort and without further physical subdivision of the beam element, thereby preserving the original grid layout. Numerical examples are included to demonstrate the superior convergence characteristics of these elements compared to that developed via the standard consistent mass matrix approach.

Numerical modelling of phase change and heat transfer during rapid solidification processes: use of control volume integrals with element subdivision

An effective interface-tracking scheme has been developed for the numerical modelling of heat transfer and phase change during rapid solidification. This technique is based on Control Volume Integrals, and achieves high-resolution tracking of the solid/liquid interface by element subdivision. It is particularly well-suited for rapid solidification with undercooling, for which the accurate prediction of the interface temperature during recalescence is very important. This approach has been used to model the Planar Flow Casting and Splat Cooling processes. Some results on temperature profiles and on interface velocity, location, undercooling, and cooling rate are shown for both processes.

Calculation of stress concentration in the manipulator element using a combined finite and boundary element method

Elastic stress concentration in a manipulator element is calculated within the framework of the two-dimensional stressed state model. The purpose here is to make recommendations for selecting the radius of joining of the beam parts of the element based on analysis of maximum stresses in the stress concentration zone. Combination of the finite element and boundary element methods is proposed for solving the problem. A coarse finite element subdivision is used for the initial calculation for the entire element. Then, the solution is refined by using boundary elements in the identified zone. Comparison of calculation results with solutions obtained by the finite element and boundary element methods points to the effectiveness of the proposed algorithm for stress concentration calculations.

Quality assurance for fracture mechanical finite element analyses

A program system for automated fracture mechanical analyses with three-dimensional (3D) finite element (FE) models has been developed. The main application has been safety analyses of pressurized components of nuclear power stations such as pipes and pipe bends containing surface cracks. The system is being extended to surface cracks in reactor pressure vessel (RPV) nozzle area. A large matrix of varying surface crack sizes in a plate under tension has been analysed and the automatically generated mesh is shown to give good accuracy. Such tests cannot guarantee the same accuracy for general loading conditions and geometries. Methods are being developed for the accuracy assessment of the results and for directing the mesh refinement. Results of a test series with plane models are promising. In the mesh refinement element sub-division was used. The same accuracy assessment approach is applied also to 3D models.

An upwind Galerkin finite element analysis of linear induction motors

An upwind Galerkin finite-element method (GFEM) for electromagnetic problems in moving media is proposed. In the conventional GFEM, when the cell Peclet number becomes greater than the critical value of 2, many undesirable flux loops due to oscillatory solutions appear in the flux plots. It is shown that the upwind GFEM can stabilize such oscillations successfully. Although the extra-fine subdivision of elements makes it possible to suppress such oscillations without upwinding, the 13 mm length of a mesh in the present model must be subdivided into 2.43 mu m in order that the Peclet number in the back iron shall not exceed the critical value of 2 or there will be a need for enormous computation time and memories. For this reason, the present GFEM is the most promising numerical method for convective diffusion equation solvers with larger cell Peclet number.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Simulation analysis of magnetic sensor for nondestructive testing by boundary element method

The use of a differential transformer-type magnetic sensor for nondestructive testing was simulated by boundary element analysis, taking the external electric secondary circuit, the eddy currents, and movements into account. The existence of an error caused by the narrow air gap is identified, an element subdivision method is proposed for decreasing the error, and this method is shown to be effective. The analytical results are shown to be in good agreement with the measurement results. It is shown that the output voltage pattern can be used to estimate the shape or size of a flaw. >

Three-dimensional boundary-element method for analyzing nonrotationally symmetric perturbations in electrostatic lenses

The three-dimensional boundary-element method (3D BEM) has been discussed in some aspects involving the subdivision of boundary elements, the quadrature of surface charge density integrals, and their singularities. The 3D BEM has been applied to the analysis of nonrotationally symmetric perturbations in electrostatic lenses. The perturbations due to machining defects (including elliptical distortions, inclined end faces, misalignments, and their combinations) have been calculated and also the asymmetric aberrations have been computed. A set of computer programs has been developed. The computed perturbation potential distributions have been compared with the theoretical ones.

Voronoi多角形表現を利用した自動領域分割法

Automatic mesh subdivision is indispensable to yield reliable input data for the finite element method or to provide geometric modeling for ultrasonic measurement. In these decades, various methodologies have been proposed to reduce the required personal labors as little as possible for this kind of automation. Block/unit subdivision method or other tactical approaches seem to be user-friendly in some specified situations, but they are unsuitable to reduce increasing amount of labors accompanied with meshing the complex geometries in practice. In the present papers direct translation is discussed from two dimensional CAD data or wire frame data to triangular and quadrilateral element subdivision; Voronoi Polygon and Delaunay Tessellation is utilized to yield node-element graph from the prescribed node pattern. Our developing algorithm is described with some comments on computer implementation and some expected issue in the actual situation. Finally, availability of our proposing methodology in three dimensional case is evaluated.

Reusable intrinsic sample point (RISP) algorithm for the efficient numerical integration of three dimensional curved boundary elements

AbstractThis paper presents an algorithm that provides an order of magnitude gain in the computational performance of the numerical integration of the boundary integral equations for three dimensional analysis. Existing algorithms for numerical integration have strategically clustered integration sample points based on the relative proximity of the load points to the boundary element being integrated using element subdivision or element co‐ordinate transformation. The emphasis in these techniques has been on minimizing the number of sample points required to obtain a given level of accuracy. The present algorithm, while closely following the spirit of these earlier approaches, employs a discrete number of sets of predetermined, customized, near‐optimum, sample point quantities associated with the intrinsic boundary element. The ability created by this approach to reuse sample point geometric information of the actual element allows for the realization of substantive computational economy. This algorithm provides accurate and efficient numerical results both when load points are far from, and when they are on the boundary element being integrated. Numerical results are provided to demonstrate the substantial economy achieved through the use of the present algorithm.

A decoupled finite element streamline-upwind scheme for viscoelastic flow problems

Parallel to a recently reported mixed finite element method by Marchal and Crochet, a new decoupled finite element streamline-upwinding scheme is developed for viscoelastic flows. While relatively cheap Picard iteration used previously in our streamline element method is maintained, the streamline integration of the constitutive equation is replaced by a Galerkin discretization with streamline-upwinding applied to the convective terms. Using a Maxwell or an Oldroyd-B model and a simple bilinear interpolation for the extra-stress without element subdivision, our calculation of the flow through a four-to-one circular contraction has reached a Weissenberg number limit slightly higher than that reached by the corresponding mixed method with a two by two element subdivision for the extra-stress. Numerical experiments also show that both the conventional Galerkin and the consistent streamline-upwind/Petrov-Galerkin methods give poorer performance than the non-consistent streamline-upwinding approach, confirming results found by the mixed method. The validity of the non-consistent upwinding approach is discussed, and we show that it leads to effectively changed constitutive models which yield smoothed solutions and increased stability.

A contribution to an accurate analysis of shallow underground openings

In the numerical analysis of a problem which has not been solved previously, it is imperative to ensure that the results of analysis are accurate enough. In the case of finite element analysis, assuming that a FEM formulation is available, it demands that the finite element subdivision of the analysis domain is adequate without making the analysis too expensive. In the analysis of shallow underground openings in which the analysis domain is discretised by a combination of finite and infinite elements, it is possible to meet this demand. It is demonstrated in this study through a finite/infinite element analysis of shallow openings of circular and elliptical shapes.

Measurement of the dynamic strain field near a crack tip using computer picture processing.

This paper presents a strain distribution measurement near the crack tip of a dynamically fracture specimen using the Point Recognition Picture Processing System. In this system, the displacement of the points marked near the crack tip is determined by the picture processing technique. The least squure approximation of the two-dimensional distribution of displacement is obtained by using the interpolation of a finite element subdivision. From the differentiation of the displacement field, the Green's strain distribution is calculated. To fracture the specimen dynamically, an electromagnetic force is employed. As the fracture event takes only few milliseconds, pictures of the marks are taken with a high-speed camera. The results are compared with those from the static three point bending test and the dynamic loading effects on strain distribution near the crack tip are discussed.

Multiple level finite element analysis and its applications to tidal current flow in Tokyo Bay

A finite element method for the analysis of a one level and a multiple level current flow is presented. The basic equations can be derived from the three-dimensional Navier-Stokes equations under the shallow water assumptions. The standard finite element method has been introduced using the linear interpolation function based on a triangular finite element. For each level, the finite element subdivisions are not required to be coincident. To integrate the discretized equations numerically in time, an improved two step explicit scheme is employed. The multiple level finite element method is applied to a tidal flow analysis of Tokyo Bay. The multiple level tidal flow analysis is performed at the entrance channel of Tokyo Bay. The density of water is assumed to be constant for each level. The vertical profiles of the numerical velocity are compared with those of the observed velocity. The flow directions and the order of velocity are both well in agreement with the observed data. The tidal flow pattern in Tokyo Bay has been shown to be expressed by the multiple level flow assuming that the density of seawater is levelwise constant. The numerical tidal flow computation of Tokyo Bay carried out using a one level model is compared with observed data. The one level numerical values will be used to specify the boundary conditions for the multiple level analysis. Both numerical and observed results correspond extremely well in this computation. The two dominant circulated residual flows have been computed, and they coincide with the observed facts.

Experimental Verification of the Method of Deformation Analysis of Coated Plain-Weave Fabrics By Biaxial Tensile Tester

Method for deformation analysis of coated plain- weave fabrics which have nonlinear mechanical properties has been reported on this journal [1]. Following this, in this paper, biaxial tensile tester developed by the authors and the crucial specimen for the tester are introduced.And convergence properties of solution given by application of the method on the crucial specimen model of calculation are studied concerning to the coarseness of subdivision of finite ele ment and to the number of steps of iterative calculation.Finally, the methods are verified comparing biaxial stress-strain curves given by the calculation and the measurement.As a result, it is concluded that the method can be progressed toward the application to deformation analysis of membrane structures.

Structurally compatible fluid finite element for solid fluid interaction studies

This study develops a fluid finite element compatible with existing structural finite elements with the ultimate objective of analysing solid-fluid interaction problems. This type of problem is of interest in the design of nuclear components involving geometric complexities and nonlinearities. Employing the weighted residual method, the differential equations governing the pressure distribution in a two-dimensional viscous flow subjected to small amplitude oscillations are discretized on finite element subdivisions of the fluid region. The elemental inertia, damping and volumetric fluidity matrices are computed for plane, axisymmetric, triangular and quadrilateral fluid elements. These matrices are then assembled for all the system elements and the final differential equations are integrated numerically in time to obtain the pressure and velocity distribution in the flow region. The analysis is verified analytically by solving a wave propagation flow problem consisting of fluid between two flat plates initially at rest and accelerated suddenly by applying a step pressure at one end.