Use Of Isoparametric Elements Research Articles

Mathematical Modeling of the Water Saturation Algorithm of the Mountain Slope on the Example of the Catastrophic Landslide of the Northern Tien Shan Ak Kain

The purpose of this article is to present the developed methodology, a brief algorithm of mechanical-and-mathematical modeling to investigate the causes and mechanism of soil disruption from the hillsides and the results of its use for restoring the pre-landslide stress state using the example of one of the tragic landslides. The numerical finite element algorithm of studying the stress–strain state (SSS) of soil deposits of slopes of the inclined-layered structure is briefly described, with specific features of the use of isoparametric elements of the quadrangular shape with four nodes of arbitrary shape. For detailed studying the SSS, the cover soils of the steep slope of the inclined-layered structure, in height from the arch to the foot, are conventionally divided into three zones, each of which has layered structures. Studies of the geometry of its area and the angle of inclination of the slope showed that the two-layer structure of its original structure made a curved path repeating the outline of the gorge. The finite element method helped to model the soil deposits of the slope with the granite-basalt rock as close as possible to the landslide initial shape. The proposed methodology, the mechanical-mathematical model, algorithms and calculation examples allow predicting the possible occurrence of landslides on other countless hillsides of the Northern Tien Shan by determining stress concentration zones.

Free element collocation method: A new method combining advantages of finite element and mesh free methods

In this paper, a new numerical method, named as the Free Element Collocation Method (FECM), is proposed for solving general engineering problems governed by the second order partial differential equations (PDEs). The method belongs to the group of the collocation method, but the spatial partial derivatives of physical quantities are computed based on the isoparametric elements as used in FEM. The key point of the method is that the isoparametric elements used can be freely formed by the nodes around the collocation node. To achieve a narrow bandwidth of the final system of equations, elements with a central node are recommended. For this purpose, a new 21-node quadratic element for 3D problems is constructed for the first time. Attributed to the use of isoparametric elements, FECM can result in more stable results than the traditional collocation method. In addition, the elements can be freely formed by local nodes, FECM has the advantage of mesh-free methods to fit complicated geometries of engineering problems. A number of numerical examples of 2D and 3D thermal and mechanical problems are given to demonstrate the correctness and efficiency of the proposed method.

Transient analysis of grounding systems for wind turbines

The paper deals with transient analysis of grounding systems wind turbines. A typical wind turbine grounding system arrangement based on ring electrode is analyzed. Special attention is focused to the influence of additional vertical and horizontal electrodes, respectively. Influence of grounding wire placed in cable trench on the transient behavior is studied in detail. The mathematical formulation in the frequency domain is based on the thin wire antenna theory and the related set of Pocklington integro-differential equations. The corresponding transient response is obtained by means of the Inverse Fourier Transform (IFT). The set of Pocklington integro-differential equations is solved by the Galerkin-Bubnov Indirect Boundary Element Method (GB-IBEM) featuring the use of isoparametric elements. A number of illustrative computational examples are presented in the paper.

Weak consistency of the cell-centered Lagrangian GLACE scheme on general meshes in any dimension

We study the consistency in the weak sense of the cell-centered Lagrangian scheme GLACE. The main result is that GLACE is weakly consistent on general meshes in any dimension. The proof relies on a new formula for some geometric vectors defined at the corners of the cell, and which are basic Lagrangian objects. It validates theoretically the use of isoparametric elements (based on Q 1 integration) for 3D Lagrangian compressible gas dynamics calculations. Finally we give the result of a simple convergence test in 2D.

On the analysis of singular stress fields Part 2: Application to complete slipping contacts

The stress state adjacent to the edge of a complete slipping contact has an implied elastic singularity. Using an asymptotic approach the order of this singularity, and hence the spatial distribution of the local stress field, may be found. The region over which it characterizes the full field solution is found by defining a generalized stress intensity factor K*. In practice, this requires a finite element (FE) analysis. However, the use of isoparametric elements leads to convergence problems which may be circumvented by using special singular elements which incorporate the required shape function. Here, these elements are applied to a complete contact problem for which there is an analytical solution, for comparison purposes, i.e. a rigid square-ended punch sliding along an elastic half-plane. It is shown that the singular elements are able to reproduce the singular field accurately, and that they significantly accelerate convergence when compared with a conventional mesh of isoparametric elements. Additionally, a comparison between the asymptotic and FE solutions reveals the domain over which the process (plastic) zone is controlled by the singular solution. The implications of the technique for defining the fretting fatigue strength of complete contacts will be discussed.

An isoparametric boundary solution for thermal radiation

AbstractIn order to solve problems of re‐radiation and reflection in finite element thermal analysis, a discretization consisting of flat isothermal surfaces is usually assumed. Such an approximation is clearly inconsistent if an isoparametric model is used for any surrounding solid. In addition, geometric view‐factors are often required explicitly, but their calculation is generally considered to be tedious and error prone. The representation of radiative exchange by a boundary integral equation is a standard analytical technique. The use of such a representation in conjunction with finite element analysis, however, appears to be quite recent. The present work describes a scheme whereby standard finite element/boundary element coupling theory may be applied to yield a method which is both simple and consistent. The use of isoparametric elements allows varying temperatures and curved surfaces to be modelled. For an empty enclosure the kernel of the integral equation is simply related to the differential geometric view‐factor. Re‐radiation and reflection are implicit.

Use of isoparametric elements in an experimental study of strain fields under low-cycle loading conditions

Use of isoparametric elements in an experimental study of strain fields under low-cycle loading conditions

A new method of integration over polynomal finite element boundaries

AbstractIn this note we are developing integration techniques for triangular regions in which one side is curved. Specifically, we are considering (a) general polynomial boundaries and (b) various combinations of elliptical boundaries. Integration is performed over all of these explicitly.One definite and considerable improvement achieved is the introduction of a new method of integration over polynomial type boundaries. This new method is not only exact for polynomials or other analytic functions, but also reduces the computing time considerably; for example, if for a sixth order polynomial the number of operations necessary (using previously available methods) to perform the integration was n, the method introduced here requires a number proportional to n1/6. Furthermore, coding time is also reduced considerably. It may be of value to mention that the availability of the results presented here could obviate the need for the use of isoparametric elements in some regions with curved boundaries.For completeness, explicit integration formulas for elliptic shaped regions are also listed.