scholarly journals A Novel Shape-Free Plane Quadratic Polygonal Hybrid Stress-Function Element

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Pei-Lei Zhou ◽  
Song Cen
Keyword(s):  
Stress Function ◽  
Quadrilateral Elements ◽  
Polygonal Element ◽  
Polygonal Elements ◽  
Displacement Based ◽  
Function Element ◽  
Free Plane ◽  
Fundamental Analytical Solutions ◽  
Element Shape ◽  
Hybrid Stress

A novel plane quadratic shape-free hybrid stress-function (HS-F) polygonal element is developed by employing the principle of minimum complementary energy and the fundamental analytical solutions of the Airy stress function. Without construction of displacement interpolation function, the formulations of the new model are much simpler than those of the displacement-based polygonal elements and can be degenerated into triangular or quadrilateral elements directly. In particular, it is quite insensitive to various mesh distortions and even can keep precision when element shape is concave. Furthermore, the element does not show any spurious zero energy modes. Numerical examples show the excellent performance of the new element, denoted by HSF-AP-19β, in both displacement and stress solutions.

scholarly journals Displacement and Stress Function-based Linear and Quadratic Triangular Elements for Saint-Venant Torsional Problems

2018 ◽  
Vol 20 (2) ◽  
pp. 70 ◽  
Author(s):  
Joko Purnomo ◽  
Wong Foek Tjong ◽  
Wijaya W.C. ◽  
Putra J.S.
Keyword(s):  
Cross Sections ◽  
Stress Function ◽  
Torsional Rigidity ◽  
Structural Members ◽  
Finite Element Program ◽  
Element Program ◽  
Standard Linear ◽  
Triangular Elements ◽  
Displacement Based ◽  
High Degree

Torsional problems commonly arise in frame structural members subjected to unsym­metrical loading. Saint-Venant proposed a semi inverse method to develop the exact theory of torsional bars of general cross sections. However, the solution to the problem using an analytical method for a complicated cross section is cumbersome. This paper presents the adoption of the Saint-Venant theory to develop a simple finite element program based on the displacement and stress function approaches using the standard linear and quadratic triangular elements. The displacement based approach is capable of evaluating torsional rigidity and shear stress distribution of homogeneous and nonhomogeneous; isotropic, orthotropic, and anisotropic materials; in singly and multiply-connected sections.  On the other hand, applications of the stress function approach are limited to the case of singly-connected isotropic sections only, due to the complexity on the boundary conditions. The results show that both approaches converge to exact solutions with high degree of accuracy.

A singular element of shape-free hybrid stress-function finite elements in anisotropic materials

2019 ◽  
Vol 101 ◽  
pp. 103-112 ◽  
Author(s):  
Yuebing Li ◽  
Mingjue Zhou ◽  
Yan Shang ◽  
Weiya Jin ◽  
Shuiqing Zhou ◽  
...  
Keyword(s):  
Finite Elements ◽  
Stress Function ◽  
Anisotropic Materials ◽  
Singular Element ◽  
Hybrid Stress

The Critical Time Step for Finite-Element Solutions to Two-Dimensional Heat-Conduction Transients

1978 ◽  
Vol 100 (1) ◽  
pp. 120-127 ◽  
Author(s):  
G. E. Myers
Keyword(s):  
Boundary Conditions ◽  
Nodal Point ◽  
Critical Time ◽  
Time Step ◽  
Various Boundary Conditions ◽  
Quadrilateral Elements ◽  
Triangular Elements ◽  
The Finite Difference Method ◽  
Critical Time Step ◽  
Element Shape

Computationally-useful methods of estimating the critical time step for linear triangular elements and for linear quadrilateral elements are given. Irregular nodal-point arrangements, position-dependent properties, and a variety of boundary conditions can be accommodated. The effects of boundary conditions and element shape on the critical time step are discussed. Numerical examples are presented to illustrate the effect of various boundary conditions and for comparison to the finite-difference method.

scholarly journals Nonlinear analysis for the polygonal element

2019 ◽  
Vol 272 ◽  
pp. 01020
Author(s):  
Qiang Xu ◽  
Jian Yun Chen ◽  
Jing Li ◽  
Gui Bing Zhang ◽  
Hong Yuan Yue ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Complex Geometry ◽  
Geometric Model ◽  
Academic Research ◽  
Triangular Element ◽  
Interpolation Function ◽  
Quadrilateral Elements ◽  
Polygonal Element ◽  
Element Method

As an important method for solving boundary value problems of differential equations, the finite element method (FEM) has been widely used in the fields of engineering and academic research. For two dimensional problems, the traditional finite element method mainly adopts triangular and quadrilateral elements, but the triangular element is constant strain element, its accuracy is low, the poor adaptability of quadrilateral element with complex geometry. The polygon element is more flexible and convenient in the discrete complex geometric model. Some interpolation functions of the polygon element were introduced. And some analysis was given. The numerical calculation accuracy and related features of different interpolation function were studied. The damage analysis for the koyna dam was given by using the polygonal element polygonal element of Wachspress interpolation function. The damage result is very similar to that by using Xfem, which shows the calculation accuracy of this method is very high.

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