8- and 12-node plane hybrid stress-function elements immune to severely distorted mesh containing elements with concave shapes

2011 ◽  
Vol 200 (29-32) ◽  
pp. 2321-2336 ◽  
Author(s):  
Song Cen ◽  
Xiang-Rong Fu ◽  
Ming-Jue Zhou
Keyword(s):  
Stress Function ◽  
Distorted Mesh ◽  
Hybrid Stress

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

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.

Hybrid stress analysis of a near-surface circular hole in finite structures

2019 ◽  
Vol 234 (7) ◽  
pp. 1366-1381
Author(s):  
Abdullah Alshaya ◽  
Shiang-Jiun Lin
Keyword(s):  
Stress Analysis ◽  
Hybrid Method ◽  
Complex Variable ◽  
Stress Function ◽  
Thermoelastic Stress ◽  
Concentrated Load ◽  
Near Surface ◽  
Hybrid Complex ◽  
The Individual ◽  
Hybrid Stress

The ability to stress-analyze complicated structures from recorded load-induced temperatures is demonstrated. The considered structures have a near-surface hole and subjected to a concentrated load. The complexity of the structure is simplified by conformal mapping, the traction-free condition on the boundary of the hole is analytically satisfied by analytic continuation, and the equilibrium and compatibility conditions are satisfied by means of Airy stress function in complex-variable formulation. For isotropic member that is cyclically loaded within its elastic range, the produced in-phase temperature variations are linearly proportional to the local changes in the normal stresses. Even though no recorded thermal data were used at or near to the edges, the present hybrid method simultaneously separates the load-induced temperatures into the individual stress components, determines reliably the boundary stress and hence the stress concentration, and smooths the measured input data. Unlike prior capabilities of using geometrical symmetry to simply the stress function representation, the present analysis retains all the terms in the stress functions. Therefore, the considered hybrid stress analysis approach of such complex structures extends significantly the applicability of thermoelastic stress analysis compared to prior capabilities and is considered to be the most complicated formulation of the hybrid complex-variable method to date. To support the reliability of the present hybrid method, the results were compared with finite element predictions and previous results based on Mitchell solution.

Quasi-Static Crack Propagation Modeling Using Shape-Free Hybrid Stress-Function Elements with Drilling Degrees of Freedom

2016 ◽  
Vol 13 (03) ◽  
pp. 1650014 ◽  
Author(s):  
Song Cen ◽  
Yi Bao ◽  
Chen-Feng Li
Keyword(s):  
Crack Propagation ◽  
Stress Function ◽  
Degrees Of Freedom ◽  
Singular Element ◽  
Propagation Modeling ◽  
Drilling Degrees Of Freedom ◽  
Simulation Step ◽  
Crack Tips ◽  
Modeling Strategy ◽  
Hybrid Stress

A new plane shape-free multi-node singular hybrid stress-function (HS-F) element with drilling degrees of freedom, which can accurately capture the stress intensity factors at the crack tips, is developed. Then, a quasi-static 2D crack propagation modeling strategy is established by combination of the new singular element and a shape-free 4-node HS-F plane element with drilling degrees of freedom proposed recently. Only simple remeshing with an unstructured mesh is needed for each simulation step. Numerical results show that the proposed scheme is an effective and robust technique for dealing with the crack propagation problems.

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