High Order Local Approximations to Derivatives in the Finite Element Method

1977 ◽  
Vol 31 (139) ◽  
pp. 652 ◽  
Author(s):  
Vidar Thomee
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Order ◽  
The Finite Element Method ◽  
Local Approximations ◽  
Element Method

Reduction of stress concentration around a hole in a uniaxially loaded plate

1983 ◽  
Vol 18 (2) ◽  
pp. 135-141 ◽  
Author(s):  
U C Jindal
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Concentration ◽  
Circular Hole ◽  
High Order ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Loaded Plate ◽  
Hole Geometry ◽  
Element Method

The stress concentration around a circular hole in a plate can be reduced by up to 21 per cent by introducing auxiliary holes on either side of the original hole. But this approach of auxiliary holes creates two more regions of stress concentration in the plate. In the present study, the hole geometry has been modified to effect stress reductions as high as 22 per cent. The problem has been analysed numerically by the finite element method and experimentally by two-dimensional photoelasticity. It has been observed that by making the hole oblong in the direction of loading, a high order of reduction in stress concentration around the hole can be obtained.

scholarly journals k-Version of Finite Element Method for BVPs and IVPs

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1333
Author(s):  
Karan S. Surana ◽  
Celso H. Carranza ◽  
Sai Charan Mathi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Tensor Product ◽  
Differential Operators ◽  
Higher Order ◽  
The Finite Element Method ◽  
Order Continuity ◽  
Local Approximations ◽  
Linear Differential ◽  
Element Method

The paper presents k-version of the finite element method for boundary value problems (BVPs) and initial value problems (IVPs) in which global differentiability of approximations is always the result of the union of local approximations. The higher order global differentiability approximations (HGDA/DG) are always p-version hierarchical that permit use of any desired p-level without effecting global differentiability. HGDA/DG are true Ci, Cij, Cijk, hence the dofs at the nonhierarchical nodes of the elements are transformable between natural and physical coordinate spaces using calculus. This is not the case with tensor product higher order continuity elements discussed in this paper, thus confirming that the tensor product approximations are not true Ci, Cijk, Cijk approximations. It is shown that isogeometric analysis for a domain with more than one patch can only yield solutions of class C0. This method has no concept of finite elements and local approximations, just patches. It is shown that compariso of this method with k-version of the finite element method is meaningless. Model problem studies in R2 establish accuracy and superior convergence characteristics of true Cijp-version hierarchical local approximations presented in this paper over tensor product approximations. Convergence characteristics of p-convergence, k-convergence and pk-convergence are illustrated for self adjoint, non-self adjoint and non-linear differential operators in BVPs. It is demonstrated that h,p and k are three independent parameters in all finite element computations. Tensor product local approximations and other published works on k-version and their limitations are discussed in the paper and are compared with present work.

Simulation of tuning graphene plasmonic behaviors by ferroelectric domains for self-driven infrared photodetector applications

Nanoscale ◽  
2019 ◽  
Vol 11 (43) ◽  
pp. 20868-20875 ◽  
Author(s):  
Junxiong Guo ◽  
Yu Liu ◽  
Yuan Lin ◽  
Yu Tian ◽  
Jinxing Zhang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interfacial Effect ◽  
Infrared Photodetector ◽  
The Finite Element Method ◽  
Ferroelectric Domains ◽  
Element Method

We propose a graphene plasmonic infrared photodetector tuned by ferroelectric domains and investigate the interfacial effect using the finite element method.

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