Element edge quadrature method for 4-node quadrilateral element for the evaluation of element stiffness matrix

2020 ◽  
pp. 2050015
Author(s):  
Shyjo Johnson ◽  
T. Jeyapoovan ◽  
D. Nagarajan
Keyword(s):  
Stiffness Matrix ◽  
Integration Scheme ◽  
Quadrature Method ◽  
Quadrilateral Element ◽  
Element Analysis ◽  
Element Stiffness Matrix ◽  
Quadrature Scheme ◽  
Numerical Integration Scheme ◽  
Edge Method ◽  
Accuracy Of Results

This research paper focuses on the objective of developing a quadrature for evaluating the element stiffness matrix for the four-node quadrilateral element in finite element analysis (FEA). The proposed integration scheme is defined as an element edge method (EEM), which mimics the Gauss numerical integration scheme. This integration scheme consists of five sampling points and weights where four integration point locations are at the edges and one is at the center of the quadrilateral element. The proposed quadrature scheme has been tested using various benchmarked problems designed by various researchers to study the convergence of the results, accuracy of results, and stability of values.

A sampling point quadrature method for 3-node triangular element for the evaluation of element stiffness matrix in finite element analysis

2020 ◽  
Vol 09 (02) ◽  
pp. 2050008
Author(s):  
Shyjo Johnson ◽  
T. Jeyapoovan ◽  
D. Nagarajan
Keyword(s):  
Stiffness Matrix ◽  
Triangular Element ◽  
Integration Scheme ◽  
Sampling Point ◽  
Quadrilateral Element ◽  
Element Analysis ◽  
Element Stiffness Matrix ◽  
Sampling Points ◽  
Edge Sampling ◽  
Accuracy Of Results

Recently, many literature studies have focused on the development on new elements in finite elements. This paper aims to develop a new quadrature for the 3-node triangular element for the purpose of evaluation of element stiffness matrix. The analysis of triangular element is usually done in a quadrilateral element by dividing the quadrilateral element into two. The edge sampling point quadrature is a mimics of Gauss numerical integration scheme. This sampling integration scheme consists of five sampling points and weights where four sampling points are at the edge and one at the center of the element. Accuracy of results, convergence of the results and stability of values have been tested using the standard benchmarked problems defined by various research studies.

A Parallel Elastoplastic Reanalysis Based on GPU Platform

2016 ◽  
Vol 14 (05) ◽  
pp. 1750051 ◽  
Author(s):  
Guanqiang He ◽  
Hu Wang ◽  
Guangxin Huang ◽  
Haitao Liu ◽  
Guangyao Li
Keyword(s):  
Parallel Computation ◽  
Stiffness Matrix ◽  
Suggested Method ◽  
Elastoplastic Analysis ◽  
Elastic Analysis ◽  
Load Increment ◽  
Numerical Examples ◽  
Element Stiffness Matrix ◽  
Accuracy Of Results

An efficient parallel elastoplastic reanalysis method is suggested. The main backbone of the suggested method is based on combined approximation (CA) reanalysis. GPU parallel computation is used to accelerate assembling the stiffness matrix. Assembling process is divided into the offline part for strain matrix and online part for element stiffness matrix, which makes the structure of the program more reasonable and efficient. Pseudo elastic analysis is introduced and extended to load increment method to make the CA method more feasible. The numerical examples show that the suggested method can improve the efficiency of elastoplastic analysis significantly and the accuracy of results can also be ensured.

Evaluation of stiffness matrix in finite element analysis using element edge method for the 8-node brick element

2019 ◽  
Vol 08 (04) ◽  
pp. 1950018
Author(s):  
Shyjo Johnson ◽  
T. Jeyapoovan
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Integration Method ◽  
Large Data ◽  
Computational Time ◽  
Element Analysis ◽  
Sampling Points ◽  
Brick Element ◽  
Edge Method

An element edge method is developed for the evaluation of stiffness matrix for the 8-node brick element. Handling of large data leads to take more computational time in finite element analysis. The new set of quadrature consist of 13 sampling points and weights out which 12 points are at the edges of the brick element and one point is considered at the center of the element. The new set of sampling points is a mimic of Gauss numerical integration method. Finally, the proposed element edge method is evaluated using the standard benchmarked problems and compared the results with conventional Gauss integration method and found that CPU execution time for the evaluation of finite element problems are found to be reduced considerably without compromising in the results mainly consist of accuracy of values and convergence rate.

scholarly journals On Hydromechanical Interaction during Propagation of Localized Damage in Rocks

Minerals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 162
Author(s):  
A.A. Jameei ◽  
S. Pietruszczak
Keyword(s):  
Numerical Study ◽  
Fluid Pressure ◽  
Implicit Time ◽  
Integration Scheme ◽  
Internal Length ◽  
Element Analysis ◽  
Equivalent Permeability ◽  
Mechanical Coupling ◽  
Splitting Test ◽  
Localized Damage

This paper provides a mathematical description of hydromechanical coupling associated with propagation of localized damage. The framework incorporates an embedded discontinuity approach and addresses the assessment of both hydraulic and mechanical properties in the region intercepted by a fracture. Within this approach, an internal length scale parameter is explicitly employed in the definition of equivalent permeability as well as the tangential stiffness operators. The effect of the progressive evolution of damage on the hydro-mechanical coupling is examined and an evolution law is derived governing the variation of equivalent permeability with the continuing deformation. The framework is verified by a numerical study involving 3D simulation of an axial splitting test carried out on a saturated sample under displacement and fluid pressure-controlled conditions. The finite element analysis incorporates the Polynomial-Pressure-Projection (PPP) stabilization technique and a fully implicit time integration scheme.

An Exact Three-Dimensional Beam Element With Nonuniform Cross Section

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
M. Jafari ◽  
M. J. Mahjoob
Keyword(s):  
Cross Section ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Direct Method ◽  
Three Dimensional ◽  
Curved Beams ◽  
Element Analysis ◽  
Shear Loads ◽  
Line Passing ◽  
Exact Stiffness Matrix

In this paper, the exact stiffness matrix of curved beams with nonuniform cross section is derived using direct method. The considered element has two nodes and 12 degrees of freedom, with three forces and three moments applied at each node. The noncoincidence effect of shear center and center of area is also considered in this element. The deformations of the beam are due to bending, torsion, tensile, and shear loads. The line passing through center of area is a general three-dimensional curve and the cross section properties may change arbitrarily along it. The method is extended to deal with distributed loads on the curved beams. The stiffness matrix of some selected types of beams is determined by this method. The results are compared (where possible) with previously published results, simple beam finite element analysis and analytic solution. It is shown that the determined stiffness matrix is exact and that any type of beam can be analyzed by this method.

Dynamic Analysis of Shipping Cask Subjected to Sequential Bolt Preload and Impact Loads

2009 ◽  
Author(s):  
Tsu-te Wu
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Numerical Integration ◽  
Dynamic Responses ◽  
Integration Scheme ◽  
Impact Loads ◽  
Element Mesh ◽  
Bolt Preload ◽  
Numerical Integration Scheme ◽  
Structural Responses

This paper presents an improved methodology for evaluating the dynamic responses of shipping casks subjected to the sequential HAC impact loads. The methodology utilizes the import technique of the finite-element mesh and the analytical results form one dynamic analysis using explicit numerical integration scheme into another dynamic analysis also using explicit numerical integration scheme. The new methodology presented herein has several advantages over conventional methods. An example problem is analyzed to illustrate the application of the present methodology in evaluating the structural responses of a shipping cask to the sequential HAC loading.

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