Computations of Singular Stresses Along Three-Dimensional Corner Fronts by a Super Singular Element Method

2017 ◽  
Vol 14 (06) ◽  
pp. 1750065 ◽  
Author(s):  
Xuecheng Ping ◽  
Mengcheng Chen ◽  
Wei Zhu ◽  
Yihua Xiao ◽  
Weixing Wu
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Three Dimensional ◽  
Stress Singularity ◽  
Stress Fields ◽  
Singular Element ◽  
Singular Stress ◽  
Numerical Studies ◽  
Enriched Finite Element ◽  
Singular Stress Fields

In order to consider corner configurations with straight corner fronts in three-dimensional (3D) solids, a super polygonal prismatic element containing a straight corner front is established by using the numerical eigensolutions of singular stress fields and the Hellinger–Reissner variational principle. Singular stresses near the corner front subject to far-field boundary conditions can be obtained by incorporating the super singular element with conventional 3D brick elements. The numerical studies are conducted to demonstrate the simplicity of the proposed technique in handling fracture problems of 3D corner configurations and cracks. The usage of the super singular element can avoid mesh refinement near the corner front domain that is necessary for conventional and enriched finite element methods, and lead to high accuracy and fast convergence. Compared with the conventional finite element methods and existing analytical methods, the present method is more suitable for dealing with complicated problems of stress singularity in elasticity including multiple defects.

A Super Singular Element for Three-Dimensional Corner Fronts

2016 ◽  
Author(s):  
Xuecheng Ping ◽  
Mengcheng Chen ◽  
Wei Zhu
Keyword(s):  
Three Dimensional ◽  
Stress Singularity ◽  
High Accuracy ◽  
Stress Fields ◽  
Singular Element ◽  
Field Boundary ◽  
Singular Stress ◽  
Numerical Studies ◽  
Singular Stress Fields ◽  
Eigen Solutions

Three-dimensional (3-D) solids containing corner configurations with straight corner fronts are considered. A super polygonal prismatic element containing a straight corner front is established by using the numerical eigen-solutions of singular stress fields and Hellinger-Reissner variational principle. Singular stresses near corner fronts for far-field boundary conditions can be obtained by incorporating the super singular element with the conventional three-dimensional (3-D) brick elements. The numerical studies are conducted to demonstrate the simplicity of the proposed technique in handling fracture problems of 3-D through-thickness cracks. The usage of the super singular element can avoid mesh refinement near the corner front domain, and the simulation results have high accuracy and fast convergence speed. Compared with the conventional finite element methods and existing analytical methods, the present method is more suitable for dealing with complicated problems of stress singularity in elasticity including multiple defects.

Analysis of Singular Stress Fields at 3D Piezoelectric Bonded Joints Using a Conservative Integral

2016 ◽  
Author(s):  
Chonlada Luangarpa ◽  
Hideo Koguchi
Keyword(s):  
Three Dimensional ◽  
Stress Singularity ◽  
Stress Fields ◽  
Bonded Joints ◽  
Singular Stress ◽  
Conservative Integral ◽  
Dimensional Finite Element ◽  
Refined Meshes ◽  
Singular Stress Fields ◽  
Three Dimensional Finite Element

Singular stress fields at a vertex of the interface in three-dimensional piezoelectric bonded joints are analyzed. A conservative integral based on the Betti reciprocal principle is applied for calculating the intensities of singularities. Eigenanalysis formulated using a three-dimensional finite element method (FEM) is used to calculate the order of stress singularity, angular functions of mechanical displacements, stresses, electric displacements and electric potential. A bimaterial bonded joint with three terms of singularities is investigated. In order to study the influence of mesh refinement and integral area on the accuracy of the results, two models with different element sizes and various integral areas are used. The results are compared with those obtained from conventional FEM, in which using extremely refined meshes near the singular point.

scholarly journals Singular Stress Fields of Anisotropic Bimaterial Wedges with Imperfect Interfaces

2003 ◽  
Vol 19 (1) ◽  
pp. 203-210
Author(s):  
Anil C. Wijeyewickrema ◽  
Somsak Leungvichcharoen ◽  
Piya Poonsawat
Keyword(s):  
Stress Singularity ◽  
Imperfect Interface ◽  
Stress Fields ◽  
Radial Coordinate ◽  
Singular Stress ◽  
Free Boundary Conditions ◽  
Singular Stress Fields ◽  
Displacement Jumps ◽  
Anisotropic Bimaterial ◽  
Composite Wedge

ABSTRACTThe effect of an imperfect interface on the stress singularity of anisotropic bimaterial wedges subjected to traction free boundary conditions are investigated. The interfacial tractions are assumed to be continuous, directly proportional to the displacement jumps and inversely proportional to the radial coordinate. The characteristic equation for the order of singularity is obtained and numerical results are given for the angle-ply bimaterial composite wedge.

Finite element analysis of cracked and uncracked tubular T-joint

1986 ◽  
Vol 13 (3) ◽  
pp. 261-269 ◽  
Author(s):  
G. S. Bhuyan ◽  
M. Arockiasamy ◽  
K. Munaswamy ◽  
O. Vosikovsky
Keyword(s):  
Finite Element ◽  
Crack Front ◽  
Three Dimensional ◽  
Singular Element ◽  
Singular Stress ◽  
Element Analysis ◽  
Joint Stress ◽  
Weld Toe ◽  
Singular Stress Field ◽  
Bending Loads

A welded tubular T-joint is analysed using finite element methods to obtain through-thickness and surface stresses due to axial and in-plane bending loads. The effects of a shallow weld toe crack on the stress redistribution are studied. The two-dimensional analysis of the joint includes the membrane stiffness representation by plane stress element and the flexural stiffness by plate bending element. For the three-dimensional analyses, the joint is modelled using incompatible solid elements to improve flexural characteristics. The embedded elliptical crack front is modelled by straight-line segments. The region at the vicinity of the crack is discretized using special elements, which produce a singular stress field at the crack front. Key words: tubular joint, stress analysis, weld toe crack, incompatible element, singular element.

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