scholarly journals APPLICATION OF QUARTER-POINT SINGULAR ELEMENT IN FINITE ELEMENT METHOD TO SIMULATION OF CRACK TIP BEHAVIOR

2010 ◽  
Vol 13 (2) ◽  
pp. 5-13
Author(s):  
Thien Tich Truong ◽  
Bang Kim Tran
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Crack Tip ◽  
Singular Element ◽  
Displacement Fields ◽  
Mathematical Background ◽  
Stress And Displacement Fields ◽  
Calculation Results ◽  
Element Method

Fracture mechanics is a new branch in engineering. The development of modern mathematical background with different numerical methods has supported fracture mechanics to solve many complex fracture problems in practice effectively. This article introduces the application of quarter - point singular element in finite element method to simulate crack tip behavior in two dimensional problems. The ANSYS and FRANC2D programs are used to compute stress intensity factor, simulate the stress and displacement fields near crack tip and simulate crack propagation. The calculation results are compared with analytical results and the results in other articles.

Complete Polynomial Displacement Fields for Finite Element Method

1968 ◽  
Vol 72 (687) ◽  
pp. 245-246 ◽  
Author(s):  
P. C. Dunne
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Uniform Strain ◽  
Displacement Fields ◽  
Displacement Pattern ◽  
Displacement Patterns ◽  
Element Method

It is generally accepted that the displacement patterns chosen to represent the deformation of a finite element should be such that there is complete compatibility with adjacent elements. Although some writers have doubted the necessity for the complete satisfaction of compatibility away from the reference nodes, provided the displacement pattern is capable of assuming certain uniform strain states, the desirability of complete compatibility is not in question. The displacement fields suggested in this note satisfy complete compatibility.

scholarly journals Prediction of Characteristic Length and Fracture Toughness in Ductile-Brittle Transition

2008 ◽  
Author(s):  
Z. X. Wang ◽  
H. M. Li ◽  
Y. J. Chao ◽  
P. S. Lam
Keyword(s):  
Finite Element Method ◽  
Fracture Toughness ◽  
Finite Element ◽  
Characteristic Length ◽  
Crack Tip ◽  
Critical Distance ◽  
Transition Regime ◽  
Temperature Dependent ◽  
Brittle Transition ◽  
Element Method

Finite element method was used to analyze the three-point bend experimental data of A533B-1 pressure vessel steel obtained by Sherry, Lidbury, and Beardsmore [1] from −160 to −45 °C within the ductile-brittle transition regime. As many researchers have shown, the failure stress (σf) of the material could be approximated as a constant. The characteristic length, or the critical distance (rc) from the crack tip, at which σf is reached, is shown to be temperature dependent based on the crack tip stress field calculated by the finite element method. With the J-A2 two-parameter constraint theory in fracture mechanics, the fracture toughness (JC or KJC) can be expressed as a function of the constraint level (A2) and the critical distance rc. This relationship is used to predict the fracture toughness of A533B-1 in the ductile-brittle transition regime with a constant σf and a set of temperature-dependent rc. It can be shown that the prediction agrees well with the test data for wide range of constraint levels from shallow cracks (a/W = 0.075) to deep cracks (a/W = 0.5), where a is the crack length and W is the specimen width.

scholarly journals INFORMATIZATION OF CONSTRUCTION MANAGEMENT AS A BASIS FOR PREVENTING MAN-MADE ACCIDENTS

2021 ◽  
Vol 4 (4) ◽  
pp. 11-31
Author(s):  
S. Koryagina
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
The Finite Element Method ◽  
Calculation Results ◽  
Definition Of ◽  
Deep Pits ◽  
Geotechnical Problems ◽  
Seismic Impacts ◽  
Base Structure ◽  
Element Method

the article presents the principles and algorithms of the finite element method in solving geotechnical prob-lems taking into account seismic impacts for determining the stress-strain state of structures and slope stabil-ity, implemented in the Midas GTS NX software package. GTS NX allows you to perform calculations of various types of geotechnical problems and solve complex geotechnical problems in a single software envi-ronment. GTS NX covers the entire range of engineering and geotechnical projects, including calculations of the "base-structure" system, deep pits with various mounting options, tunnels of complex shape, consolida-tion and filtration calculations, as well as calculations for dynamic actions and stability calculations. At the same time, all types of calculations in GTS NX can be performed both in 2D and in 3D. The author does not claim to be the author of the finite element method, but he cannot do without pointing out the basic equa-tions, as this affects the definition of the boundaries of use, the formulation of algorithms for constructing calculation schemes and the analysis of calculation results.

scholarly journals The Numerical Simulation of the Crack Elastoplastic Extension Based on the Extended Finite Element Method

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Xia Xiaozhou ◽  
Zhang Qing ◽  
Wang Hong ◽  
Jiang Qun
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Basis Function ◽  
Extended Finite Element Method ◽  
Crack Tip ◽  
Function Form ◽  
Extended Finite Element ◽  
Polar Radius ◽  
Radius Function ◽  
Element Method

In the frame of the extended finite element method, the exponent disconnected function is introduced to reflect the discontinuous characteristic of crack and the crack tip enrichment function which is made of triangular basis function, and the linear polar radius function is adopted to describe the displacement field distribution of elastoplastic crack tip. Where, the linear polar radius function form is chosen to decrease the singularity characteristic induced by the plastic yield zone of crack tip, and the triangle basis function form is adopted to describe the displacement distribution character with the polar angle of crack tip. Based on the displacement model containing the above enrichment displacement function, the increment iterative form of elastoplastic extended finite element method is deduced by virtual work principle. For nonuniform hardening material such as concrete, in order to avoid the nonsymmetry characteristic of stiffness matrix induced by the non-associate flowing of plastic strain, the plastic flowing rule containing cross item based on the least energy dissipation principle is adopted. Finally, some numerical examples show that the elastoplastic X-FEM constructed in this paper is of validity.

Analysis by the mixed method of statically indeterminate frames with elements of increased rigidity and numerical verification of the calculation results using the finite element method

2021 ◽  
Vol 14 (2) ◽  
pp. 54-66
Author(s):  
Svetlana Sazonova ◽  
Viktor Asminin ◽  
Alla Zvyaginceva
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Initial Data ◽  
Mixed Method ◽  
Numerical Verification ◽  
Bending Moments ◽  
The Finite Element Method ◽  
Calculation Results ◽  
Internal Forces ◽  
Element Method

The sequence of application of the mixed method for calculating internal forces in statically indeterminate frames with elements of increased rigidity is given. The main system is chosen for the frame with one kinematic and one force unknown. The canonical equations of the mixed method are written, taking into account their meaning. Completed the construction of the final diagram of the bending moments and all the necessary calculations and checks. When calculating integrals, Vereshchagin's rule is applied. The solution of the problem is checked by performing the calculation using the computer program STAB12.EXE; the results of the calculations are numerically verified using the finite element method. An example of the formation of the initial data for the STAB12.EXE program and the subsequent processing of the calculation results, the rules for comparing the numerical results and the results obtained in the calculation of the frame by the mixed method are given.

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