Stress distributions of anisotropic three-dimensional semi-infinite bodies by a refined finite difference formulation

2002 ◽  
Vol 6 (4) ◽  
pp. 447-455
Author(s):  
Sang Youl Lee ◽  
Suk Yoon Chang
Keyword(s):  
Finite Difference ◽  
Three Dimensional ◽  
Stress Distributions ◽  
Finite Difference Formulation

3-D finite‐difference modeling of elastic waves in borehole environments

Geophysics ◽  
1992 ◽  
Vol 57 (6) ◽  
pp. 793-804 ◽  
Author(s):  
Kwi‐Hyon Yoon ◽  
George A. McMechan
Keyword(s):  
Finite Difference ◽  
Finite Differences ◽  
Elastic Waves ◽  
Three Dimensional ◽  
Fixed Time ◽  
Cylindrical Symmetry ◽  
Staggered Grid ◽  
Finite Difference Formulation ◽  
Borehole Waves ◽  
Sonic Logs

Full‐wavefield sonic logs may be simulated for arbitrarily complicated three‐dimensional (3-D) borehole environments using 3-D elastic finite differences. To ensure reliability through large contrasts in Poisson’s ratio (across mud‐casing‐lithology contacts), a staggered grid finite‐difference formulation is used. Cylindrical symmetry is not assumed so the responses of features such as asymmetrical washouts and dipping structure are easily obtained. When features are asymmetrical, seismic responses vary significantly at various points around the hole circumference at any depth. Even for simple hole geometries, observed responses are complicated because of coupling between waves inside and outside the hole. Observations are also sensitive to the source‐receiver separation. Output formats include fixed‐time snapshots of displacement, divergence, and curl, and seismograms for the center and edge of a borehole; this allows detailed arrival identification and interpretation. To our knowledge, this is the most comprehensive and flexible scheme for modeling borehole waves that has been implemented to date.

Development of Three-Dimensional PML Boundary Conditions for Aeroacoustics Applications

2002 ◽  
Vol 1 (3) ◽  
pp. 307-327
Author(s):  
J-F. Dietiker ◽  
K.A. Hoffmann ◽  
M. Papadakis ◽  
R. Agarwal
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Perfectly Matched Layer ◽  
Optimum Combination ◽  
Curvilinear Coordinates ◽  
Main Program ◽  
Governing Equations ◽  
Compact Finite Difference ◽  
Finite Difference Formulation

Perfectly Matched Layer (PML) boundary conditions are derived in generalized curvilinear coordinates for three-dimensional aeroacoustic applications. The resulting governing equations are solved numerically by a four-stage Runge-Kutta scheme, with 4th/6th order compact finite difference formulation. The PML equations are programmed in a subroutine, which is easily incorporated to the main program LINEULER (Linearized Euler's equation solver). Two and three-dimensional benchmarks problems are solved to investigate the efficiency and accuracy of the PML boundary conditions. Investigations on the PML parameters have been conducted to determine the optimum combination of parameters used in the computations.

scholarly journals Comparison of Tooth- and Bone-Borne Appliances on the Stress Distributions and Displacement Patterns in the Facial Skeleton in Surgically Assisted Rapid Maxillary Expansion—A Finite Element Analysis (FEA) Study

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1152
Author(s):  
Rafał Nowak ◽  
Anna Olejnik ◽  
Hanna Gerber ◽  
Roman Frątczak ◽  
Ewa Zawiślak
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Element Model ◽  
Rapid Maxillary Expansion ◽  
Stress Distributions ◽  
Maxillary Expansion ◽  
Facial Skeleton ◽  
Element Analysis ◽  
Maxillary Constriction

The aim of this study was to compare the reduced stresses according to Huber’s hypothesis and the displacement pattern in the region of the facial skeleton using a tooth- or bone-borne appliance in surgically assisted rapid maxillary expansion (SARME). In the current literature, the lack of updated reports about biomechanical effects in bone-borne appliances used in SARME is noticeable. Finite element analysis (FEA) was used for this study. Six facial skeleton models were created, five with various variants of osteotomy and one without osteotomy. Two different appliances for maxillary expansion were used for each model. The three-dimensional (3D) model of the facial skeleton was created on the basis of spiral computed tomography (CT) scans of a 32-year-old patient with maxillary constriction. The finite element model was built using ANSYS 15.0 software, in which the computations were carried out. Stress distributions and displacement values along the 3D axes were found for each osteotomy variant with the expansion of the tooth- and the bone-borne devices at a level of 0.5 mm. The investigation showed that in the case of a full osteotomy of the maxilla, as described by Bell and Epker in 1976, the method of fixing the appliance for maxillary expansion had no impact on the distribution of the reduced stresses according to Huber’s hypothesis in the facial skeleton. In the case of the bone-borne appliance, the load on the teeth, which may lead to periodontal and orthodontic complications, was eliminated. In the case of a full osteotomy of the maxilla, displacements in the buccolingual direction for all the variables of the bone-borne appliance were slightly bigger than for the tooth-borne appliance.

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