scholarly journals Surface Flaw Reliability Analysis of Ceramic Components With the SCARE Finite Element Postprocessor Program

1987 ◽  
Vol 109 (3) ◽  
pp. 274-281 ◽  
Author(s):  
J. P. Gyekenyesi ◽  
N. N. Nemeth
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Reliability Analysis ◽  
Surface Flaw ◽  
Modulus Of Rupture ◽  
Distribution Model ◽  
External Boundary ◽  
Mixed Mode Fracture ◽  
Boundary Area ◽  
Fast Fracture

The SCARE (Structural Ceramics Analysis and Reliability Evaluation) computer program on statistical fast fracture reliability analysis with quadratic elements for volume-distributed imperfections is enhanced to include the use of linear finite elements and the capability of designing against concurrent surface flaw-induced ceramic component failure. The SCARE code is presently coupled as a postprocessor to the MSC/NASTRAN general purpose, finite element analysis program. The improved version now includes the Weibull and Batdorf statistical failure theories for both surface and volume flaw-based reliability analysis. The program uses the two-parameter Weibull fracture strength cumulative failure probability distribution model with the principle of independent action for polyaxial stress states, and Batdorf’s shear-sensitive as well as shear-insensitive statistical theories. The shear-sensitive surface crack configurations include the Griffith crack and Griffith notch geometries, using the total critical coplanar strain energy release rate criterion to predict mixed-mode fracture. Weibull material parameters based on both surface and volume flaw-induced fracture can also be calculated from modulus of rupture bar tests, using the least-squares method with known specimen geometry and grouped fracture data. The surface flaw reliability prediction uses MSC/NASTRAN stress, temperature, and external boundary area output, obtained from the use of linear or quadratic shell and three-dimensional isoparametric finite elements. The statistical fast fracture theories for surface flaw-induced failure, along with selected input and output formats and options, are summarized. A sample problem to demonstrate various features of the program is included.

scholarly journals SCARE: A Postprocessor Program to MSC/NASTRAN for Reliability Analysis of Structural Ceramic Components

1986 ◽  
Vol 108 (3) ◽  
pp. 540-546 ◽  
Author(s):  
J. P. Gyekenyesi
Keyword(s):  
Least Squares Method ◽  
Three Dimensional ◽  
Strain Energy Release ◽  
Maximum Tensile Stress ◽  
Strength Distribution ◽  
Modulus Of Rupture ◽  
Distribution Model ◽  
Mixed Mode Fracture ◽  
Ceramic Components ◽  
Fast Fracture

A computer program is developed for calculating the statistical fast fracture reliability and failure probability of ceramic components. The program includes the two-parameter Weibull material fracture strength distribution model, using the principle of independent action for polyaxial stress states and Batdorf’s shear-sensitive as well as shear-insensitive crack theories, all for volume distributed flaws in macroscopically isotropic solids. Both penny-shaped cracks and Griffith cracks are included in the Batdorf shear-sensitive crack response calculations, using Griffith’s maximum tensile stress or critical coplanar strain energy release rate criteria to predict mixed mode fracture. Weibull material parameters can also be calculated from modulus of rupture bar tests, using the least-squares method with known specimen geometry and fracture data. The reliability prediction analysis uses MSC/NASTRAN stress, temperature, and volume output, obtained from the use of three-dimensional, quadratic, isoparametric, or axisymmetric finite elements. The statistical fast fracture theories employed, along with selected input and output formats and options, are summarized. A sample problem to demonstrate various features of the program is included.

scholarly journals A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

2020 ◽  
Vol 20 (4) ◽  
pp. 799-813
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Asymptotic Relation ◽  
Probabilistic Approach ◽  
Random Variable ◽  
High Order ◽  
Relative Accuracy ◽  
The Difference ◽  
New Perspective

AbstractThe aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements {P_{k}} and {P_{m}} ({k<m}). Then we analyze the asymptotic relation between these two probabilistic laws when the difference {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

DISCRETE COMPACTNESS FOR p AND hp 2D EDGE FINITE ELEMENTS

2003 ◽  
Vol 13 (11) ◽  
pp. 1673-1687 ◽  
Author(s):  
DANIELE BOFFI ◽  
LESZEK DEMKOWICZ ◽  
MARTIN COSTABEL
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Model Problem ◽  
Finite Element Approximation ◽  
Stability Estimate ◽  
Element Approximation ◽  
Dimensional Model ◽  
Compactness Property ◽  
One Dimensional ◽  
Discrete Compactness

In this paper we discuss the hp edge finite element approximation of the Maxwell cavity eigenproblem. We address the main arguments for the proof of the discrete compactness property. The proof is based on a conjectured L2 stability estimate for the involved polynomial spaces which has been verified numerically for p≤15 and illustrated with the corresponding one dimensional model problem.

An Extrapolation Method to Compute Far-Field Pressures From Near-Field Pressures Obtained by Finite Element Method

1995 ◽  
Author(s):  
Jamal Assaad ◽  
Christian Bruneel ◽  
Jean-Michel Rouvaen ◽  
Régis Bossut
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Near Field ◽  
Radiation Condition ◽  
Directivity Pattern ◽  
Extrapolation Method ◽  
External Boundary ◽  
Finite Width ◽  
Far Field ◽  
Element Method

Abstract The finite element method is widely used for the modeling of piezoelectric transducers. With respect to the radiation loading, the fluid is meshed and terminated by an external nonreflecting surface. This reflecting surface can be made up with dipolar damping elements that absorb approximately the outgoing acoustic wave. In fact, with dipolar dampers the fluid mesh can be quite limited. This method can provides a direct computation of the near-field pressure inside the selected external boundary. This paper describes an original extrapolation method to compute far-field pressures from near-field pressures in the two-dimensional (2-D) case. In fact, using the 2-D Helmholtz equation and its solution obeying the Sommerfeld radiation condition, the far-field directivity pattern can be expressed in terms of the near-field directivity pattern. These developments are valid for any radiation problem in 2D. One test example is described which consists of a finite width planar source mounted in a rigid or a soft baffle. Experimental results concerning the far-field directivity pattern of lithium niobate bars (Y-cut) are also presented.

scholarly journals A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake

2016 ◽  
Vol 9 (10) ◽  
pp. 3803-3815 ◽  
Author(s):  
Gheorghe-Teodor Bercea ◽  
Andrew T. T. McRae ◽  
David A. Ham ◽  
Lawrence Mitchell ◽  
Florian Rathgeber ◽  
...  
Keyword(s):  
Finite Element ◽  
Performance Evaluation ◽  
Finite Elements ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Data Layout ◽  
Element System ◽  
Continuous Galerkin ◽  
Performance Penalty ◽  
The Cost

Abstract. We present a generic algorithm for numbering and then efficiently iterating over the data values attached to an extruded mesh. An extruded mesh is formed by replicating an existing mesh, assumed to be unstructured, to form layers of prismatic cells. Applications of extruded meshes include, but are not limited to, the representation of three-dimensional high aspect ratio domains employed by geophysical finite element simulations. These meshes are structured in the extruded direction. The algorithm presented here exploits this structure to avoid the performance penalty traditionally associated with unstructured meshes. We evaluate the implementation of this algorithm in the Firedrake finite element system on a range of low compute intensity operations which constitute worst cases for data layout performance exploration. The experiments show that having structure along the extruded direction enables the cost of the indirect data accesses to be amortized after 10–20 layers as long as the underlying mesh is well ordered. We characterize the resulting spatial and temporal reuse in a representative set of both continuous-Galerkin and discontinuous-Galerkin discretizations. On meshes with realistic numbers of layers the performance achieved is between 70 and 90 % of a theoretical hardware-specific limit.

Sign in / Sign up

Export Citation Format

Share Document