Convex Models for Uncertain Imperfection Control in Multimode Dynamic Buckling

1992 ◽  
Vol 59 (4) ◽  
pp. 937-945 ◽  
Author(s):  
H. E. Lindberg
Keyword(s):  
Quality Control ◽  
Fourier Coefficients ◽  
Fourier Transforms ◽  
Dynamic Buckling ◽  
Mode Number ◽  
Uniform Bounds ◽  
Additional Information ◽  
Probabilistic Distribution ◽  
Finite Fourier Transforms

Control of uncertain imperfections by means of convex bounds on finite Fourier transforms is shown to be more direct and not as overly conservative as control based on uniform bounds, i.e., bounding maximum and minimum imperfections. With either method, conservatism in bounds on buckling response is reduced by filtering the imperfection measurements. Extraction of the needed filtered information by operating directly on the Fourier coefficients is straightforward and allows use of additional information on the variation of the coefficients with mode number. Use of this information in example multimode buckling problems gives a bound on maximum possible buckling response that is a factor of1.6 larger than the response at a reliability of 99.5 percent for hypothetical (but reasonably representative) probabilistic imperfections. The bounding response itself, of course, does not depend on any assumptions concerning the probabilistic distribution of imperfections. Two additional combined uniform and Fourier ellipsoid bound models further reduce this factor to 1.1 and 0.5, and require only a simple, unfiltered imperfection bound measurement during quality control inspection.

An Evaluation of Convex Modeling for Multimode Dynamic Buckling

1992 ◽  
Vol 59 (4) ◽  
pp. 929-936 ◽  
Author(s):  
Herbert E. Lindberg
Keyword(s):  
Quality Control ◽  
Finite Element ◽  
Probabilistic Model ◽  
Numerical Evaluation ◽  
Probabilistic Models ◽  
Model Solution ◽  
Dynamic Buckling ◽  
Convex Model ◽  
Uniform Bounds ◽  
Impulsive Loads

Convex and probabilistic model solutions are obtained for multimode dynamic buckling of cylindrical shells with uncertain imperfections under symmetric radial impulsive loads. It is found that the maximum possible buckling deformations for any imperfection within uniform bounds ± δˆ can be made comparable to the buckling deformations from the probabilistic models at a reliability of about 99.5 percent. Numerical evaluation and interpretation of the convex model is much simpler than for the probabilistic models, and the convex model solution provides means for quality control of each and every shell by simply recording δˆ from appropriately filtered imperfection measurements. The power and simplicity of convex modeling for multimode buckling shows promise for more complex problems than require finite element modal analysis.

Finite Fourier Transforms

1971 ◽  
pp. 167-187
Author(s):  
Paul L. Butzer ◽  
Rolf J. Nessel
Keyword(s):  
Fourier Transforms ◽  
Finite Fourier Transforms

scholarly journals Proteasome and thiol involvement in quality control of glycosylphosphatidylinositol anchor addition

1998 ◽  
Vol 332 (1) ◽  
pp. 111-118 ◽  
Author(s):  
Barry WILBOURN ◽  
Darren N. NESBETH ◽  
Linda J. WAINWRIGHT ◽  
Mark C. FIELD
Keyword(s):  
Quality Control ◽  
Cysteine Residue ◽  
Retention Mechanism ◽  
Secretory Proteins ◽  
Aggregate Formation ◽  
Er Quality Control ◽  
Additional Information ◽  
Intracellular Degradation ◽  
Processing Signal ◽  
Ubiquitination System

Improperly processed secretory proteins are degraded by a hydrolytic system that is associated with the endoplasmic reticulum (ER) and appears to involve re-export of lumenal proteins into the cytoplasm for ultimate degradation by the proteasome. The chimaeric protein hGHDAF28, which contains a crippled glycosylphosphatidylinositol (GPI) C-terminal signal peptide, is degraded by a pathway highly similar to that for other ER-retained proteins and is characterized by formation of disulphide-linked aggregates, failure to reach the Golgi complex and intracellular degradation with a half life of ∼ 2 h. Here we show that N-acetyl-leucinal-leucinal-norleucinal, MG-132 and lactacystin, all inhibitors of the proteasome, protect hGHDAF28; hGHDAF28 is still proteolytically cleaved in the presence of lactacystin or MG-132, by the removal of ∼ 2 kDa, but the truncated fragment is not processed further. We demonstrate that the ubiquitination system accelerates ER-degradation of hGHDAF28, but is not essential to the process. Overall, these findings indicate that GPI quality control is mediated by the cytoplasmic proteasome. We also show that the presence of a cysteine residue in the GPI signal of hGHDAF28 is required for retention and degradation, as mutation of this residue to serine results in secretion of the fusion protein, implicating thiol-mediated retention as a mechanism for quality control of some GPI signals. Removal of the cysteine also prevents inclusion of hGHDAF28 in disulphide-linked aggregates, indicating that aggregate formation is an additional retention mechanism for this class of protein. Therefore our data suggest that an unpaired terminal cysteine is the retention motif of the hGHDAF28 GPI-processing signal and that additional information may be required for efficient engagement of ER quality control systems by the majority of GPI signals which lack cysteine residues.

scholarly journals KERNEL CONVERGENCE ESTIMATES FOR DIFFUSIONS WITH CONTINUOUS COEFFICIENTS

2011 ◽  
Vol 14 (07) ◽  
pp. 979-1004
Author(s):  
CLAUDIO ALBANESE
Keyword(s):  
Convergence Rate ◽  
Convergence Rates ◽  
Fourier Transforms ◽  
Uniform Continuity ◽  
Time Step ◽  
Uniform Bounds ◽  
Kernel Convergence ◽  
Discretization Schemes ◽  
A New Technique ◽  
Derivatives Of

Bidirectional valuation models are based on numerical methods to obtain kernels of parabolic equations. Here we address the problem of robustness of kernel calculations vis a vis floating point errors from a theoretical standpoint. We are interested in kernels of one-dimensional diffusion equations with continuous coefficients as evaluated by means of explicit discretization schemes of uniform step h > 0 in the limit as h → 0. We consider both semidiscrete triangulations with continuous time and explicit Euler schemes with time step so small that the Courant condition is satisfied. We find uniform bounds for the convergence rate as a function of the degree of smoothness. We conjecture these bounds are indeed sharp. The bounds also apply to the time derivatives of the kernel and its first two space derivatives. The proof is constructive and is based on a new technique of path conditioning for Markov chains and a renormalization group argument. We make the simplifying assumption of time-independence and use longitudinal Fourier transforms in the time direction. Convergence rates depend on the degree of smoothness and Hölder differentiability of the coefficients. We find that the fastest convergence rate is of order O(h2) and is achieved if the coefficients have a bounded second derivative. Otherwise, explicit schemes still converge for any degree of Hölder differentiability except that the convergence rate is slower. Hölder continuity itself is not strictly necessary and can be relaxed by an hypothesis of uniform continuity.

Variance of Signals and Their Finite Fourier Transforms

2010 ◽  
pp. 53-76 ◽  
Author(s):  
D. V. Chudnovsky ◽  
G. V. Chudnovsky ◽  
T. Morgan
Keyword(s):  
Fourier Transforms ◽  
Finite Fourier Transforms
Sign in / Sign up

Export Citation Format

Share Document