An approach to variable metric bundle methods

1994 ◽  
pp. 144-162 ◽  
Author(s):  
Claude Lemaréchal ◽  
Claudia Sagastizábal
Keyword(s):  
Bundle Methods ◽  
Variable Metric

Variable metric bundle methods: From conceptual to implementable forms

1997 ◽  
Vol 76 (3) ◽  
pp. 393-410 ◽  
Author(s):  
Claude Lemaréchal ◽  
Claudia Sagastizábal
Keyword(s):  
Bundle Methods ◽  
Variable Metric

Optimal conditioning of self-scaling variable Metric algorithms

1976 ◽  
Vol 10 (1) ◽  
pp. 70-90 ◽  
Author(s):  
Shmuel S. Oren ◽  
Emilio Spedicato
Keyword(s):  
Variable Metric ◽  
Variable Metric Algorithms ◽  
Optimal Conditioning

Self-Scaling Variable Metric (SSVM) Algorithms

1974 ◽  
Vol 20 (5) ◽  
pp. 863-874 ◽  
Author(s):  
Shmuel S. Oren
Keyword(s):  
Variable Metric

scholarly journals A stochastic quasigradient algorithm with variable metric

1992 ◽  
Vol 39 (1) ◽  
pp. 251-267 ◽  
Author(s):  
S. P. Uryas'ev
Keyword(s):  
Variable Metric

Evaluation methods for predicting the elastic constants of C/Epoxy plain-weave composites by considering the realistic mesostructures

2018 ◽  
Vol 53 (2) ◽  
pp. 197-208 ◽  
Author(s):  
Shan-yuan Jiang ◽  
Hao Wang ◽  
Zhong-wei Wang
Keyword(s):  
Mechanical Properties ◽  
Elastic Constants ◽  
Stochastic Theory ◽  
Textile Composites ◽  
Analytical Models ◽  
Plane Shear ◽  
Elliptical Cross ◽  
Variable Metric ◽  
Plain Weave ◽  
Feature Parameters

Variabilities of mesostructures existing in textile composites can affect their mechanical properties. Most of the deterministic mechanical models are based on the assumptions of ideal Representative Volume Element, which cannot predict the mechanical properties accurately. Two analytical models predicting the elastic constants of C/Epoxy plain-weave composites by considering the realistic mesostructures are presented in this paper. These models utilize the variable metric stochastic theory to introduce the fluctuations of yarn feature parameters (yarn path and elliptical cross-section parameters) into the model of macro elastic properties. C/Epoxy plain-weave composite is taken as an example to quantify the influences of realistic yarn feature parameters on the elastic constants of the composite. The predicted elastic constants by analytical models and finite element method are verified by the results of mechanical experiments. It can be concluded that for C/Epoxy plain-weave composite the stochastic fluctuations of yarn feature parameters reduce in-plane elastic moduli by a maximum of 4%, and increase the in-plane shear modulus and Poisson’s ratio by a maximum of 15% and 33%, respectively.

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