Global Sensitivity Analysis for the Elastic Properties of Unidirectional Carbon Fibre Reinforced Composites Based on Metamodels

2018 ◽  
Vol 26 (3) ◽  
pp. 205-221 ◽  
Author(s):  
Chao Zhu ◽  
Ping Zhu ◽  
Jiahai Lu
Keyword(s):  
Mechanical Properties ◽  
Sensitivity Analysis ◽  
Carbon Fibre ◽  
Elastic Properties ◽  
Global Sensitivity Analysis ◽  
Structural Parameters ◽  
Elastic Response ◽  
High Dimensional Model Representation ◽  
Global Sensitivity ◽  
Elastic Responses

A fast and effective numerical method to predict mechanical properties of carbon fibre reinforced polymer (CFRP) composites, even elastic properties, is complicated due to the mismatch of mechanical properties among the constituents. Furthermore, it is not possible to completely characterise the influence of multiple parameters including mechanical and structural parameters on the bulk properties of CFRP by experiments. In this study, a three-phase finite-element model consisting of matrix, carbon fibre and interface was developed to predict the elastic mechanical behaviour of unidirectional CFRP. The elastic properties in terms of two Young's moduli, two Poisson's ratios and a shear modulus were calculated by means of a homogenisation method. High-accuracy Kriging surrogate models were constructed to fast-calculate the elastic responses for a large number of samples. Combining Kriging and high-dimensional model representation (HDMR) methods, a global sensitivity analysis was performed to study how the microscopic parameters influence the elastic responses to get a deeper understanding of elastic property-structure relationship. Eleven parameters, including mechanical and geometry properties of constituent phases, were chosen as inputs. Independent and cooperative effects of input parameters on the elastic properties of the studied composites were surveyed via first- and second-order sensitivity indices, respectively. An importance ranking of these parameters for each elastic response was derived directly by these indices. The procedure proposed in this work could serve as a theoretical guide for further design optimisation of CFRP.

Comprehensive global sensitivity analysis of a repository model using different types of transformations and metamodeling techniques

2021 ◽  
Author(s):  
Sabine M. Spiessl ◽  
Dirk-A. Becker ◽  
Sergei Kucherenko
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Higher Order ◽  
Model Parameters ◽  
High Dimensional Model Representation ◽  
Model Output ◽  
Global Sensitivity ◽  
Sparse Polynomial ◽  
Sensitivity Indices ◽  
Highly Nonlinear

<p>Due to their highly nonlinear, non-monotonic or even discontinuous behavior, sensitivity analysis of final repository models can be a demanding task. Most of the output of repository models is typically distributed over several orders of magnitude and highly skewed. Many values of a probabilistic investigation are very low or even zero. Although this is desirable in view of repository safety it can distort the evidence of sensitivity analysis. For the safety assessment of the system, the highest values of outputs are mainly essential and if those are only a few, their dependence on specific parameters may appear insignificant. By applying a transformation, different model output values are differently weighed, according to their magnitude, in sensitivity analysis. Probabilistic methods of higher-order sensitivity analysis, applied on appropriately transformed model output values, provide a possibility for more robust identification of relevant parameters and their interactions. This type of sensitivity analysis is typically done by decomposing the total unconditional variance of the model output into partial variances corresponding to different terms in the ANOVA decomposition. From this, sensitivity indices of increasing order can be computed. The key indices used most often are the first-order index (SI1) and the total-order index (SIT). SI1 refers to the individual impact of one parameter on the model and SIT represents the total effect of one parameter on the output in interactions with all other parameters. The second-order sensitivity indices (SI2) describe the interactions between two model parameters.</p><p>In this work global sensitivity analysis has been performed with three different kinds of output transformations (log, shifted and Box-Cox transformation) and two metamodeling approaches, namely the Random-Sampling High Dimensional Model Representation (RS-HDMR) [1] and the Bayesian Sparse PCE (BSPCE) [2] approaches. Both approaches are implemented in the SobolGSA software [3, 4] which was used in this work. We analyzed the time-dependent output with two approaches for sensitivity analysis, i.e., the pointwise and generalized approaches. With the pointwise approach, the output at each time step is analyzed independently. The generalized approach considers averaged output contributions at all previous time steps in the analysis of the current step. Obtained results indicate that robustness can be improved by using appropriate transformations and choice of coefficients for the transformation and the metamodel.</p><p>[1] M. Zuniga, S. Kucherenko, N. Shah (2013). Metamodelling with independent and dependent inputs. Computer Physics Communications, 184 (6): 1570-1580.</p><p>[2] Q. Shao, A. Younes, M. Fahs, T.A. Mara (2017). Bayesian sparse polynomial chaos expansion for global sensitivity analysis. Computer Methods in Applied Mechanics and Engineering, 318: 474-496.</p><p>[3] S. M. Spiessl, S. Kucherenko, D.-A. Becker, O. Zaccheus (2018). Higher-order sensitivity analysis of a final repository model with discontinuous behaviour. Reliability Engineering and System Safety, doi: https://doi.org/10.1016/j.ress.2018.12.004.</p><p>[4] SobolGSA software (2021). User manual https://www.imperial.ac.uk/process-systems-engineering/research/free-software/sobolgsa-software/.</p>

Investigation of the uncertainty of the in-plane mechanical properties of composite laminates

2011 ◽  
Vol 226 (7) ◽  
pp. 1739-1750 ◽  
Author(s):  
Tian Longfei ◽  
Lu Zhenzhou ◽  
Hao Wenrui
Keyword(s):  
Mechanical Properties ◽  
Sensitivity Analysis ◽  
Composite Laminates ◽  
Global Sensitivity Analysis ◽  
Nonlinear Models ◽  
Analysis Method ◽  
Global Sensitivity ◽  
Response Variance ◽  
Sensitivity Analysis Method ◽  
Input Variables

The uncertainty of the in-plane mechanical properties of the laminate used in an aircraft wing structure is investigated. Global sensitivity analysis is used to identify the source of the uncertainties of the response performance. Due to the limitations of the existing global sensitivity analysis method for nonlinear models with correlated input variables, a new one using nonlinear regression is proposed. Furthermore, a contribution matrix is defined for engineering convenience. Two nonlinear numerical examples are employed in this article to demonstrate the ability of the proposed global sensitivity analysis method. After applying the proposed global sensitivity analysis method to the laminate model, the contribution matrices are obtained; from these matrices, researchers can identify the dominant variance contributions that contribute the most to the response variance. Factor analysis is then employed to analyze the global sensitivity analysis results and determine the most efficient methods to decrease the variances of the in-plane elastic constants. Monte Carlo simulation is used to demonstrate the efficiency of the methods in decreasing the variances.

Analytical global sensitivity analysis with Gaussian processes

2017 ◽  
Vol 31 (3) ◽  
pp. 235-250 ◽  
Author(s):  
Ankur Srivastava ◽  
Arun K. Subramaniyan ◽  
Liping Wang
Keyword(s):  
Sensitivity Analysis ◽  
Gaussian Processes ◽  
Global Sensitivity Analysis ◽  
Decomposition Methods ◽  
Variance Decomposition ◽  
Model Representation ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
Sobol Indices ◽  
Global Sensitivity

AbstractMethods for efficient variance-based global sensitivity analysis of complex high-dimensional problems are presented and compared. Variance decomposition methods rank inputs according to Sobol indices that can be computationally expensive to evaluate. Main and interaction effect Sobol indices can be computed analytically in the Kennedy and O'Hagan framework with Gaussian processes. These methods use the high-dimensional model representation concept for variance decomposition that presents a unique model representation when inputs are uncorrelated. However, when the inputs are correlated, multiple model representations may be possible leading to ambiguous sensitivity ranking with Sobol indices. In this work, we present the effect of input correlation on sensitivity analysis and discuss the methods presented by Li and Rabitz in the context of Kennedy and O'Hagan's framework with Gaussian processes. Results are demonstrated on simulated and real problems for correlated and uncorrelated inputs and demonstrate the utility of variance decomposition methods for sensitivity analysis.

scholarly journals The Effects of Structural Parameter Variation on Cable Force of Fast Cable-Net Structure

2014 ◽  
Vol 6 ◽  
pp. 912158
Author(s):  
Qiming Wang ◽  
Peng Jiang ◽  
Xu Kong
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Structural Parameters ◽  
Element Model ◽  
Design Parameters ◽  
Structural Parameter ◽  
Global Sensitivity ◽  
Fatigue Stress ◽  
Cutting Length ◽  
Cable Force

Five-hundred-meter aperture spherical radio telescope (FAST) is supported by a cable-net structure, which enables its surface to form a real-time paraboloid by active control. FAST project is currently in the construction and implementation stage. However, there are always a considerable amount of errors that existed in practice which may result in the deviation of the structure from its ideal model or design. Therefore, structural parameter sensitivity analysis was discussed, which is indispensable. However, such deformation operation would lead to about 500 MPa of fatigue stress variation amplitude in the cable-net structure. Optimized deformation strategy is proposed to release the fatigue stress of the cable-net structure, which would be of advantage to improve the reliability of the cable-net structure. In the paper, the variation ranges of structural parameters were rationally determined. Based on local sensitivity analysis and global sensitivity analysis method, finite element model was used to study the effect of different structural parameters on the static behavior. It can be concluded that the effect of several key design parameters such as the cutting length and the elastic modulus of cable on the cable force is significant. The global sensitivity analysis indicates that the cable force range of the cable-net is −19% to 27%.

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