Uncertainty Assessment of Large Finite Element Systems: A Comprehensive Guide

Uncertainty Assessment of Large Finite Element Systems (Lecture Notes in Applied and Computational Mechanics Book 24)

by Christian A. Schenk

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Language	:	English
File size	:	3111 KB
Text-to-Speech	:	Enabled
Print length	:	166 pages
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Uncertainty is an inherent aspect of any engineering system. It arises from various sources, such as material properties, loading conditions, and modeling approximations. Uncertainty assessment is, therefore, essential for reliable engineering predictions and decision-making. In the context of finite element (FE) analysis, uncertainty assessment plays a critical role in ensuring the accuracy and robustness of numerical simulations.

This comprehensive guide provides an in-depth exploration of uncertainty assessment for large finite element systems. It covers the fundamental concepts, established methodologies, and practical applications of this important topic. By delving into these lecture notes, readers will gain a thorough understanding of the techniques and tools required to effectively quantify and manage uncertainty in FE-based engineering analysis.

Types of Uncertainty

Uncertainty in FE analysis can be broadly categorized into two main types:

• Aleatory Uncertainty: This type of uncertainty arises from inherent randomness or variability in the system. It is often associated with material properties, loading conditions, and environmental factors.
• Epistemic Uncertainty: This type of uncertainty stems from a lack of knowledge or information about the system. It may involve uncertainties in model parameters, boundary conditions, or computational methods.

Uncertainty Quantification Techniques

A range of techniques can be employed to quantify uncertainty in FE analysis. These techniques can be broadly classified into two main approaches:

• Probabilistic Methods: These methods involve representing uncertainty using probability distributions. They allow for the quantification of the likelihood and magnitude of uncertain parameters and their impact on the system response.
• Non-Probabilistic Methods: These methods do not rely on probability distributions but instead use alternative approaches to represent and characterize uncertainty. They can be particularly useful when limited data or information is available.

Uncertainty Propagation Methods

Once uncertainty has been quantified, it is necessary to propagate it through the FE analysis to assess its impact on the system response. Several methods are available for uncertainty propagation, including:

• Monte Carlo Simulation: This method involves repeatedly sampling from the probability distributions of uncertain parameters and running the FE analysis multiple times to obtain a statistical distribution of the system response.
• Latin Hypercube Sampling: This method is a more efficient variation of Monte Carlo simulation that reduces the number of required samples while maintaining accuracy.
• Perturbation Methods: These methods involve perturbing the uncertain parameters by small amounts and analyzing the resulting changes in the system response.

Sensitivity Analysis

Sensitivity analysis is an important aspect of uncertainty assessment. It helps identify the most influential uncertain parameters and their relative contributions to the uncertainty in the system response. Various methods can be used for sensitivity analysis, including:

• Morris Method: This method is an efficient screening technique that can identify the most important uncertain parameters with a relatively small number of simulations.
• Variance-Based Methods: These methods quantify the contribution of each uncertain parameter to the variance of the system response.
• Regression Analysis: This method involves fitting a regression model to the simulation data to identify the relationship between the uncertain parameters and the system response.

Applications of Uncertainty Assessment

Uncertainty assessment has a wide range of applications in engineering analysis, including:

• Structural Mechanics: Assessing the safety and reliability of structures under uncertain loads and material properties.
• Computational Fluid Dynamics: Quantifying the uncertainty in fluid flow simulations due to uncertain boundary conditions and material properties.
• Solid Mechanics: Evaluating the uncertainty in stress and strain predictions due to uncertain material properties and loading conditions.
• Risk Analysis: Assessing the likelihood and consequences of failure events in complex engineering systems.

Uncertainty assessment is a critical aspect of finite element analysis that enables engineers to quantify and manage the uncertainties inherent in engineering systems. By understanding the principles, techniques, and applications of uncertainty assessment, engineers can make more informed decisions and ensure the reliability and accuracy of their numerical simulations. These lecture notes provide a comprehensive guide to Uncertainty Assessment of Large Finite Element Systems, empowering engineers with the knowledge and tools to harness the power of this essential engineering practice.

Uncertainty Assessment of Large Finite Element Systems (Lecture Notes in Applied and Computational Mechanics Book 24)

by Christian A. Schenk

5 out of 5

Language	:	English
File size	:	3111 KB
Text-to-Speech	:	Enabled
Print length	:	166 pages
Screen Reader	:	Supported

FREE