This book explains uncertainty analysis for finite elements and general nonlinear problems. It starts with the fundamentals of the topic and progresses to complex methods through 9 chapters. Each chapter focuses on a specific, relevant topic and provides information in a structured reading format for advanced learners. The author explains different models relevant to the topic where applicable, in an effort to cover the diverse aspects of mathematical analysis.
Uncertainty Analysis in Finite Elements Models is an ideal reference for advanced courses in mathematical analysis and engineering that require students to understand the basics of uncertainty analysis and basic reliability calculations.
Topics covered in the book include:
- Nonlinear stochastic finite element methods
- Reliability calculations
- Static analysis of interval finite element
- Linear and nonlinear vibration analysis
- Stochastic, random, fuzzy and mixed fields
- Mixed finite element analysis
Uncertainty Analysis in Finite Elements Models is an ideal reference for advanced courses in mathematical analysis and engineering that require students to understand the basics of uncertainty analysis and basic reliability calculations.
Table of Contents
- Introduction
- General Nonlinear Problems
- Taylor Expansion Method
- Perturbation Technology
- Neumann Stochastic Finite Element
- Elastic-Plastic Problem
- Concluding Remarks
- References
- Introduction
- Reliability Calculation of Static Problems
- Structural Reliability Calculation of Linear Vibration
- Reliability of Nonlinear Structures
- Concluding Remarks
- References
- Introduction
- Fuzzy Reliability Calculation of Static Problems Based on Stochastic Finite Element
- Fuzzy Reliability Calculation of Structures with Linear Vibration
- Fuzzy Reliability of Nonlinear Structures
- Fuzzy Reliability of Structures with Nonlinear Vibration
- Concluding Remarks
- References
- Introduction
- Taylor Expansion for Interval Finite Element
- Interval Finite Element Using Neumann Expansion
- Interval Finite Element Using Sherman-Morrison-Woodbury Expansion
- a New Iterative Method (Nim)
- Concluding Remarks
- References
- Introduction
- Interval Perturbation Finite Element for Linear Vibration
- Interval Neumann Finite Element for Linear Vibration
- Interval Sherman-Morrison-Woodbury Expansion Finite Element for Linear Vibration
- a New Iterative Method (Nim)
- Concluding Remarks
- References
- Introduction
- General Nonlinear Problems
- Elastoplastic Problem
- the Homotopy Perturbation Method (Mihpd)
- Concluding Remarks
- References
- Interval Perturbation Finite Element for Nonlinear Vibration
- Interval Neumann Finite Element for Nonlinear Vibration
- Interval Taylor Finite Element Used for Nonlinear Vibration
- Interval Sherman-Morrison-Woodbury Expansion Finite Element
- the Homotopy Perturbation Method (Mihpd)
- Concluding Remarks
- References
- Introduction
- Stochastic Field
- Improved Interpolation Method
- Interval Field
- References
- Introduction
- Stochastic and Interval Finite Element
- Neumann Expansion Method
- Taylor Expansion Method
- Neumann Expansion Method
- Concluding Remarks
- References
- Subject Index
Author
- Wenhui Mo
