Author: Wenhui Mo

### Uncertain Analysis in Finite Elements Models

eBook: US \$49 Special Offer (PDF + Printed Copy): US \$78
Printed Copy: US \$54
ISBN: 978-981-5079-07-4 (Print)
ISBN: 978-981-5079-06-7 (Online)
Year of Publication: 2022
DOI: 10.2174/97898150790671220101

#### Introduction

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.

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.

Audience: Engineering and Mathematics students and teachers.

# Preface

There are three kinds of uncertainties in engineering problems. One is randomness, the second is fuzziness, and the third is non probability. Sometimes, the impact of uncertainty on engineering problems can not be ignored. Uncertainty has a great impact on buildings, dams, nuclear power plants, bridges, aircraft, machinery, vehicles, warship, etc. The material properties, geometry parameters and loads of the structure are assumed to be random, fuzzy and non probabilistic.

In the first chapter, nonlinear stochastic finite elements for general nonlinear problems and elastoplastic problems are discussed, and three methods are proposed. In Chapter 2, the calculation formula of stochastic finite element is given by using the third-order Taylor expansion and a simple calculation method is addressed. The stress-strength interference model, Monte Carlo simulation, a new iterative method (NIM) of reliability calculation for the linear static problem and linear vibration are proposed. Reliability calculation methods using the homotopy perturbation method (MIHPD) and second order reliability method for the nonlinear static problem and nonlinear vibration are proposed. In Chapter 3, the structural fuzzy reliability calculation of static problem, linear vibration, nonlinear problem and nonlinear vibration is studied by using the stochastic finite element method. The normal membership function is selected as the membership function, and the calculation formula of fuzzy reliability is presented. In Chapter 4, Taylor expansion, Neumann expansion, Sherman Morrison Woodbury expansion and a new iterative method (NIM) for interval finite element calculation of static problems are proposed. In Chapter 5, Perturbation technology, Taylor expansion, Neumann expansion, Sherman Morrison Woodbury expansion and a new iterative method (NIM) for interval finite element calculation of structural linear vibration are addressed. Chapter 6 proposes five calculation methods of nonlinear interval finite element for general nonlinear problems and elastoplastic problems. In the seventh chapter, five methods of interval finite element calculation methods for nonlinear structures are presented. In the eighth chapter, two improved methods of random field are proposed. The midpoint method, local average method, interpolation method and improved interpolation method of interval field and fuzzy field are proposed. The calculation method of mixed field is introduced. In the last chapter, calculation methods of random interval finite element, random fuzzy finite element and random fuzzy and interval finite element are proposed by using Taylor expansion and Neumann expansion.

Not applicable.

##### CONFLICT OF INTEREST

The authors declare no conflict of interest, financial or otherwise.

##### ACKNOWLEDGEMENT

Declared none.

Wenhui Mo
School of Mechanical Engineering
Hubei University of Automotive Technology
China