The book “Uncertain Analysis in Finite Elements Models” 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.

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, and a new iterative method (NIM) of reliability calculation for linear static problems and linear vibration are proposed. Reliability calculation methods using the homotopy perturbation method (MIHPD) and second order reliability method for nonlinear static problems 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 the 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.