Stochastic Finite Element Methods

This collection covers all fields of mathematics, a must-have for the aspiring maths students and scholars alike.

sections dealing with fuzzy functions and fuzzy random functions are certain to be of special interest. The reader is expected to be in command of the knowledge gained in a basic university mathematics course, with the inclusion of stochastic elements. A specification of uncertainty in any particular case is often difficult. For this reason Chaps. 3 and 4 are devoted solely to this problem. The derivation of fuzzy variables for representing informal and lexical uncertainty reflects the subjective assessment of objective conditions in the form of a membership function. Techniques for modeling fuzzy random variables are presented for data that simultaneously exhibit stochastic and nonstochastic properties. The application of fuzzy randomness is demonstrated in three fields of civil engineering and computational mechanics: structural analysis, safety assessment, and design. The methods of fuzzy structural analysis and fuzzy probabilistic structural analysis developed in Chap. 5 are applicable without restriction to arbitrary geometrically and physically nonlinear problems. The most important forms of the latter are the Fuzzy Finite Element Method (FFEM) and the Fuzzy Stochastic Finite Element Method (FSFEM).

This book provides a complete probabilistic analysis method and a performance-based seismic safety evaluation for high concrete faced rockfill dam (CFRD). Combined with random sample generation and reliability analysis methods, the dynamic response characteristics and reliability level of CFRD under various random factors are comprehensively described. In Chapter 2, a random ground motion model based on spectral representation-random function and a high-dimensional random variable generation method based on GF- discrepancy are established. Combined with probability density evolution method (PDEM) and the random sample generation methods to verify its effectiveness and reliability for nonlinear complex geotechnical engineering.