The Finite Element Method For Solid And Structural Mechanics

This brief provides guidance for the application of cohesive models to determine damage and fracture in materials and structural components. This can be done for configurations with or without a pre-existing crack. Although the brief addresses structural behaviour, the methods described herein may also be applied to any deformation induced material damage and failure, e.g. those occurring during manufacturing processes. The methods described are applicable to the behaviour of ductile metallic materials and structural components made thereof. Hints are also given for applying the cohesive model to other materials.

The basic idea of this introduction to the finite element method is based on the concept of explaining the complex method using only one-dimensional elements. Thus, the mathematical description remains largely simple and straightforward. The emphasis in each chapter is on explaining the method and understanding it itself. The reader learns to understand the assumptions and derivations in various physical problems in structural mechanics and to critically assess the possibilities and limitations of the finite element method.

The book provides a self-contained treatment of stochastic finite element methods. It helps the reader to establish a solid background on stochastic and reliability analysis of structural systems and enables practicing engineers to better manage the concepts of analysis and design in the presence of uncertainty. The book covers the basic topics of computational stochastic mechanics focusing on the stochastic analysis of structural systems in the framework of the finite element method.

Fracture mechanics has established itself as an important discipline of growing interest to those working to assess the safety, reliability and service life of engineering structures and materials. In order to calculate the loading situation at cracks and defects, nowadays numerical techniques like finite element method (FEM) have become indispensable tools for a broad range of applications.