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Über dieses Buch

This revision and work book offers a very specific concept for learning the finite element method applying it to problems from statics of: It skips all the classical derivations and focusses only the essential final results. Based on these `essentials', fully solved example problems are presented. To facilitate the initial learning process, the authors compiled 10 recommended steps for a linear finite element solution procedure (`hand calculation') and all the solved examples follow this simple scheme.
These 10 recommended steps help engineering students to master the finite element method and guide through fundamental standard problems, although there are neither 10 recommended steps for real-life engineering problems nor 10 standard problems that cover all possible problems that a young engineer may face during his first years of professional work.
This revision course accompanies the textbook "Computational Statics and Dynamics: An Introduction Based on the Finite Element Method" by the same authors.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Review of Engineering Mathematics

Abstract
This chapter briefly reviews two important mathematical topics in the scope of the finite element context. To solve a finite element problem means finally to solve a system of equations. This is, in the simplest case, a linear system of equations and this chapter introduces two simple solution strategies, i.e. the Gaussian elimination and the inversion of the coefficient matrix. The second topic covers the analytical and numerical integration which is needed, for example, to evaluate the elemental stiffness matrix and the column matrix of equivalent nodal loads.
Zia Javanbakht, Andreas Öchsner

Chapter 2. Rods and Trusses

Abstract
This chapter treats the rod or bar member. The three basic equations of continuum mechanics, i.e. the kinematics relationship, the constitutive law and the equilibrium equation, are summarized as well as the describing partial differential equation. A general solution for constant material and geometrical properties is presented. Furthermore, typical boundary conditions and the internal reactions are briefly mentioned. The finite element formulation is focused on rod elements with two nodes under the assumption of constant material and geometrical properties. The post-computation, which is based on the nodal results, is treated in detail. The chapter concludes with the spatial arrangement of rod elements in a plane to form a plane truss structure.
Zia Javanbakht, Andreas Öchsner

Chapter 3. Euler–Bernoulli Beams and Frames

Abstract
This chapter treats the simple or Euler–Bernoulli beam member. This beam theory, also called the shear-rigid theory, assumes that the shear forces do not contribute to the beam deflection. The three basic equations of continuum mechanics, i.e. the kinematics relationship, the constitutive law and the equilibrium equation, are summarized as well as the describing partial differential equation. A general solution for constant material and geometrical properties is presented. Furthermore, typical boundary conditions and the internal reactions are briefly mentioned. The finite element formulation is focused on beam elements with two nodes under the assumption of constant material and geometrical properties. Furthermore, the beam element is superimposed with a rod element to form a generalized beam element, which considers both elongation and deflection. The post-computation, which is based on the nodal results, is treated in detail. The chapter concludes with the spatial arrangement of beam elements in a plane to form a plane frame structure.
Zia Javanbakht, Andreas Öchsner

Chapter 4. Timoshenko Beams

Abstract
This chapter treats the shear-flexible or Timoshenko beam member. This beam theory assumes that the shear forces contribute to the beam deflection. The three basic equations of continuum mechanics, i.e. the kinematics relationship, the constitutive law and the equilibrium equation, are summarized as well as the describing partial differential equations. A general solution for constant material and geometrical properties is presented. Furthermore, typical boundary conditions and the internal reactions are briefly mentioned. The finite element formulation is focused on beam elements with two nodes under the assumption of constant material and geometrical properties, as well as linear shape functions. The post-computation, which is based on the nodal results, is treated in detail.
Zia Javanbakht, Andreas Öchsner

Chapter 5. Symmetry

Abstract
Previsioning the deformed configuration of a structure provides the engineer an understanding of the overall behavior of that structure. Some patterns are recognizable in terms of translations and rotations—specially in symmetrical structures. Additionally, some properties of symmetry can be used to simplify the structural analysis and to reduce the computational costs. Herein, the concept of planar symmetry is reviewed and the symmetric and antisymmetric loading regimes are briefly investigated in terms of their generated deformations, reactions and internal forces. Some examples and supplementary problems conclude the chapter.
Zia Javanbakht, Andreas Öchsner

Backmatter

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