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About this book

The derivation and understanding of Partial Differential Equations relies heavily on the fundamental knowledge of the first years of scientific education, i.e., higher mathematics, physics, materials science, applied mechanics, design, and programming skills. Thus, it is a challenging topic for prospective engineers and scientists.

This volume provides a compact overview on the classical Partial Differential Equations of structural members in mechanics. It offers a formal way to uniformly describe these equations. All derivations follow a common approach: the three fundamental equations of continuum mechanics, i.e., the kinematics equation, the constitutive equation, and the equilibrium equation, are combined to construct the partial differential equations.

Table of Contents

Frontmatter

Chapter 1. Introduction to Structural Modeling

Abstract
The first chapter classifies the content as well as the focus of this textbook. In engineering practice, the description of processes is centered around partial differential equations, and all the classical approximation methods such as the finite element method, the finite difference method, the finite volume method, and the boundary element method offer different ways of solving these equations.
Andreas Öchsner

Chapter 2. Rods or Bars

Abstract
This chapter covers the continuum mechanical description of rod/bar members. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law and the equilibrium equation, the partial differential equation, which describes the physical problem, is derived.
Andreas Öchsner

Chapter 3. Euler–Bernoulli Beams

Abstract
This chapter covers the continuum mechanical description of thin beam members. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law and the equilibrium equation, the partial differential equation, which describes the physical problem, is derived.
Andreas Öchsner

Chapter 4. Timoshenko Beams

Abstract
This chapter covers the continuum mechanical description of beam members under the additional influence of shear stresses. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law and the equilibrium equation, the partial differential equations, which describe the physical problem, are derived.
Andreas Öchsner

Chapter 5. Plane Members

Abstract
This chapter covers the continuum mechanical description of plane elasticity members. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law and the equilibrium equation, the partial differential equation, which describes the physical problem, is derived.
Andreas Öchsner

Chapter 6. Classical Plates

Abstract
This chapter covers the continuum mechanical description of classical plate members. Classical plates are thin plates where the contribution of the shear force on the deformations is neglected. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation, the partial differential equation, which describes the physical problem, is derived.
Andreas Öchsner

Chapter 7. Shear Deformable Plates

Abstract
This chapter covers the continuum mechanical description of thick plate members. Thick plates are plates where the contribution of the shear force on the deformations is considered. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation, the partial differential equations, which describes the physical problem, is derived.
Andreas Öchsner

Chapter 8. Three-Dimensional Solids

Abstract
This chapter covers the continuum mechanical description of solid or three-dimensional members. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation, the partial differential equation, which describes the physical problem, is derived.
Andreas Öchsner

Chapter 9. Introduction to Transient Problems: Rods or Bars

Abstract
This chapter introduces to transient problems, i.e. problems where the state variables are time-dependent. The general treatment of transient problems is illustrated at the example of the rod or bar member.
Andreas Öchsner
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