Partial Differential Equations of Classical Structural Members: A Consistent Approach

✍ Scribed by Andreas Öchsner

• Publisher: Springer International Publishing
• Year: 2020
• Tongue: English
• Leaves: 96
• Series: SpringerBriefs in Applied Sciences and Technology
• Edition: 1st ed. 2020
• Category: Library

✦ Synopsis

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

Front Matter ....Pages i-viii
Introduction to Structural Modeling (Andreas Öchsner)....Pages 1-3
Rods or Bars (Andreas Öchsner)....Pages 5-11
Euler–Bernoulli Beams (Andreas Öchsner)....Pages 13-29
Timoshenko Beams (Andreas Öchsner)....Pages 31-46
Plane Members (Andreas Öchsner)....Pages 47-55
Classical Plates (Andreas Öchsner)....Pages 57-68
Shear Deformable Plates (Andreas Öchsner)....Pages 69-80
Three-Dimensional Solids (Andreas Öchsner)....Pages 81-88
Introduction to Transient Problems: Rods or Bars (Andreas Öchsner)....Pages 89-92

✦ Subjects

Physics; Classical Mechanics; Partial Differential Equations