Öchsner A. Partial Differential Equations of Classical Structural Members: A Consistent Approach

Springer, 2020. — 96 p. — (SpringerBriefs in Applied Sciences and Technology: Continuum Mechanics). — ISBN: 978-3-030-35310-0.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.Introduction to Structural Modeling
Rods or Bars
Euler–Bernoulli Beams
Timoshenko Beams
Plane Members
Classical Plates
Shear Deformable Plates
Three-Dimensional Solids
Introduction to Transient Problems: Rods or Bars