Abstract
The first chapter introduces to major idea and the continuum mechanical background to model structural members. It is explained that physical problems are described based on differential equations. In the context of structural mechanics, these differential equations are obtained by combining the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation. Furthermore, some explanations on the choice of the coordinate system for bending problems are provided.
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Notes
- 1.
For some problems, Eq. (1.1) must be generalized to a system of differential equations.
- 2.
The common approach in analytical mechanics is to align the x-axis with the longitudinal axis of the beam. However, in the context of the finite element method, the local z-axis might be oriented along the element, see [11].
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Öchsner, A. (2021). Introduction to Continuum Mechanical Modeling. In: Classical Beam Theories of Structural Mechanics. Springer, Cham. https://doi.org/10.1007/978-3-030-76035-9_1
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DOI: https://doi.org/10.1007/978-3-030-76035-9_1
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