Abstract
The three basic modes of deformation, i.e. tension, torsion and bending, can occur in an arbitrary combination. This chapter serves to introduce how the stiffness relation for a general 1D element can be composed. The stiffness relations of the basic types build the foundation. For ‘simple’ loadings the three basic types can be regarded separately and can easily be superposed. A mutual dependency is nonexistent. The generality of the 1D element also relates to the arbitrary orientation within space. Transformation rules from local to global coordinates are provided. As an example, structures in the plane as well as in three-dimensional space will be discussed. Furthermore, there will be a short introduction in the subject of numerical integration.
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Notes
- 1.
Other definition results in a different transformation.
Reference
Onate E (2009) Structural analysis with the finite element method. Springer, Berlin
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Öchsner, A., Merkel, M. (2018). General 1D Element. In: One-Dimensional Finite Elements. Springer, Cham. https://doi.org/10.1007/978-3-319-75145-0_6
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DOI: https://doi.org/10.1007/978-3-319-75145-0_6
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