Discussion Overview
The discussion revolves around the definition and characteristics of "linear elements" in the context of finite element methods (FEM), specifically in one-dimensional scenarios. Participants explore various interpretations and implications of linearity in finite elements, including their geometric properties and the nature of shape functions.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- Some participants suggest that a finite element is considered linear if the shape (interpolation) functions are linear in the 1D variable.
- Others propose that linearity may refer to the trial function being linear in the 1D variable.
- One participant mentions that "linear element" could mean the element is geometrically a straight or curved line, such as a rod or beam, rather than a surface or solid element.
- Another viewpoint indicates that linear elements might only be applicable for linear elastic materials, excluding plasticity and creep.
- It is also noted that the formulation may be limited to small strain and small displacement problems.
- A later reply clarifies that "linear element" typically refers to the use of linear shape functions for mapping geometric elements, distinguishing it from material linearity.
Areas of Agreement / Disagreement
Participants express multiple competing views regarding what constitutes a linear element in FEM, indicating that the discussion remains unresolved with no consensus reached.
Contextual Notes
The discussion highlights the ambiguity in the term "linear element," with various interpretations depending on context, such as geometric properties, shape functions, and material behavior. Limitations in definitions and assumptions are noted but not resolved.
Who May Find This Useful
This discussion may be useful for individuals studying finite element methods, particularly those interested in the nuances of element classification and the implications of linearity in FEM applications.