Various finite elements based on mixed formulations have been proposed for the solution of boundary value problems involving strain-gradient models. The relevant literature, however, does not provide details on some important theoretical aspects of these elements. In this work we first present the existing elements within a novel, single mathematical framework, identifying some theoretical issues common to all of them that affect their robustness and numerical efficiency. We then proceed to develop a new family of mixed elements that addresses these issues, while being simpler and computationally cheaper. The behaviour of the new elements is further demonstrated through a numerical example.
|Journal||International Journal for Numerical Methods in Engineering|
|Early online date||6 Nov 2018|
|Publication status||Published - 24 Feb 2019|
- Strain-gradient models
- Finite element method
- mixed formulation
- penalty formulation