New Nonconforming Elements for Linear Strain Gradient Elastic Model
For researchers in computational mechanics, this provides new elements for strain gradient elasticity, but the work is incremental as it builds on existing element types.
The paper proposes new nonconforming finite elements for the linear strain gradient elastic model, proving uniform convergence rates through new interpolation error estimates, with numerical results matching theoretical predictions.
Based on a new H$^2-$Korn's inequality, we propose new nonconforming elements for the linear strain gradient elastic model. The first group of elements are H$^1-$conforming but H$^2-$nonconforming. The tensor product NTW element [Tai:2001] and the tensor product Specht triangle are two typical representatives. The second element is based on Morley's triangle with a modified elastic strain energy. We proved new interpolation error estimates for all these elements, which are key to prove uniform rates of convergence for the proposed elements. Numerical results are reported and they are consistent with the theoretical prediction.