{lambda} and p-version elements for two-dimensional singular problems in solid mechanics -- A mesh independent approach
- Univ. of Kansas, Lawrence, KS (United States). Dept. of Mechanical Engineering
This paper presents a new finite element formulation called {lambda} elements for two dimensional singular problems in solid mechanics where the strength of the singularity is known. The element approximation functions and the corresponding nodal degrees of freedom are generated by taking tensor product of the one dimensional {lambda} approximation function and the corresponding nodal variable operators in the r coordinate system with the one dimensional p-version approximation functions and the corresponding nodal variable operators in the {theta} coordinate system. The origin of the local (r, {theta}) coordinate system is located at the singularity (r = 0). The {lambda} elements presented here are of C{sup 0} type and provide interelement C{sup 0} continuity with p-version elements. The {lambda} elements do not require a precise knowledge of the extent of the singular zone, i.e., their use can be extended beyond the singular zone. When {lambda} elements are used in the singular zone, a singular problem behaves like a smooth problem thereby eliminating the need for h.p-adaptive processes. The element matrices and equivalent load vectors are developed using variational approach (Galerkin method) for plane stress and plane strain cases. Numerical results are presented for a cantilever block, an L-shaped block, and a single edge crack panel in uniaxial tension. Numerical examples demonstrate the faster convergence rate, better accuracy, and mesh independent characteristics of {lambda} elements regardless of the strength of singularity.
- OSTI ID:
- 376023
- Report Number(s):
- CONF-960154--; ISBN 0-9648731-8-4
- Country of Publication:
- United States
- Language:
- English
Similar Records
{lambda} elements for singular problems in CFD: Newtonian fluids
{lambda} elements for singular problems in CFD: Non-Newtonian fluids