Numerical simulation of singularities in laminated composites using {lambda} and p-version elements -- A mesh independent approach
- Univ. of Kansas, Lawrence, KS (United States). Dept. of Mechanical Engineering
This paper presents an investigation of the numerical simulation of point singularities in laminated composites with multimaterial interfaces using {lambda} and p-version elements. In multimaterial interfaces with point singularities, the strength of the singularity is often unknown. For such problems, the use of {lambda} elements designed using a power series in r{sup {lambda}} is investigated. The element approximation functions and the corresponding nodal degrees of freedom are generated by taking tensor product of the one dimensional {lambda} approximation functions 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 inter element C{sup 0} continuity with p-version elements in the {theta} direction. 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 at the singularity, 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 an L shaped block and single edge crack panel with multi-material interfaces. Numerical examples demonstrate the convergence rate, accuracy, and mesh independent characteristics of {lambda} elements regardless of the strength of singularity.
- OSTI ID:
- 376024
- Report Number(s):
- CONF-960154--; ISBN 0-9648731-8-4
- Country of Publication:
- United States
- Language:
- English
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