Strain Energy Density Bounds for Linear Anisotropic Elastic Materials
Abstract
We discuss the problem of obtaining upper and lower bounds for the strain-energy density in linear anisotropic elastic materials. One set of bounds is given in terms of the magnitude of the stress field, another in terms of the magnitude of the strain field. Results of this kind play a major role in the analysis of Saint Venant's Principle for anisotropic materials and structures. They are also useful in estimating global quantities such as total energies, buckling loads, and natural frequencies. For several classes of elastic symmetry (e.g., cubic, transversely isotropic, hexagonal, and tetragonal symmetry) the optimal constants appearing in these bounds are given explicitly in terms of the elastic constants. This makes the results directly accessible to the design engineer. Such explicit results are rare in the filed of anisotropic elasticity. For more elaborate symmetries (e.g., orthotropic, monoclinic, and triclinic) the optimal constants depend on the solution of cubic and sextic equations, respectively. Anisotropic, Linear elasticity, Strain energy density, Optimal upper, Lower bounds.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1993
- Accession Number
- ADA271050
Entities
People
- C. O. Horgan
- M. M. Mehrabadi
- S. C. Cowin
Organizations
- University of Virginia