Computational Design of Heterogeneous Structural, Electric and Optical Components
Abstract
Many structures are hierarchical in nature and are made up of substructures distributed across several length scales. Examples include aircraft wings made from fiber reinforced laminates and naturally occurring structures like bone. From the perspective of failure initiation it is crucial to quantify the interaction between stress concentrations due to abrupt changes in structural geometry and local stress fluctuations at the level of the microstructure. The presence of geometrically induced stress or strain singularities at either the structural or substructural scale can have influence across length scales and initiate nonlinear phenomena that result in overall structural failure. During the course of the supported research this investigator has pursued two complementary sets of questions related to failure initiation in composites. The first part of the investigation focuses on quantifying the extent of overstressed zones inside composite structures due to reentrant corners, bolt holes, rivets and other stress risers. New mathematical objects beyond the well known effective elastic tensor have been introduced that deliver upper bounds on the overstressed zones near stress risers in hierarchical structures. These quantities dubbed macro stress modulation functions provide upper bounds on the distribution function of the Von Mises equivalent stress inside microstructured materials. The macro stress modulation functions can be employed in numerical methods for the optimal design of graded microstructure. A new numerical methodology is presented that enables one to design graded microstructures in order to minimize the effect of stress concentrations due to reentrant corners within a composite structure. The second line of investigation develops optimal lower boundary on the point wise maximum local stress or strain fields inside random microstructure due to macroscopic loading.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 31, 2004
- Accession Number
- ADA430832
Entities
People
- Robert Lipton
Organizations
- Louisiana State University